Direct estimation of child mortality from birth histories

Background

In this section, we focus on the use of data from full birth histories (FBH) or truncated birth histories (TBH). The key characteristics of such data are that for each birth included, the date of birth, survival status and (if dead) age at death are recorded. Analysis of the data typically uses life table approaches. Indirect estimation of child mortality, and estimation of child mortality from survival of a recent birth, are covered in the section on indirect estimation of child mortality [1] and the section about the preceding birth technique [2].

Data requirements and assumptions

Data required

For each woman of reproductive age (in some settings for cultural reasons information collection is limited to ever-married women):

• the name of each child born alive;
• the month and year of birth of each child;
• the child’s sex (optional);
• Whether the child is still alive; and
• if the child has died, the age at death (age at death in the DHS program is collected in days for deaths that occur in the first 28 days of life, in months for deaths at ages one to 23 months, and in years thereafter).

Important assumptions

• Children still alive and children dead are reported with similar accuracy.
• Dates of birth and ages at death are reported with reasonable accuracy.
• No correlation exists between mortality risks of children and survival rates of mothers (whether as a result of mortality or migration) in the population.

Caveats and warnings

The dangers associated with working with directly-collected data arise from two sources. The first is the risk of survivor bias as only living mothers are asked the detailed birth histories used to generate the data. In situations where it is anticipated that deceased mothers might have had different fertility, or different mortality among their children, from surviving mothers, there is a risk of appreciable bias in the estimates derived. Aspects of survivor bias are discussed in the section on the introduction to child mortality analysis [3] the section on the effects of HIV on child mortality estimation [4].

The second danger is that if an upper age limit is applied to the women from whom detailed birth history data are collected, truncation bias becomes more significant the further back in time one looks. If an age limit of 49 is applied to the collection of the data, this means that for the period 10 years before the survey, information is only available for women who were then aged up to age 39. Hence, child mortality estimated from such data for earlier time periods will be increasingly based on the experience of younger women. In turn, this might lead to measurement bias, as this truncation results in an over-representation of first births among younger women, meaning that child mortality thus estimated is likely to be increasingly overestimated for earlier time periods. There is some evidence that such over-estimation is counter-balanced by underestimation arising from recall bias (and selective omission of children who have died in periods longer in the past).

Data evaluation and data analysis

Regardless of how data have been collected, or of one’s knowledge of how thoroughly interviewers were trained and supervised, careful review of data quality is an essential first step of any analysis. All data sets contain errors. These can result from many sources, such as an interviewer cutting corners or an interviewee simply not knowing the correct answer to a question. Each section below starts with a description of data evaluation techniques, before progressing to analysis methods. These evaluation techniques examine both internal consistency within a data set, and external consistency with other data sets for the same population. It should be noted in passing that the presence of data errors does not necessarily mean that a data set should not be analyzed; the important thing is to know how large the errors are, and take them into account when interpreting the findings.

The full birth history: data quality assessment

The first step in a thorough data quality assessment is to examine the extent of missing values. In an FBH, values may be missing for a number of reasons. For example, whole households included in the original sampling frame may be missing. Further, eligible women within interviewed households may have no data because the woman could not be interviewed. In addition, individual items within an FBH may be missing because the interviewed woman did not know a child’s birth date, or whether a child was still alive, or (if the child had died) the age at death. The proportions of events potentially affected by these errors need to be examined. Missing items may be imputed during data cleaning, but imputed values should be flagged. The absence of missing values should not be taken as strong evidence of data quality, and may in fact be taken as a warning flag: in some surveys, interviewers and supervisors are trained to avoid missing values, and in such cases data may be more or less made up by the interviewer.

The second step in the data quality assessment is to examine the aggregate results for implausible irregularities. The irregularities most often identified are in sex ratios at birth, in annual distributions of live births, and in ages at death. In the absence of intervention, sex ratios in human populations are generally in the range of 100 to 106 males per 100 females. Sex ratios for birth cohorts outside this range are probably indicative of error. Sex ratios that increase for cohorts born a longer time before the survey are particularly clear indicators of an error, in this case under-reporting of female births that occurred in the distant past.

In the absence of major positive or negative events, births will normally be fairly smoothly distributed by calendar year (in that while seasonality is common, this should not affect the annual numbers. Possible errors can be identified by calculating 'birth ratios', defined as

$$\frac{2B_t}{B_{t-1}+B_{t+1}}$$

where B_t is the number of births reported in a given year, t. 

An error commonly found in DHS data sets has come to be called “birth transference”. DHS surveys collect a substantial amount of additional data about children born since some cut-off date, usually 1 January of the calendar year five years before the survey. It is often the case that births that occurred in that year are reported as occurring in the previous year, presumably to reduce work load. This results in a deficit of births in the year following the cut-off, and a surplus in the year immediately before the cut-off. Birth ratios will highlight this error, since the birth ratio for the year starting with the cut-off will be low, and that for the preceding year will be high. Very often, this birth transference is greater for children who have died than for those who are still alive, so it is good practice to calculate separate ratios for surviving and dead children.

Irregularities in reporting ages at death can similarly be identified by calculating ratios of deaths at some age x to the average number of deaths at ages (x-1) and (x+1). In DHS data sets, there is generally an excess of deaths at age 7 days, to a lesser extent at age 14 days, and at age 12 months.

DHS conveniently publishes these data quality indicators at aggregate (national) level in survey reports (often in Appendix C). Analysts wishing to carry out sub-national analyses will need to calculate indicators themselves.

The data quality indicators described above measure internal plausibility. However, data can be internally plausible and still wrong. Data should also be evaluated by comparison with other surveys for the same population. Cohort comparisons are particularly powerful, for example comparing the average number of children ever borne by women aged 30-34 reported in one survey to the average number borne by women aged 35-39 reported in another survey five years later. Similar comparisons can be made of average numbers of children dead. Sequences of births by single calendar year for overlapping periods can also be compared, though one has to bear in mind that births in the past are increasingly truncated in birth histories limited to women aged 15-49 at the time of the survey.

The full birth history: Calculation of child mortality indicators for birth cohorts

Widely used indicators of child mortality are expressed as probabilities. Thus the Infant Mortality Rate (IMR) is (approximately – as conventionally defined, the IMR is infant deaths in a year divided by births in the year, a value which closely approximates ₁q₀) the probability of dying by exact age 1, ₁q₀, and the Under-five Mortality Rate (U5MR) is the probability of dying by age 5, ₅q₀. Strictly speaking, probabilities are real cohort measures, even though most life tables calculate synthetic cohort measures for specified time periods from age-period mortality rates. Calculating cohort probabilities from FBH data is very straightforward. For example, the cohort IMR for births in the 12 to 23 months before the survey is simply the number of such births that died before the age of 1 divided by the number of births. Similarly, the cohort U5MR for births 5 to 9 years before the survey is the number of such births reported to have died before exact age 5 divided by the number of such births. Figure 1 shows the Lexis diagram representation of the age-cohort probability of dying by age 1 for the cohort born in July 2001 (in green), and the age-period mortality of 5-month olds in calendar year 2002 (the blue rectangle, relating to the example used later in this section).

Figure 1: Lexis diagram representation of age-cohort mortality by age 1 (green) and age-period mortality for 5-month olds (blue) [5]

Table 1 shows the relevant numbers and calculations for age-cohort probability of dying by age 1 for the cohort born in the 12-23 months before the survey and for the probability of dying by age 5 for the cohort born in the 5 to 9 years before the survey, using data from the 2004 Malawi DHS. Note that there is no period interpretation of such cohort values; in the U5MR example, the cohort probability reflects mortality risks in every one of the 10 years before the survey. Also note that the probability of dying by age x can only be calculated for cohorts that were born at least x years before the survey. Both these considerations limit the value of the cohort measures, since for most purposes analysts and policy-makers are more interested in time period measures.

Table 1: Calculation of IMR and U5MR for cohorts: Malawi 2004 DHS

Period of births	Births	Of which, deaths before 12 months	Child mortality indicator	Cohort estimate per 1 000 births
12-23 months before the survey	2,229	143	1q0	64.2
		Of which, deaths before 5 years
60 to 119 months before the survey	7,178	1,568	5q0	218.4
Note: weighted data; events in month of interview excluded

The full birth history: Calculation of child mortality indicators for time periods

Period-specific measures are estimated using the synthetic cohort concept. Mortality rates for narrow age ranges and defined calendar periods are calculated on the basis of events and exposure in these rectangles in the Lexis Diagram. The rates are then converted into implied probabilities, using standard demographic relations (see, for example, Preston, Heuveline and Guillot (2001)) and making generally mild assumptions about the distribution of deaths in each rectangle. Finally, the probabilities of dying are applied successively to an initial hypothetical cohort of births to compute a survivorship curve ℓ(x) for each age x, from which it is easy to derive probabilities of dying.

FBH data lend themselves to these life table calculations quite easily. If data are collected following the standard DHS practice – as month and year of birth and age at death in days, months or years, depending on the age – deaths  can be located with little ambiguity in age-period rectangles of the Lexis Diagram. (There will be some residual ambiguity, because of the imprecision of the information on date of birth and age at death, but the impact will depend on the sizes of the rectangles.) Here we describe an approach based on the calculation of age-specific mortality rates for a single calendar year (age-period rates) for mortality up to age 5. Extension to other time periods is straightforward. It is assumed that data are in standard DHS format, that is, birth dates are recorded in century month (CMC) format, and ages at death in days, months or years. Unit record data must be available. The unit of age used is the month. The basic calculations are therefore of age-specific mortality rates by month of age and calendar year. These rates are converted into corresponding probabilities of dying in each month. These probabilities are then converted into probabilities of surviving, and are chained together over whatever age range is required (typically up to age 5). The key to the calculation is to assign deaths and exposure time to one-month age segments across a calendar year.

Data manipulation

Four variables in a DHS birth data set are required:

1. b3, date of birth in CMC;
2. b5, whether child is still alive;
3. b6, age at death, where the first digit represents the unit (1 indicating days; 2, months; and 3, years) and the second and third digits represent the value given that unit; and
4. v005, sample weight, expressed in millions.

Note that variable b7, age at death (months-imputed) is not used. This variable does not lend itself to the mortality rate approach described here, because in cases in which age at death is recorded in years, the 'imputed' month is actually the lower bound of the age interval; that it, if age at death is recorded as '3 years', the imputed age at death in months is recorded as 36 months. Using this variable will result in systematic mis-location of deaths in time.

Application of method

Step 1: Manipulation of age at death and calculation of estimated birth date and age at death

We want to locate deaths in a calendar month of occurrence. Since we do not have a precise date of birth (only CMC), and in general we do not have a precise age at death (except for neonatal deaths), we need to impute both a date of birth and an age at death. We can perform this imputation using random numbers.

It is evidently undesirable – for reasons of lack of reproducibility, amongst others – to make use of a true random number generator to produce the random numbers referred to above. In addition, ‘true’ randomization risks creating a spurious impression of precision. As an alternative, we propose creating pseudo-random numbers from variables that are routinely available in DHS data and that can be applied in the algorithm above. It is an easy matter to create new variables apportioning the records into deciles based on the reported day of interview (v016 in a DHS) and household number (v002). (These variables have been chosen on the grounds that there is unlikely to be any correlation between them and child mortality). These new variables will take the values in the range (0, 1 … 9). Dividing each by 10, and adding 0.05 results in two new uniformly distributed variables, random1 and random2, taking values in the range (0.05, 0.15, … , 0.95). 

It is then straightforward to impute a date of birth (dob, in months) if births in the month of interview are excluded from analysis by adding random1 to b3 (the CMC of the child’s date of birth). The method for imputing an age at death (in units of months) depends on the ‘unit’. For ‘unit’ = 1 (i.e. age at death measured in days), age at death (aad) can be estimated as (‘value’+ random2)/31 (for age at death in days this is not necessary, but is described for symmetry); for ‘unit’ = 2, age at death is ‘value’ + random2; and for ‘unit’ = 3, age at death is (‘value’ + random2)*12.

Step 2: Location of deaths in target year

For each month-of-age mortality rate, the events consist of deaths at that age in the period of investigation. Step 1 has imputed age at death in months. The date of death dod is given by the sum of imputed month of birth dob and imputed age of death aad. If imputed age at death is within the age range and the imputed date of death falls within the period of investigation, we have a relevant event.

Step 3: Derivation of exposure to risk

The calculation of exposure to risk is intricate, but relatively straightforward. The age range of the investigation refers to those ages (defined in appropriate units) for which we want to measure mortality. We define the lower bound of the age range to be x_l, and the upper bound to be x_u.

The period of investigation is the measure of the time period for which we seek to estimate mortality, and is defined as the period (t₂ - t₁), where t₂ is the end date of the period of investigation, and t₁ the start date, measured in the same units as that defined by the age range.

Graphically, then, we seek to measure mortality in the age and period defined by the heavy lines in Figure 2.

Figure 2: Lexis diagram showing calculation of exposure to risk [6]

An individual’s life course by age and period is represented by the diagonal lines (as with a conventional Lexis diagram). Five possible scenarios (labelled (a) through (e)) are portrayed. Any individual’s position in the space can be defined by their age at t₁, x_t1. It follows, further, that any person aged x at t₁, if she or he does not die before t₂, would be aged x_t2 = x_t1 +(t₂ - t₁) at time t₂. We define the age at death of those deaths that occur in the specified age range in the period of investigation to be x_d. The relative contribution of each scenario to the exposure to risk is determined by the algorithms in Table 2.

Table 2: Algorithm for determining exposure to risk

Scenario	Description	Defining rule(s)	Exposure for survivors in the period of investigation	Exposure for decedents (where death occurs in the period of investigation)
(a)	Aged older than xh at t1	xt1>xh	0	0
(b)	Aged between xl and xh at t1. Attains xh in the period of investigation	xl< xt1<xh xt1+(t2-t1) > xh	xh-xt1	xd-xt1
(c)	Attains xl and xh in the period of investigation	xl > xt1 xt1+(t2-t1) > xh	xh-xl	xd-xl
(d)	Attains xl in the period of investigation but period ends before attainment of xh	xl > xt1 xl  < xt1+(t2-t1) < xh	xt1+(t2-t1) - xl	xd-xl
(e)	Does not attain xl in the period of investigation	xt1+(t2-t1) < xl	0	0

Applying these rules to define the exposure in the age range in the period of investigation for each individual and aggregating gives the total exposure to risk, which is the denominator for the mortality rate. Summing the deaths occurring in the age range in the period of investigation provides the numerator.

Step 4: Weighting and cumulating events and exposure time

The sample weight variable in a standard DHS recode file is v005. This variable has a mean of 1,000,000. To avoid the appearance of huge sample sizes (and much too narrow confidence intervals) it is recommended first to recalculate the weight as (v005/1,000,000). Let us call this new variable wgt. Mortality rates can be calculated by considering the contributions of each of the N children in the survey to the number of events and the total exposure time. The age-specific mortality rate age x to x + 1 (in months) in a period, j, is

$$M\left(x,j\right)=\frac{{\displaystyle \sum _{i=1}^{N}D\left(i,x,j\right).wgt\left(i\right)}}{{\displaystyle \sum _{i=1}^{N}E\left(i,x,j\right).wgt\left(i\right)}}$$

where M(x,j) is the age specific rate for age x and year j, D(i,x,j) is a binary variable indicating the death of child i at age x in year j (1 if the death occurs, 0 otherwise), E(i,x,j) is the exposure time of child i at age x in year j, and wgt(i) is the sample weight (mean 1.0) of child i.

Step 5: Calculating probabilities of dying from age-specific mortality rates

The rates calculated in Step 4 are per month of age exposure. It is therefore necessary to adapt the standard formula for deriving a period probability of dying from a rate to take this into account. Given that we have made a number of simplifying assumptions and are working with narrow age ranges, it is adequate to assume that deaths are evenly distributed across each single month age range. We can then calculate q(x) as

mlf_2184.mml

$$q\left(x,j\right)=\frac{\frac{M\left(x,j\right)}{12}}{\left(1+\frac{M\left(x,j\right)}{24}\right)}$$

Survivorship probabilities from birth to any age can then be obtained by chaining together survivorship by month (i.e. (1-q(x,j)) ) terms. Thus for instance

$${}_{5}q{}_{{}_0}^j=1-{\displaystyle \prod _{x=0}^{59}\left(1-q\left(x,j\right)\right)}$$

Worked example

As noted above, direct estimation of child mortality from a birth history requires working with unit record data rather than tabulations. As a worked example, we will therefore illustrate with a limited number of records adapted from a DHS, specifically the mortality of 5-month olds in 2002 from the 2004 Malawi DHS. Only children born between 1 July 2001 and 31 July 2002 are at risk of dying at age 5 months in calendar year 2002 (children born before 1 July 2001 would be aged 6 months or more by the beginning of calendar year 2002, and those born after 31 July 2002 would not have reached age 5 months in the year). Only relevant records are shown, that is, those for births between month 1218 and 1230 in CMC terms (July 2001 to July 2002). In practice, we would also exclude any births that died before five months of age, but we will include them in the example to show that we exclude them from calculations.

Table 3 shows the key variables for 50 records from the 2004 Malawi DHS; note that these are birth records, not woman records.

Table 3: Basic birth history data for direct estimation of child mortality

Record	b3	b5	b6	v005
1	1223	yes	.	469061
2	1223	yes	.	469061
3	1222	no	107	469061
4	1224	yes	.	469061
5	1223	yes	.	469061
6	1218	no	205	469061
7	1230	yes	.	2171218
8	1225	yes	.	704240
9	1230	yes	.	704240
10	1224	yes	.	704240
11	1224	no	202	704240
12	1221	yes	.	1106470
13	1225	yes	.	1106470
14	1224	no	205	1106470
15	1221	yes	.	1106470
16	1221	yes	.	1106470
17	1218	no	205	1106470
18	1229	yes	.	3900164
19	1230	yes	.	1247934
20	1224	yes	.	1247934
21	1226	no	201	1247934
22	1221	yes	.	537170
23	1218	yes	.	537170
24	1227	yes	.	537170
25	1226	yes	.	537170
26	1224	yes	.	1095220
27	1230	no	205	1594776
28	1225	yes	.	1594776
29	1221	yes	.	1594776
30	1225	yes	.	1594776
31	1229	no	208	1538303
32	1223	yes	.	1538303
33	1220	yes	.	1538303
34	1226	yes	.	1538303
35	1225	yes	.	1538303
36	1220	yes	.	1538303
37	1224	no	205	1538303
38	1228	yes	.	1538303
39	1219	yes	.	3789587
40	1228	yes	.	2011510
41	1223	no	302	2011510
42	1220	yes	.	2011510
43	1220	yes	.	2011510
44	1221	yes	.	686252
45	1228	no	201	686252
46	1229	yes	.	2451926
47	1219	yes	.	2451926
48	1219	yes	.	1043244
49	1224	yes	.	1043244
50	1230	no	205	1043244

 

Step 1: Manipulation of age at death and calculation of estimated birth date and age at death

Random numbers random1 and random2 are derived as described above, resulting in revised values of dates of birth and age at death, dob' and aad'. The date of death dod' is estimated as the sum of the imputed month of birth dob' and imputed month of death aad'. Column 10 of Table 4 shows dod'.

Table 4: Derivation of imputed date of birth, age at death and date of death, Malawi, 2004 DHS (50 cases)

Record	b3	b5	b6	v005	random 1	random 2	dob'	aad'	dod'
1	1223	yes	.	469061	0.55		1223.55
2	1223	yes	.	469061	0.85		1223.85
3	1222	no	107	469061	0.15	0.05	1222.15	0.2758	1222.426
4	1224	yes	.	469061	0.25		1224.25
5	1223	yes	.	469061	0.25		1223.25
6	1218	no	205	469061	0.05	0.45	1218.05	5.45	1223.5
7	1230	yes	.	2171218	0.55		1230.55
8	1225	yes	.	704240	0.55		1225.55
9	1230	yes	.	704240	0.25		1230.25
10	1224	yes	.	704240	0.35		1224.35
11	1224	no	202	704240	0.55	0.75	1224.55	2.75	1227.3
12	1221	yes	.	1106470	0.45		1221.45
13	1225	yes	.	1106470	0.75		1225.75
14	1224	no	205	1106470	0.85	0.25	1224.85	5.25	1230.1
15	1221	yes	.	1106470	0.35		1221.35
16	1221	yes	.	1106470	0.45		1221.45
17	1218	no	205	1106470	0.95	0.65	1218.95	5.65	1224.6
18	1229	yes	.	3900164	0.45		1229.45
19	1230	yes	.	1247934	0.65		1230.65
20	1224	yes	.	1247934	0.65		1224.65
21	1226	no	201	1247934	0.75	0.85	1226.75	1.85	1228.6
22	1221	yes	.	537170	0.65		1221.65
23	1218	yes	.	537170	0.85		1218.85
24	1227	yes	.	537170	0.95		1227.95
25	1226	yes	.	537170	0.85		1226.85
26	1224	yes	.	1095220	0.95		1224.95
27	1230	no	205	1594776	0.15	0.65	1230.15	5.65	1235.8
28	1225	yes	.	1594776	0.15		1225.15
29	1221	yes	.	1594776	0.85		1221.85
30	1225	yes	.	1594776	0.05		1225.05
31	1229	no	208	1538303	0.65	0.85	1229.65	8.85	1238.5
32	1223	yes	.	1538303	0.45		1223.45
33	1220	yes	.	1538303	0.15		1220.15
34	1226	yes	.	1538303	0.55		1226.55
35	1225	yes	.	1538303	0.95		1225.95
36	1220	yes	.	1538303	0.45		1220.45
37	1224	no	205	1538303	0.25	0.85	1224.25	5.85	1230.1
38	1228	yes	.	1538303	0.35		1228.35
39	1219	yes	.	3789587	0.35		1219.35
40	1228	yes	.	2011510	0.15		1228.15
41	1223	no	302	2011510	0.65	0.55	1223.65	30.6	1254.25
42	1220	yes	.	2011510	0.35		1220.35
43	1220	yes	.	2011510	0.25		1220.25
44	1221	yes	.	686252	0.95		1221.95
45	1228	no	201	686252	0.85	0.35	1228.85	1.35	1230.2
46	1229	yes	.	2451926	0.25		1229.25
47	1219	yes	.	2451926	0.05		1219.05
48	1219	yes	.	1043244	0.85		1219.85
49	1224	yes	.	1043244	0.95		1224.95
50	1230	no	205	1043244	0.35	0.35	1230.35	5.35	1235.7

Step 2: Location of deaths in target year

A relevant death in terms of period is one with a CMC between 1224 to 1235. The deaths in records 3, 6, 31 and 41 of Table 4 are therefore not relevant because they are deemed not to have occurred in 2002. The deaths in records 11 and 45 are not relevant because the child died at 2 months (11) or 1 month (45) of age, and therefore was not exposed to the risk of dying at age 5 months.

Step 3: Derivation of exposure to risk

Table 5 presents the calculation of the exposure to risk for the 50 cases described above. The rule used to determine the exposure is presented in the column headed ‘Scenario’. The resulting exposure is presented in the following two columns for those who survive the period of investigation and those that die during the period.

For children who survive to age 6 months, those born in months 1219 to 1229 contribute a full month of exposure time to the age-period of interest (i.e. from exactly 5 to exactly 6 months). Thus record 1 (born 1223.55) contributes a full month. A child born in month 1218 will contribute (dob - 1218) months, so record 23 (born 1218.85) contributes 0.85 of a month; and a child born in month 1230 will contribute (1231 - dob) months, so record 7 contributes 1231 - 1230.55 = 0.45 months. The children born in months 1219 to 1229 who die at age 5 months will contribute (aad - 5) months of exposure; thus the death in record 14 occurs at 5.25 months and contributes 0.25 months of exposure.

Table 5: Derivation of exposure to risk for estimation of child mortality, Malawi, 2004 DHS (50 cases)

						Exposure to risk		Weighted
Record	dob'	aad'	dod'	v005	Scenario	Survivors	Deaths	Exposure	Deaths
1	1223.55			469061	c	1		0.469
2	1223.85			469061	c	1		0.469
3	1222.15	0.25	1222.4	469061	N/A	N/A	N/A	0.000
4	1224.25			469061	c	1		0.469
5	1223.25			469061	c	1		0.469
6	1218.05	5.45	1223.5	469061	N/A	N/A	N/A	0.000
7	1230.55			2171218	d	0.45		0.977
8	1225.55			704240	c	1		0.704
9	1230.25			704240	d	0.75		0.528
10	1224.35			704240	c	1		0.704
11	1224.55	2.75	1227.3	704240	c	1		0.704
12	1221.45			1106470	c	1		1.106
13	1225.75			1106470	c	1		1.106
14	1224.85	5.25	1230.1	1106470	c		0.25	0.277	1.106
15	1221.35			1106470	c	1		1.106
16	1221.45			1106470	c	1		1.106
17	1218.95	5.65	1224.6	1106470	b		0.6	0.664	1.106
18	1229.45			3900164	c	1		3.900
19	1230.65			1247934	d	0.35		0.437
20	1224.65			1247934	c	1		1.248
21	1226.75	1.85	1228.6	1247934	c	1		1.248
22	1221.65			537170	c	1		0.537
23	1218.85			537170	b	0.85		0.457
24	1227.95			537170	c	1		0.537
25	1226.85			537170	c	1		0.537
26	1224.95			1095220	c	1		1.095
27	1230.15	5.65	1235.8	1594776	d		0.65	1.037	1.595
28	1225.15			1594776	c	1		1.595
29	1221.85			1594776	c	1		1.595
30	1225.05			1594776	c	1		1.595
31	1229.65	8.85	1238.5	1538303	c	1		1.538
32	1223.45			1538303	c	1		1.538
33	1220.15			1538303	c	1		1.538
34	1226.55			1538303	c	1		1.538
35	1225.95			1538303	c	1		1.538
36	1220.45			1538303	c	1		1.538
37	1224.25	5.85	1230.1	1538303	c		0.85	1.308	1.538
38	1228.35			1538303	c	1		1.538
39	1219.35			3789587	c	1		3.790
40	1228.15			2011510	c	1		2.012
41	1223.65	32.35	1256	2011510	c	1		2.012
42	1220.35			2011510	c	1		2.012
43	1220.25			2011510	c	1		2.012
44	1221.95			686252	c	1		0.686
45	1228.85	1.35	1230.2	686252	c	1		0.686
46	1229.25			2451926	c	1		2.452
47	1219.05			2451926	c	1		2.452
48	1219.85			1043244	c	1		1.043
49	1224.95			1043244	c	1		1.043
50	1230.35	5.35	1235.7	1043244	d		0.35	0.365	1.043
TOTAL								59.317	6.389

Step 4: Weighting and cumulating events and exposure time

The final step before calculating the death rate is to take account of the record sample weight in both the deaths and the exposure time, and then sum the weighted deaths and exposure. Columns 6 and 7 of Table 5 show the exposure to risk for survivors and relevant deaths. Columns 8 and 9 then multiply columns 6 and 7 respectively by the sample weight v005/1,000,000. The age-specific mortality rate M(5,2002) is then calculated by dividing the sum of the weighted deaths by the sum of the weighted exposure time:

$$M\left(x,j\right)=\frac{{\displaystyle \sum _{i=1}^{N}D\left(i,x,j\right)*wgt\left(i\right)}}{{\displaystyle \sum _{i=1}^{N}E\left(i,x,j\right)*wgt\left(i\right)}}=\frac{6.389}{59.317}=0.1077$$

Step 5: Calculating probabilities of dying from age-specific mortality rates

The rates calculated in Step 4 are per month of exposure. It is therefore necessary to adapt the standard formula for deriving a period probability of dying from a rate. Given that we have made a number of simplifying assumptions and are working with narrow age ranges, it is adequate to assume that deaths are evenly distributed across each single month age range, even for the first month of life. We can then calculate q(x) as

$$q\left(5,2002\right)=\frac{\frac{M\left(5,2002\right)}{12}}{\left(1+\frac{M\left(5,2002\right)}{24}\right)}=\frac{\frac{0.1077}{12}}{\left(1+\frac{0.1077}{24}\right)}=\frac{.008975}{1+0.004488}=0.008935$$

Once all the q(x,j)s have been calculated, they can be converted into their complements, probabilities of surviving, and chained together to produce survivorship probabilities and probabilities of dying from birth to any desired age.

To obtain rates and probabilities for periods longer than a single calendar year, the weighted sums obtained in Step 4 are summed across years as required. Step 5 remains exactly the same.

Note that the procedure described here differs from that used by DHS. The DHS approach calculates probabilities directly for quasi-cohorts (Rutstein and Rojas 2003). Calculations are made for eight age groups: neonatal, 1-2 months, 3-5 months, 6-11 months, and years from age 1 to age 4. For each age range, period deaths are derived from date of birth and age at death. The risk set is an approximation of the number of children who enter that age range during the period. This approximation is the sum of all children who enter the age range and leave the age range (or would do so if they survived) during the time period, plus half of those who enter the age range during the period but would leave it after the period, plus half of those who enter the age range before the period but would leave it during the period.

Whichever procedure is used, individual-level data from the FBH will be required. Although the calculations could be carried out from detailed tables, it would be very tedious to do so. Use of a suitable computer routine is strongly recommended.

Interpretation

The key characteristic of direct child mortality estimation, namely that information is provided by surviving women who still live in surveyed households, needs to be borne in mind when interpreting results as there is risk of respondent selection bias. In particular, the mortality experience of children born in a community whose mothers no longer live in the community will not be included in the measures. If such children have higher mortality than those born to mothers who do still live in the community, mortality will be under-estimated. The most severe form of this bias is likely to result from substantial levels of HIV prevalence in the community, since such prevalence in the absence of widespread antiretroviral therapy will result in a strong positive correlation between survival of child and survival of mother (see effects of HIV/AIDS on child mortality estimation [4]). However, some positive correlation between mother and child survival is almost certain in any population. Other reasons for bias may exist. For example, high in-migration rates will result in women reporting on the survival of children born and raised elsewhere, while high out-migration will remove responses about children who were born and raised in the community. Although it is impossible to know a priori the direction or magnitude of such biases, the analyst needs to keep in mind their potential effect. Non-response may also be an issue if women absent from the community for an extended period cannot be interviewed in person, but may have experienced different risks to their children, or may not be present in part because their children have experienced different risks.

Extension to the method: Truncated birth histories

Truncated birth history: Data quality assessment

The truncated birth history (TBH) provides fewer opportunities for data quality checks than the full birth history (FBH) because the time series of events reported is by definition truncated. If the truncation is by time period, the events reported should be representative of the time period covered, whereas if the truncation is by number of events, the events reported may be representative only of all events in quite a short period prior to the survey, and this will complicate any assessment of the sequence of events in time.

As with the full birth history, the first step should be to examine the data for missing values. The second step should involve the examination of sex ratios at birth and heaping on ages at death.

No direct assessment of birth transference will be possible, because no detailed information about dates of births is available prior to the truncation point. However, an indirect assessment is possible. A TBH should always involve the initial collection of a summary birth history. The births and child deaths for an age group of women defined as at the survey date can therefore be calculated both at the time of the survey (from the summary birth history) and (only approximately for the deaths) at the truncation point, by subtracting the births and child deaths reported in the TBH. The calculation for births is precise, but for child deaths is approximate because some of the child deaths reported in the summary birth history (SBH) will have occurred during the post-truncation period to children born before the truncation point; typically, however, the number of such extra deaths will be small given that child mortality risks drop rapidly with age of child. The data quality assessment is therefore the comparison of the proportion dead (by age group of mother at the time of the survey) of the children born after the cut-off date to that of the children born before the cut-off date.

There are two reasons why the former proportion will generally be smaller than the latter. First, the children will have been exposed to the risk of dying for a shorter period. Second, if child mortality is falling over time, they will have been exposed to lower age-specific risks as well. However, if children who have died are systematically omitted from the post-truncation period, or if they are reported in the summary birth history but not reported as having been born in the period, the ratio of the two will be inflated by data error. We can estimate a plausible error-free ratio if data are available from a full birth history for the same population at an earlier or later date. Table 6 shows data from Mongolia: three Reproductive Health Surveys, one in 1998 that included a full birth history and two – one in 2003 and one in 2008 – that collected only TBHs. The 1998 full birth history data are used to calculate proportions dead for children born before and after a comparably-defined cut-off date, and compared to the proportions calculated from the 2003 and 2008 TBH data. As can be seen, the TBH ratios are several times larger than the full birth history ratios, providing compelling evidence of transference of dead children out of the post-truncation period. In the absence of a country-specific baseline, such as that provided here by the 1998 RHS survey, ratios of 3 or higher should be taken as evidence of probable omission of dead children from the recent reference period.

Table 6: Proportions of children dead by whether the birth occurred before or during the TBH date window, Mongolia, 1998, 2003 and 2008 RHS

Age group	RHS 1998 (FBH)			RHS 2003 (TBH)			RHS 2008 (TBH)
	Proportion dead		Ratio	Proportion dead		Ratio	Proportion dead		Ratio
	Before	After		Before	After		Before	After
20-24	0.106	0.070	1.5	0.222	0.035	6.3	0.052	0.041	1.2
25-29	0.140	0.061	2.3	0.122	0.036	3.4	0.083	0.024	3.5
30-34	0.128	0.082	1.6	0.117	0.022	5.4	0.081	0.015	5.3
35-39	0.072	0.064	1.1	0.120	0.025	4.7	0.097	0.010	10.2
40-44	0.119	0.068	1.8	0.150	0.051	3.0	0.095	0.010	9.6
45-49	0.213	0.000	*	0.066	0.048	1.4	0.119	0.000	*

The truncated birth history: Calculation of child mortality indicators for cohorts

The calculation of cohort probabilities of dying from a TBH follows the same principle as that followed with a FBH: the probability of dying by age x is calculated as the number of dead children to the number of children ever born in some defined cohort born no less than x years before the survey. There is an important difference, however, as made clear in the Lexis Diagram in Figure 1, namely that the value of x is constrained by the truncation date. For example, if the truncation date is 5 years before the survey, no birth cohort will have been fully exposed to the full risk of dying by age 5, and the cohorts exposed fully to risks up to age 2 are limited to births 2, 3 and 4 years before the survey. Thus there are limits to the range of ages for which mortality indicators can be derived.

The truncated birth history: Calculation of child mortality indicators for time periods

The basic approach to calculating standard indicators from a TBH follows the same principles as that used for a full birth history: to calculate age-specific rates for a specified time period, convert them into estimates of probabilities of dying in successive age intervals, and apply the probabilities to a synthetic cohort of births to create the life table. The problem with analyzing a TBH in this way is the same, however, as that faced in calculating cohort indicators, namely that cases and exposure time become progressively more restricted as age increases. Thus if the cut-off point is five years before the survey, the measures for ages 3 and 4 will be based on small numbers and have wide sampling errors.

References

Preston SH, P Heuveline and M Guillot. 2001. Demography: Measuring and Modelling Population Processes. Oxford: Blackwell.

Rutstein S and G Rojas. 2003. Guide to DHS Statistics. Calverton, MD: ORC Macro.

Childhood mortality estimated from health facility data: the Preceding Birth Technique

Background

In the introduction to child mortality [3] section, we have already drawn attention to the possibility of using data collected at health facilities to measure early childhood mortality. Setting selection issues aside for the moment, the most useful technique for obtaining such mortality measures is based on a simple question put to a mother when expecting or delivering her next child, here referred to as the index child. At the time of the pregnancy or delivery, the supplementary information needed is whether or not the previous live birth is alive or dead at the time of the subsequent pregnancy or birth of the index child. For a set of mothers (generally not less than 1,000 respondents), the proportions dead amongst the previous live-born children are then converted into a measure of early childhood mortality. This measure is usually close to ₂q_0, but can be closer to ₃q₀ when birth intervals are long. Variations of the method also allow the proportions of preceding children dead obtained before the delivery of the index child, for example at the time of an antenatal visit, or after the delivery of the index child, to be converted into measures of early childhood survival.

There are several attractive features of child survival information gathered in this way from hospitals, clinics and other health centres. First, the information often forms part of the routine health system reporting so the need for special studies and surveys is obviated. Second, when such information comes from health facilities, additional information which is difficult to obtain in retrospective surveys can be obtained relatively easily. This includes characteristics of the mother as well as key attributes of the births including sex and birth order, and birth weight. Third, the data can be disaggregated to provide detailed estimates for particular health facilities (when the population in the clinic’s catchment area is sufficiently large), for towns and small provinces. Such local or facility-based information could be useful to health authorities intent on targeting the communities with the worst infant and child mortality rates. Trends at the local level can also be used to assess the effectiveness of past health interventions. Finally, we can expect the data in health facilities to be reasonably accurate as they are mostly being collected by literate professionals. Further, clinic-based respondents may be more prepared than mothers to report events which are otherwise seen as stigmatizing (distinguishing live births, still births, abortions and miscarriages) or painful to recall (a neonatal or infant death).

Origin of the Preceding Birth Technique methods

The technique has its origins in a study of mortality in the Solomon Islands in the 1980s. In the course of this study it was noted that amongst the information routinely collected in maternity centres were answers to the questions on children ever-borne and surviving as well as a question on the survival of the preceding born child if the mother was delivering her second or subsequent child, the index birth (see Figure 1). Brass and Macrae set out to ascertain how these data could be related to conventional measures of child survival estimated from summary birth histories and the proportions dead of preceding births (Brass and Macrae 1984, 1985). Two methods were proposed. The Preceding Birth Technique (PBT) has attracted most attention since it provides a running estimate of early childhood mortality close to the current period. The theoretical basis of the method has been expanded and developed to allow applications to data on the survival of preceding children collected before and after a birth (Aguirre 1994; Aguirre and Hill 1988; Hill and Aguirre 1990). The second method (Brass and Macrae 1985), based on the total numbers of children ever-borne and surviving requires more refinement, is more complicated to apply and is not discussed further here.

Subsequently, others have applied the PBT in a variety of circumstances for different purposes – for example, in refugee camps, to measure abortion rates in antenatal clinics, for small area estimation and to measure the impact of health interventions (Bicego, Augustin, Musgrave et al. 1989; Madi 2000; Oliveras, Ahiadeke, Adanu et al. 2008; Rowe, Onikpo, Lama et al. 2011). Research in a demographic surveillance site where births and deaths had been accurately and independently recorded showed that good results could be obtained when contraception had become widespread and birth intervals had lengthened as well as when the data had been collected at antenatal rather than maternity clinics or at the time of the first vaccination of the new born (Bairagi, Shuaib and Hill 1997).

Caveats and warnings

The analyst faces several difficulties in making use of facility-based data on child mortality. The most important of these is that the population attending the facilities is not randomly selected. The resulting selection biases are important in three main ways.

The first bias in facility-based data arises because of the incomplete coverage of the population by health facilities, both public and private. This selection can work in different ways. Often, the urban population has easier access to health facilities than the rural population. The better off and better educated often make greater use of modern health services than the poor and the illiterate. This bias would likely result in estimates that are too optimistic in respect of infant and child mortality. In some cases, however, the bias can work in the other direction. The tertiary referral centres, which are generally the central maternity or teaching hospitals, often have much worse outcomes than peripheral centres simply because most complicated cases requiring surgery and other forms of advanced care are referred to these centres. Estimates based on such facilities will therefore tend to be over-estimate infant and child mortality.

The extent of this first bias is reduced when the coverage rates of health facilities used as a source of data are high. Even in sub-Saharan Africa, using the most recent DHS surveys for 38 countries, we find that 51 per cent of mothers delivered in a health facility, 76.5 per cent of mothers in urban areas. For antenatal visits, an even higher proportion, 93 per cent, were seen by a doctor or a health professional in urban areas in sub-Saharan Africa with a surprising 76 per cent being seen for antenatal care by a doctor or health professional even in rural areas (Macro International Inc 2012). With these high coverage figures, it is possible to address some of the biases associated with incomplete coverage of the population. We therefore present below a method to estimate early child mortality from the proportions of preceding born children dead when mothers attend antenatal clinics or even vaccination clinics. These options are discussed below in the section entitled "Extensions".

When coverage of the population by the health facilities is much lower, selection bias is clearly more important. Survey or census data for the whole population may be used to adjust the figures coming from health facilities by comparison of the characteristics of users and non-users of the health services. An added complication is that many countries are trying hard to extend the coverage of their health services. This may add new sub-populations with distinctive mortality patterns to the pool of information on child survival. Such changes in coverage can make the interpretation of trends over time difficult. In most large populations, however, new facilities take time to add and thus the coverage of existing facilities changes quite slowly.

The second source of systematic bias is that virtually all the women seen in maternity hospitals and health centres are attending these facilities because they are about to have a baby. Any information gathered from these women is specific to these moments in their reproductive careers. By contrast, in random sample surveys, women are interviewed without any reference to the current stage of their reproductive life and so the information obtained from them is representative of the reports from all, or all parous, women. An adjustment has been proposed to make the facility-based reports on total children ever-born and dead more like the reports in household surveys. The adjustment, however, now seems too dependent on various assumptions such as the effect of birth order on child survival and the location in time of child deaths (Brass and Macrae 1985).

A third selection bias that arises with this method is the fact that each woman’s last birth is never reported because there is no subsequent ‘index’ birth. This bias is probably trivial in high fertility settings, but in a population in which many women have only two children, there will be an over-representation of first births, which typically have above average mortality. In a population in which a substantial proportion of women have only one birth, the preceding birth technique will also not provide unbiased estimates of early childhood mortality.

Detailed description of method

A diagram helps to understand the terms used in this explanation. Figure 1 shows an idealized birth interval Ī for a woman with the three possible points of contact with the health services – for an antenatal visit, at the time of the delivery and after the delivery for a post-partum check-up or vaccination of the new born infant. Figure 1. An idealized birth interval with possible points of contact with the health services. [7]

Models and empirical data have shown that the proportions dead amongst preceding birth children, Q, collected close to the time of the delivery of the index birth are close to the probability of dying by an age which is close to 80 per cent of the mean live birth interval, Ī. Tabulation of the median birth intervals for 35 of the most recent surveys covering the period 1990-2010 in sub-Saharan African countries shows that the median birth interval was 34.8 months (Macro International Inc 2012). The only countries with median birth intervals over 40 months were Ghana (40), Namibia (42), South Africa (47) and Zimbabwe (47). The proportions of preceding births dead at the time of delivery of the index child is thus close to the proportions dead by the second birthday, in life table notation, ₂q₀.

The reason that the proportion of previously born children who have died by the time of a subsequent birth closely approximates ₂q₀ in a life table is because the proportion dead is the integrated product of two asymmetrical functions. One is the distribution of births over time before the most recent birth, b(x), and the other is the cumulative probability of dying, q(x), taken from the early part of a life table. The monthly distribution of previous births is skewed with no live births occurring during the nine months preceding the current maternity but with a concentration of births around the mean birth interval, say 30 months, and a long tail stretching back in time before the most recent birth. The cumulative probabilities of dying in childhood in any life table rise quickly during the first two years of life but thereafter, the cumulative proportions dead, q_x, flatten out beyond the age of two years (Hill and Aguirre 1990).

Figure 2 illustrates the shape of these two functions using real birth interval data (hence the slight irregularities attributable to date misreporting) and the probabilities of dying by month since birth taken from the UN General Model life table with a life expectancy at birth of 60 years.

Figure 2. Typical distributions of birth interval length by time since preceding birth and the cumulative risks of dying by age (x). [8]

We see that the proportion of previously born children who have died, Q, is thus the integrated product of these two functions.

Mathematically:

$$Q={\displaystyle \underset{0}{\overset{\infty }{\int }}b(x)q(x)dx}$$

Equation 1

where b(x) is the number of births which occurred x months before the current maternity, and q(x) is the cumulative probability of dying by age x. In short, as may be shown from models and from empirical work using birth histories to simulate data on child survival collected at the time of a subsequent birth, the proportions of previous children who have died at the time before a subsequent maternity may be taken as a good estimate of _xq₀ where x is generally equivalent to 0.8 of the mean birth interval Ī. When the birth intervals are close to 30 months, the proportions of preceding children dead will be approximately ₂q₀. Since the method is primarily designed to measure year to year changes in child survival by facility, the main interest will be in the value of the index rather than in its exact representation in the life table. However, the main confounding effect in comparing results across different populations or over time, will be due to differences in birth interval length. As Rutstein’s analysis has shown, median birth intervals have changed very slowly between the first and last DHS surveys in each country and especially in sub-Saharan Africa, so temporal effect changes in birth interval length are probably of minor importance (see Rutstein (2011: Table 2.2a)). The convention is that the proportions of preceding children dead collected at the time of a subsequent birth are simply referred to as the “index of early childhood mortality”, and taken as a close approximation to ₂q₀ in most populations and to _2.7q₀ in populations with birth intervals closer to 40 months (in Africa, mostly the countries of southern Africa with Ghana). Clearly, many low fertility countries have longer birth intervals but most such countries have good vital registration systems and so will not be the main users of the PBT.

We can estimate the possible effects of birth intervals differing from 30 months on the child mortality measures by using model life tables. We use the UN General Standard model for both sexes combined with a life expectancy at birth of 60 years to calculate the monthly probabilities of dying up to age 5. Then, we calculate the percentage differences in the measure of early childhood mortality when the birth interval differs from 30 months and the exposure time is not 0.8 * I or 24 months (₂q₀). When the birth interval is 25 months and hence the exposure time is 25 * 0.8 = 20 months, as might occur if the data are collected at ante-natal visits, then the proportions of preceding children dead is closer to _1.7q₀ or 5 per cent lower than if the birth interval had been 30 months. With birth intervals as long as 40 months, then the proportions of preceding birth children dead approximates to _2.7q₀, a 7 per cent difference from the central value of ₂q₀ associated with a birth interval of 30 months. If the interval between the birth of the preceding birth and the time the data are collected is as long as 45 months, as might occur if the mothers are seen some time after the birth of the index child, then the child mortality measure estimated is approximately ₃q₀ or 9per cent more than ₂q₀ in the model life table. Although important, these differences are not large and the percentages are likely to remain the same in the short term.

Model life tables can be used to interpolate between the various measures of child mortality derived from the PBT. With birth intervals of 30 months, we are estimating approximately ₂q₀ but by using logit transformations of model life tables, we can readily derive corresponding values of ₁q₀ (infant mortality) and ₅q₀ (the U5MR used by UNICEF). An example of the interpolation method is shown in Table 2. The same procedures can be used to derive ₂q₀ when the intervals between the preceding birth and the index birth are not 30 months, if the birth interval is curtailed by collection of the data at ante-natal visits or if the time since the birth of the preceding birth is extended by collection of the data say, at first vaccination of the index child. The associated worksheet [9] shows how to do this in detail.

Numerous questions arise from the simple result that Q≈ _{(Ī .0.8)} q₀. First is the issue of the omission of women with only one birth and thus no preceding birth. In most populations lacking full vital registration, however, most women proceed to have at least a second child so the mortality experience of first births is not omitted from the data and consequently this bias is small. There may still be a concern in low fertility populations, however, that first births are over-represented in the data. Second, women who die in childbirth may not survive long enough to report on the survival of their previous children, although clinical records are often available ahead of the death. We know that the risks of losing subsequent children are strongly associated with a maternal death, as the Bamako data bear out (Hill and Aguirre 1990) but fortunately maternal deaths are sufficiently rare as to have a small effect on the data collected this way.

The time reference of the PBT estimates is important to establish and again Figure 2 helps us to estimate the mean time at death of preceding children who died before the index birth. The combination of relatively high risks of dying early in life (see the q(x) function) combined with the concentration of births around the mean birth interval points to a mean age at death substantially less than half the birth interval. From models, Aguirre (1990) showed that the mean time location of deaths to the preceding born children was about two-thirds of the birth interval length before the date of birth of the index children. From empirical data with a wide range of birth intervals, the range was between 54 per cent and 74 per cent of the birth interval in months before the dates of birth of the index children. In most applications, it is recommended that analysts take the time reference to be two-thirds of the preceding birth interval before the birth of the index children. This assumption has been built into the accompanying estimation spreadsheets [9].

Data requirements

The key sequence of essential questions is simple, assuming the woman being interviewed in the health facility is pregnant (antenatal visit), newly delivered (in a maternity clinic or hospital) or has brought a young infant for immunization: 

• ‘Were you pregnant another time before this current pregnancy/birth?’

If ‘yes’, continue. If ‘no’, stop.

• ‘What was the result of this previous pregnancy?’ (live birth, still birth, miscarriage or abortion – spontaneous or induced).

 If ‘live birth’ continue, If other, stop.

• ‘Is this previous born child still alive today?’ (yes/no)

Date of interview (usually date of the delivery of the index child) is also needed but this generally forms part of the administrative records.

These are the basic questions. Others related to the care of the mother and her children are often added, such as the date of birth of the preceding child, its sex, its birth weight (if known), whether a singleton or multiple birth, whether still being fully breastfed and so on, depending on needs and circumstances. Similarly, some additional information on the mother (age, education residence) as well as information on the current delivery such as birth weight and place and type of delivery (normal vaginal, forceps, vacuum, caesarean etc.) can be relevant for maternal and child health care (if the mother is seen post-partum). Collecting the date of the birth of the child preceding the current delivery provides useful information on the average birth intervals in the population under study.

Often, the data are obtained in clinics in the form of registers or ledgers. An example of one is shown in Table 1 below. The content of each of the columns can be varied for different purposes but the key questions for the estimation of early child mortality are clearly the questions in columns (7) and (8). Note that in health systems gravidity (total number of pregnancies, however short their duration) often replaces the total number of live births but with training, health workers can readily distinguish the more medical definitions (gravidity, parity, confinements) from the more demographic terms (pregnancies, live births and living children).

Table 1 Example of data collection register for implementation of the preceding birth technique

Date of delivery (1)	Mother’s name or ID (2)	Mother’s age or date of birth (3)	Gravidity (total pregnancies) (4)	Live births (5)	Living children (6)	This delivery: type (live birth, still birth, abortion or miscarriage) (7)	Singleton or multiple birth? (8)	If live birth preceding birth alive today? (9)	Sex of last delivery: male/ female (10)
27 Jan 2012	Mariama Sow	31 Oct 1980	7	5	4	Live birth	Single	Yes	M
28 Jan 2012	Comfort Frempong	27 June 1991	3	3	2	Still born	N.A.	N.A.	N.A.
29 Jan 2012	Huda Khalaf	19 Oct 1992	3	2	2	Live birth	Twin	1 – Yes	M
29 Jan 2012	Huda Khalaf	19 Oct 1992	3	2	2	Live birth	Twin	2 - No	F
30 Jan 2012	Mary Kenyatta	22 yrs	3	2	1	Miscarriage	N.A.	N.A.	N.A.

 Note: In this example, words have been used instead of codes but in most applications, the optional answers would be pre-coded to standardize responses and to minimize the work by the health staff. The summary counts of pregnancies, live births and living children exclude the most recent pregnancy or birth. Twins or triplets need to be separately recorded – see table.

Worked example

The basic form of the analysis is very simple – at the time of birth of the index child, divide the number of preceding children dead (Row B in Table 2) by the total number of preceding live born children. Still births are excluded from the calculations.

Table 2. Preceding birth technique estimates of early childhood mortality for Bamako, Mali in 1985.

Measures	Preceding births	Second-to-last births
(1)	(2)	(3)
Total alive amongst preceding live births (A)	4778	3737
Total dead amongst preceding live births(B)	679	620
Proportions of preceding born children dead (B/A)	0.142	0.166

Source: Data from the Bamako maternity clinics study (Hill and Aguirre 1990).

In cases where there is an interest in estimating other life table measures, infant and under 5 mortality can be estimated using a standard from model life tables and logit transformations. In Table 3, we illustrate the steps involved in using logit transformations of model life tables values to produce values of ₁q₀ and ₅q₀. These methods are included in the associated spreadsheets.

In some circumstances, information on the survival of the second-to-last born children, the child born before the preceding birth (if any). In crude terms, the period of exposure to the risks of dying for this second-to-last born child will be slightly shorter than twice the mean birth interval, Ī. Taking Ī = 30 months, the proportions of second- to-last children dead at the time of the current maternity will thus be approximately _2.Īq₀, i.e. ₅q₀. The reported proportion of second-to-last children who have died is close to the probability of dying during the first five years of life and not some younger age in this case, as the monthly birth distribution and the cumulative probabilities of dying are much flatter around the age of five than around the age of two years. In applications, the difficulty is that these data on the second-last child have been obtained from mothers who have had at least three deliveries or at least two deliveries and a third pregnancy. Thus, the systematic selection of women with higher parities and probably with higher fecundity (shorter birth intervals) exacerbates these biases relative to the case of the simple preceding birth version of the method (Hill and Aguirre 1990). Although included in the illustration below, the use of information on the survival of second-to-last born children to estimate recent child mortality is not recommended.

Table 3. Using logits and the UN General Standard model life table to estimate values of infant and under-5 mortality from the proportions of preceding and second-to-last births dead at the time of a subsequent delivery

Measure	Observed proportions dead	Proportions alive	l(2) in UN General model life table: e(0)=60	logit l(2)	Logit l(2) observed	Alpha	1q0: estimated infant mortality	5q0: estimated under 5 mortality
Proportion of preceding births dead	0.142	0.858	0.914	-1.179	-0.899	0.280	0.120	0.166
Proportions of second-to-last births dead	0.166	0.834	0.914	-1.179	-0.807	0.372	0.141	0.193

In Figure 3, we show the relationship of the different mortality measures estimated in Table 3. The data at face value suggest that child survival was improving in the period before the data were collected in Bamako’s maternity clinics. We must remember, however, the selection effects implicit in using the data from second-to-last births since only women with three or more births provide the information used to estimate the measures in the last row of Table 3.

Figure 3. The relationship between the proportions of preceding born children dead amongst preceding and second-to-last born births, Q, and life table measures of child mortality, 1q0 and 5q0. [10]

Extensions

A common criticism of the PBT method is that the rates are necessarily calculated for the population attending the health centres and maternity clinics and tell us nothing about the child mortality rates amongst mothers not attending such centres. As noted above, in most countries more and more mothers are giving birth in health centres of one kind or another so that gradually, the PBT estimates of child mortality will become more representative. In the interim, it is often worth exploring collection of the essential information elsewhere.

The most obvious opportunity to contact a larger proportion of mothers arises at the moment of first antenatal booking. As noted above, the proportion of pregnant women who attend such clinics is now quite high even in places with very low levels of vital registration (and delivery in health facilities). Very few adjustments are needed to adapt the collection of the essential information for the PBT in antenatal clinics. The main risk is that the information is collected multiple times from the same mother. Care must therefore be taken to ensure that the preceding birth technique information is obtained at first booking and not at all subsequent visits.

The main technical issue to be resolved is that compared with the time of delivery, the preceding birth interval will be curtailed when the information is obtained during an antenatal visit. This means that the proportion dead amongst preceding births will probably be a slight underestimate of the true value of ₂q₀ in the population. In many instances, however, pregnant women do not present for the first antenatal visit until the pregnancy is well advanced. In these cases, the curtailment in the length of the birth interval will be a matter of a few months. The slight reduction in exposure has only a very small effect on the measure of early childhood mortality (Bairagi, Shuaib and Hill 1997; Hill and Aguirre 1990).

Another alternative for obtaining the key information to apply the Preceding Birth Technique method is to include the questions at the time of the first vaccination of the baby since coverage rates for vaccination are often quite high both for mothers giving birth in clinics and for mothers who give birth at home. Again the basic format of the questions remains the same. Careful wording and training is needed to distinguish the new-born child being vaccinated from the preceding birth whose survival has to be established to use the preceding birth technique. Since the vaccination protocol begins – or should begin – in the first month of the new-born baby’s life, the extension of the exposure time of the preceding child to the risks of dying compared to the time of delivery is very short. The proportions of preceding born children dead at the time of vaccination can therefore be taken as a good approximation of ₂q₀. There may be problems in preventing multiple reporting from mothers who return for several rounds of vaccination but this can be managed (Hill and Kelly 1996). More important is the effect of mortality of the new-born child since mothers who lose a child soon after birth will not appear in vaccination clinics. If mortality of successive children is not independent, this would lead to an overall under-estimate of the index of early child mortality.

Trends over time and comparisons between areas

The most appropriate application of the preceding birth technique is for the study of early childhood mortality trends in sub-populations followed over time or for the comparison of child mortality trends different sub-populations. There are several countries now ranging from Senegal and Mali to the Sultanate of Oman where ongoing estimates of early childhood mortality are derived from information collected at maternity clinics. The application below, however, is derived from the Matlab Thana surveillance site in Bangladesh where we have the added advantage of well-recorded vital registration data in parallel with the information on the survival of the previously born child collected at the time of the birth. In the Matlab Thana study area, it is possible to compare in addition the childhood mortality in the ‘Treatment’ and ‘Comparison’ areas, providing additional support for the validity of the information from the method.

In Figure 4 below, the middle lines in both the Treatment and the Comparison areas illustrate the trend in early childhood mortality derived from the questions on the survival of the preceding birth collected at the time of the birth of the index child. The lowest lines show the time trend in infant mortality derived from the vital registration system and the upper line is ₃q₀, also calculated from the vital registration data. The measure of early childhood mortality matches very closely the trend in ₃q₀ since in this population with birth intervals close to 40 months, the Preceding Birth Technique is measuring mortality to about age 2.7 years or _2.7q₀. The goodness of fit between the directly measured child mortality measures and the proportions of preceding children dead is encouraging.

Figure 4. Proportions of preceding children dead at the time of a subsequent delivery, Q, compared with infant mortality, 1q0 and mortality before the third birthday, 3q0, measured directly from the Matlab, Bangladesh surveillance data. [11]

Comparison of mortality trends in sub-populations

This illustration stems from the study of early childhood mortality in the maternity clinics of Bamako, Mali where the additional information on the birth weight of the last born child (the infant delivered in the maternity clinic) was also recorded. As Table 4 illustrates, there is a very strong relationship between the birth weight of the index child, the most recent birth, and the survival of the preceding born children. This analysis clearly illustrates the concentration of excess risks in certain mothers and makes the case for targeting such high risk women in order to reduce early childhood mortality. In the same study, there were enough births occurring in each maternity over the course of a year to be able to calculate the index of early childhood mortality for each facility. This led to a rank ordering facilities according to the proportions of preceding children dead at the time of subsequent delivery and led to the identification of underperforming facilities and populations in their catchment areas which were in need of extra resources.

Table 4 Proportions of last and second-to-last births dead by the time of a subsequent birth, by the birth weight of the most recent born child.

Birth weight of the Index child (grams)	Preceding births
	N	Proportions dead ≈ 2q0
1500-1999	76	0.197
2000-2499	409	0.161
2500-2999	1389	0.153
3000-3499	1827	0.136
3500-3999	607	0.104
4000 or more	98	0.092

Source: Bamako maternity clinics study (Hill and Aguirre 1990).

References

Aguirre A. 1990. "The Preceding Birth Technique for the Estimation of Childhood Mortality: Theory, Extensions and Applications." Unpublished PhD thesis, London: University of London.

Aguirre A. 1994. "Extension of the preceding birth technique", Genus 50(3-4):151-169.

Aguirre A and AG Hill. 1988. "Estimacion de la mortalidad de la ninez mediante la tecnica del hijo previo con datos provenientes de centros de salud o de encuestas de hogares: aspectos metodologicos. [Estimating child mortality using the previous child technique, with data from health centers and household surveys: methodological aspects]", Notas Poblacion 16(46-47):9-39.

Bairagi R, M Shuaib and AG Hill. 1997. "Estimating childhood mortality trends from routine data: a simulation using the preceding birth technique in Bangladesh", Demography 34(3):411-420. doi: http://dx.doi.org/10.2307/3038293 [12]

Bicego G, A Augustin, S Musgrave, J Allman and P Kelly. 1989. "Evaluation of a simplified method for estimation of early childhood mortality in small populations", International Journal of Epidemiology 18(4 Suppl 2):S20-32. doi: http://dx.doi.org/10.1093/ije/18.Supplement_2.S20 [13]

Brass W and S Macrae. 1984. "Childhood mortality estimated from reports on previous births given by mothers at the time of a maternity: I. Preceding-births technique", Asian and Pacific Census Forum 11(2):5-8. http://hdl.handle.net/10125/3561 [14].

Brass W and S Macrae. 1985. "Childhood mortality estimated from reports on previous births given by mothers at the time of a maternity: II. Adapted multiplying factor technique", Asian and Pacific Census Forum 11(4):5-9. http://hdl.handle.net/10125/3562 [15].

Hill AG and A Aguirre. 1990. "Childhood mortality estimates using the preceding birth technique - some applications and extensions", Population Studies 44(2):317-340. http://dx.doi.org/10.1080/0032472031000144616 [16]

Hill AG and PG Kelly. 1996. Sur la mise en place de la technique de l'accouchement precedent, Senegal, 19 au 26 Janvier 1996 [On the implementation of the Preceding Birth Technique, Senegal 19-26 January 1996]. Arlington,VA: Partnership for Child Health Care.

Macro International lnc. MEASURE DHS STATScompiler.http://www.measuredhs.com [17].

Madi HH. 2000. "Infant and child mortality rates among Palestinian refugee populations", Lancet 356(9226):312. doi: http://dx.doi.org/10.1016/S0140-6736(00)02511-3 [18]

Oliveras E, C Ahiadeke, RM Adanu and AG Hill. 2008. "Clinic-based surveillance of adverse pregnancy outcomes to identify induced abortions in Accra, Ghana", Studies in Family Planning 39(2):133-140. doi: http://dx.doi.org/10.1111/j.1728-4465.2008.00160.x [19]

Rowe AK, F Onikpo, M Lama, DM Osterholt and MS Deming. 2011. "Impact of a malaria-control project in Benin that included the integrated management of childhood illness strategy", American Journal of Public Health 101(12):2333-2341. doi: http://dx.doi.org/10.2105/AJPH.2010.300068 [20]

Rutstein S. 2011. Trends in Birth Spacing. DHS Comparative Reports No. 28. Calverton, MD: ICF Macro. http://www.measuredhs.com/pubs/pdf/CR28/CR28.pdf [21] [21]

Downloads