Data and methodology

For the present analysis, a complete birth history was obtained directly from 341 ever- married women aged 15-39 years who had at least one child under five years old. The retrospective data collected contained information on the total number of children ever born to each mother and their survival status. For each birth, separate questions were asked to determine the sex of the child, the calendar date of birth in months and years and the completed age of the surviving child at the time of the survey. In the case of child death, mothers were asked to report the date of the child’s death in months and years along with the age at death in relevant days, months or years.

Though both the age of the living child at the time of the survey and the age at death were coded in months and years, many of the respondents stated the ages in completed years and did not provide information on the additional number of months. However, the current age of the living or the age at death for children below the completed age of one year was reported in months. Beyond exact age one, the age of the child, living or dead, is therefore best seen in terms of exact years (or completed 11 or 23 months). The accuracy of the data

and avoidance of reallocation of ages of the living or the dead to other age groups were ensured by using appropriate field and demographic techniques to calculate the months and years, where needed. For example, an extensive and detailed list of the major events that had taken place in Pakistan was prepared, forming a calendar of these events to assist the respondents to provide clues to the dates of the vital events of interest.

The information obtained identified a total of 1,301 children ever born in the period up to 22 years before the survey time. These children constituted the universe of the index children to examine the risk ratios and survival of the children before the fifth year of life was completed, cross-classified by the socio-economic and other health-related factors to identify the causes of child deaths. To realistically relate to the occurrence of events, the survey was deliberately limited to relatively young mothers under 40 years whose experience of childbirth and death took place in the recent past. Also, mothers with at least one child below the age of five were included in the sample to ensure representation of each household, to be able to determine the current status of the households.

The objectives of the study were achieved through the following four steps:

1. Empirical survival distribution functions were estimated for the main sub-groups of the child population by means of life table technique to observe the survival probabilities and death rates in each age group.

2. Univariate Cox proportional hazards models were fitted for each of the independent variables of interest to obtain parameter estimates for hazard rate ratios and examine their level of significance.

3. Based on the fitted parametric functions to the data, multivariate Cox proportional hazards analysis was conducted for the estimation of several covariates effects simultaneously.

4. A multivariate model was fitted to examine the interaction effects of the covariates.

To begin with, the covariates were grouped into four broad categories: socio-economic factors, environmental and hygiene factors, demographic factors and Health Program factors. Each independent variable was divided into two or more levels depending on the number of cases and the best combination of various subdivisions to obtain fixed categorical effects for the final analysis. The per cent distributions of the children under observation by each of the variables included in these four categories are given in Appendices of tables A5.1 to A5.4.

First, using survival procedure, which produces life tables, the age of the children was divided into seven intervals, 0 months, 1-5 months, 6-11 months, 12-23 months, 24-35 months, 36-47 months and 48-59 months, to determine the time interval between an initial event (birth) and the terminal event (death) and to obtain the subgroup comparisons. Each group for each child was treated as a separate observation or unit of analysis. The explanatory variables for each of these new observations maintained the same value, as none of them contained information on change over time. The analysis of survival data poses the problem of censored observations, that is, not all index children included in the analysis were exposed to the complete period of survival time under observation. For example, children of different ages born in the period less than five years before the survey time would not have completed their first four years of life and therefore their actual survival time is not known. However, to use the information of the censored cases, the survival functions mentioned above used

Figure 5.1 Survival curve for cohort of index children aged 1-4 years

Age (months)

Source: Child Health Survey, Rawalpindi, 1992

the life table techniques based on the assumption that, with similar characteristics, the censored survival times are similar to those of the non-censored times.

Figure 5.1 shows the survival curve of the birth cohort under analysis. Graphical presentation of the survival functions for some significant covariates are given in Figures 5.2 to 5.13. These graphic displays are based on non-parametric Kaplan-Meier estimates of the survivor function and show the comparisons of the survival probabilities during the first four years of life. However, complete reliance on the abovementioned summary statistics can be m isleading since these are estim ates subject to sam pling errors and other random fluctuations; therefore in order to examine in detail the differences in the distributions, a semi-parametric approach based on Cox’s proportional hazards model (Cox, 1972) using the method of maximum partial likelihood (Cox, 1975) was employed for final analysis using EGRET procedure.

To obtain the final child survival analysis, the joint distributions of all the observations were used to maximize the log partial likelihood in the proportional hazards model. The model used takes into account the multiplicative effect of the explanatory factors on the hazards functions and includes the censorings and the failures. In the proportional hazards model, the hazard function is given by:

h (t;z) = X (t)g(z;ß) with g (z ;ß )= exp(z ß)

where z is a vector of explanatory van . regression parameters,

(t) is the baseline hazard function. ® tor censoring The log-partial likelihood in the Cox’s

1

o for censoring

where D. is the censoring indicator <

1

[ 1 for death

Note: the index i here is based on an ascending order reordering of the failure/censoring time.

Past residence ---■--- City ~ 0.94 - - 0.90 - - 0.86 - - Age (months)

Figure 5.3 Survival curve for index children by mother's educational status _{Education status}

Age (months)

Figure 5.4 Survival curve for index children by father’s educational status (years)

Education status Noeduc Someedu 0.96 - ■ --- --- Higher 0.94 - ■ 0.92 - - 2 0.90 - - 0.88 - - 0.86 - - 0.84 - - 0.82 - - Age (months)

Family members --- ■---Less than 6 6 or more 0.90 - ■ 0.88 - - Age (months)

Figure 5.6 Survival curve for index children by the type of toilet Type of toilet --- ■--- Flush Without flush 058 - - 0.96 - - 054 - - 052 - - 050 - - 058 - - 082 - - Age (months)

Figure 5.7 Survival curve for index children by the type of garbage container

Type of container --- • ---Covered 0.98 - - 0.96 - - 0.94 - • 0.92 - • 0.90 ■■ 0.88 - - 0.86 - - 0.84 - - 0.82 - - Age (months)

---■--- 1 room 2 or more 0.96 - - 0.84 - - 0.82 Age (months)

Figure 5.9 Survival curve for index children by the sex of the child Sex of child 0.98 - - 0.96 - - Female 0.94 . . 2 0.92 - ■ £ 088 - • 086 - • Age (months)

Figure 5.10 Survival curve for index children by the number of children ever born

-•---1 yr 100 0.98 - - --- 3 yrs 0.96 . . 0.94 - - 0.92 - - O. 0.90 - - > 0.88 - - 0.86 - - 0.84 • - 0.82 - - Age (months)

Figure 5.12 Survival curve for index children by mother's age at marriage (years)

Age at marriage 12-19 yrs 0.98 - - 20-24 yrs 0.96 -• 25-31 yrs 0.94 - - 092 - - 0.90 - - 0.88 - - 0.86 - • 0.84 0.82 -- Age (months)

Figure 5.13 Survival curve for index children by use of contraception Contraceptive use ---Users 0.96 - - _Non-users 0.96 • • ~ 0.94 • • 0.92 - - £ 0.90 - - 0.88 - • t 0.86 - - 0.84 . . Age (months)

Before the proportional hazards models were fitted, an attempt was made to split the data into three different groups by year of birth to observe any comparable differences in the cumulative survival probabilities and measure any changes in mortality levels over time. Each group was to be treated as a separate unit of analysis, cross-classified by the covariates of interest to examine the patterns of differences in child survival. For instance, the survival of the children born in the first ten years of the 22-year period under observation could possibly have had a linear relationship with a covariate, the impact of which may have changed over time for children born in recent years. Analysis of this order, however, was terminated as there were hardly any differences in the survival probabilities of children in the three cohorts. Using the World Fertility Surveys for 29 countries conducted during 1975, Rutstein (1983:17-19) found that several countries including Pakistan had an increased under-five mortality in the most recent period over that of the period 5-9 years before the survey and that these countries had fluctuating mortality rates within an overall declining trend observed in the 20 years before the survey.

Table 5.1 Univariate hazards models for selected variables on child mortality _______ __ ______________ ____________________________ (N= 1301) M o d el _{S c a le d} D e v ia n c e L ik e lih o o d R a tio D e g r e e s o f F r e e d o m Null _1853.40

M other’s past residence 1848.30 5.10* 1

M other’s present residence 1853.37 0.03 1

Religion _{1851.36 2.04 1}

M other’s occupation 1853.11 0.29 1

Father’s occupation 1852.92 0.48 2

M other’s education status 1847.30 6.10* 2

Father’s education status 1845.86 7.54* 2

Total household income 1852.90 0.50 2

Typs of toilet 1849.51 3.89* 1

Typs of garbage container 1849.33 4.07* 1

No. of rooms in the house 1849.16 4.24* 1

Possession of television 1853.30 0.09 1

Possession of refrigerator 1851.69 1.71 1

Chi d ’s sex 1853.40 0.00 1

Chi dren ever born 1834.60 18.80* 3

Birth order 1850.35 3.05 3

Birth interval 1838.74 14.65* 3

M o.her’s age at birth 1849.51 3.89 2

M o.her’s current age 1847.65 5.75 4

M o h er’s age at marriage 1848.31 5.09 2

Cortraceptive use in past 1844.39 9.01* 1

* Significant at 5 per cent level

Soiree: Child Health Survey, Rawalpindi, 1992

For ths final analysis, using the categorical variables constructed, univariate hazards models for ea;h of the independent variables of interest were fitted to obtain parametric estimates of the hazard ratios. Any of the categories created could be taken as a reference category for purposes of comparison. The significance of these variables was based on the likelihood

ratio test obtained as a result of the difference between the initial deviance, based on the null hypothesis, and the deviance obtained on fitting the model. The values of the scaled deviances were checked across the critical points of the chi square distribution depending on the degrees of freedom to determine its statistical significance strictly at the level of 5 per cent. The scaled deviances with associated degrees of freedom for selected variables considered separately are presented in Table 5.1.

After analysis of the differentials across the main socio-demographic variables, the next step was to conduct multivariate analysis for estimation of several covariate effects simultaneously. This was done to control for any potential confounding between these variables and eliminate bias in order to take into account the effects of the more important covariates. The multivariate model was built up using a forward stepwise procedure. Based on the scaled deviance and the associated degrees of freedom, the most significant variable affecting the survival probability was first entered into the model. The model was gradually built up by adding one variable at a time. As stated above, the inclusion of an additional variable depended on the significance of the overall maximum likelihood ratio test and the estim ated param eters and their standard errors. Variables which were statistically insignificant previously were fitted into the model after the addition of every new variable to verify if the newly constructed model changed its significance level.

The final model obtained included only those variables which were statistically significant at 5 per cent level, presenting the estimated parameters, standard errors and the level of significance, based on the two-tail normal distribution z statistic; Bracher et al. (1993:409- 411) give a detailed account of such an approach. Finally, the pairwise interaction effects between these variables were examined using a similar forward stepwise procedure.