Study Design and Analysis
Our population of interest is children who were born between January 1, 2003 and December 31, 2007 and who lived in the slums before their 5th birthday during this 5-year period. The children born in the slums are observed from birth. For the children born out of the slums, we use a 4-month minimum duration of residence threshold. In that way, the analytical definition does not depend on the operational migration definition in the Nairobi Urban Health and Demographic Surveillance System (NUHDSS), since the threshold period for in- and out-migration in the NUHDSS was 3 months between 2003 and 2006 and changed at the beginning of 2007 to 4 months.
In principle, we could have taken into account the children who were born before 2003 in the analysis. These would have been left-censored from January 1, 2003. However, the place of birth and the migration status of children born before 2003 were not collected. These children are thus excluded from the analysis.
Analysis of migration patterns16 shows some inconsistencies in the data on the first two and the last two quarters of our observation period. Inconsistent migration trends were observed before July 2003 and reflecting unstable data collection procedures. Migration trends were also found inconsistent after July 2007 but that reflects the “hanging cases,” i.e., when some people who are reported to have made an internal movement are only found in any other location in the demographic surveillance area (DSA) several rounds of visit later. To avoid these migration biases affecting our analyses, we excluded data collected during these four quarters. Therefore, the outcome of interest was the death of children who resided in the slums after July 1, 2003: The 10,445 children at risk lived 13,114 person-years and 465 of them died by June 31, 2007. Because of the period restriction, we will be able to measure mortality until 48 months (4 years) and not 60 months (5 years).
We used a semi-parametric proportional hazards (Cox) model to assess the effect of the mother and child’s migration on childhood survival rates, after controlling for the effect of a number of determinants. For each child, the observation time was age, starting at birth (if born in the study area) or at age reached after 4 months of in-migration in the slums (if born outside the study area) between July 2003 and June 2007. The observation ending either at their 4th birthday, at the occurrence of the event of interest (death) or dates of censoring due to refusal, loss to follow-up, emigration, or end of the follow-up when the observation time was truncated for the children who were still alive on June 31, 2007. We allowed gaps in the observation time, meaning that children could out-migrate and return to the slums.
We used a number of demographic and socioeconomic factors known to affect child survival as control variables. We have three types of control variables: (1) those directly related to the child (sex, migrant status), (2) those related to the mother (age, migrant status, ethnicity, and level of education), including her survival status as a time-varying covariate, i.e., a covariate that changes value from the time of occurrence of the change, (3) those related to the household economic status for the household where the child lives at any given time (access to tap water; access to own toilet; floor finish; roof finish; access to Kenya Power and Lighting Company (KPLC) electricity; ownership of dwelling unit; ownership of phone, radio, and TV), and (4) those related to the context (slum area, trimester introduced as a time-varying continuous variable to measure the overall trend over the study period). Unfortunately, classic determinants of child mortality such as birth interval and birth order were not available for all children and therefore could not be included in the model.
The focus of this paper is on the variable that combines place of birth of the child (in or out of the slums) and duration of residence of the mother in the slums. As explained earlier, this information was not available for children born prior to 2003. Children were classified according to the duration of residence of their mother in the slums at their birth in four categories. The children born before their mothers migrated to the slums form the first category, which is the reference category in the regression analysis. The second category is constituted of the children born within 8 months of the mother’s migration, i.e., children who have most likely been conceived before their mothers migrated to the slums. Because their mothers migrated while pregnant, the migration might actually be motivated by the pregnancy. The migration might also have represented a stress for the migrant mother, with possible long-term consequences on the child survival. The children born within 9 to 19 months following mother’s migration constitute a third category. These children were conceived within 1 year of mother’s migration to the slums, at a time when their mother might have been particularly vulnerable socially and economically. The fourth category is formed by the children born 20 months or more after the mother’s migration (i.e., conception most likely to have occurred after 1 year of mother’s migration in the slums). Children born of non-migrant mothers are included in this last category, called the long-term migrants for convenience.Footnote 2
One out of five babies born after their mother’s migration were actually delivered out of the slums, the mother thus spending some weeks or months out of the slums, while still considered in the HDSS system as residents because they spend less than 4 months out of the slums for delivery. Therefore, a child can either be born out of or in the slums whatever the above categories except the first (born before mother’s migration in the slums). When born out of the slums, the child is included in the population at risk 4 months after his or her migration in the slums. This means that deaths occurring in the first 4 months following in-migration are not taken into account. Our mortality estimates are therefore conservative since we exclude deaths that could have been caused by conditions prevailing before in-migration. So we are comparing death rates of seven categories of children, as depicted in Table 1. Out-migration of the mother without the child is not controlled for in the present analysis. We assume that the mother and the child are living together over the exposure period.
Table 1 Crude death rates per 1000 by mother’s migration status at birth and place of birth (Viwandani and Korogocho slums, Nairobi, July 2003–June 2007)
Migration in Longitudinal Analysis of Mortality
One of the most critical issues that one should take note of and possibly control for in longitudinal analyses is attrition, especially in cases where those leaving the study area are predisposed to different risks of dying compared with the general population. Attrition is particularly important in the NUHDSS setting because of the non-permanence of housing structures, unreliability of livelihood opportunities, and the consequent high levels of population mobility both within and outside the location. The two main sources of attrition in the NUHDSS are mainly out-migration and to a lesser extent loss to follow-up. Analysis of data of people who migrated to the slum settlements between 2003 and 2007 shows that the median duration of stay for the new migrants was 22 months for males and 26 months for females in Korogocho and 18 months for females and 22 months for males in Viwandani.14
The NUHDSS field team sometimes fails to observe some individuals and households because it is hard to find an eligible respondent at home. The most difficult cases of loss to follow-up are named “hanging cases,” which are cases where the fieldworker confirms that the respondent has left the housing unit where he/she was living during the last visit and is informed that the person has moved to another location within the study area. However, fieldworkers sometimes fail to trace the person in the new location for several rounds. These cases are called “hanging cases” because they are part of the health and demographic surveillance system (HDSS) since they have not died or out-migrated, but they are not found at any other DSA location either. Because the effect of hanging cases is the same as out-migration (in that no events or updates can be done regarding the person), out-migration and hanging cases are combined in one category to form the overall attrition. Out-migration is by far the most dominant source of attrition from the NUHDSS population. The NUHDSS data show that out of the 60,207 people (total population) who left the surveillance population between 2003 and 2007, out-migration accounted for 92%, while hanging cases and deaths accounted for 5% and 3%, respectively.17
Therefore, migration is a major source of population change in HDSS. The smaller the study area, the larger the migration is compared with other demographic phenomena. In Nairobi slums, the annual in-migration rate is 27.1% while the out-migration rate is 26.7%. This results in a dramatic turn-over of the slum population. The rates are even higher for the children under 5 years, respectively, 36.9% for in-migration and 31.4% for out-migration.16 It is imperative to understand the effect of such intense migration on health outcomes.
Other studies in Africa already showed that sending areas (mainly with prominently rural environment) experience an excess mortality due to people “returning home to die”.18,19 It is expected, therefore, that receiving areas would experience the opposite in that mortality might be underestimated due to migrants returning to the sending areas “to die” when they get (or are deemed at risk of getting) sick. It is not quite clear whether this pattern could apply to children as well, considering that it is not them who make the decision to migrate but their parents. Yet our hypothesis is that when children are deemed at risk of getting sick, as they often would in a very deplorable environment that is conducive to the spread of infectious diseases, their mothers would rather out-migrate to their origin area or send their children to this area for better care. The mortality should therefore be underestimated in a context of high circular migration pattern in a poor health environment. As we do not have follow-up data on the return migrants in their origin area to support that (it might be that the health conditions are not better than in the slums), we use a modeling approach to verify this hypothesis, as explained in the next section.
Two-Stage Equation Models to Control for Selection
The semi-parametric proportional hazards (Cox) model used in this analysis makes the assumption that all covariates have a proportional effect on survival whatever the age. The relative risk associated with a given covariate x is assumed to be the same on mortality rate λ
0(t) at each age t:
$$ {\lambda_x}\left( {t{|}x} \right) = {\lambda_0}(t){\hbox{ex}}{{\hbox{p}}^{{\rm{x}}\beta }}. $$
However, because not all children are born in the slums, the non-slum-born effect can only be computed after the children have reached 4 months of age (t = 4), which is the minimum time to be considered a resident in the slums. To check the effect of this limitation, we compared regression results in Table 2 with data excluding the first 4 months for both slum-born and non-slum-born and found no difference in direction or significance of covariates, including slum-born effect.
Table 2 Risk factors of migration and child mortality (Viwandani and Korogocho slums, Nairobi, July 2003–June 2007)
All event history analyses make the explicit assumption of independence between censoring and event. When censoring is not independent from the event of interest (e.g., migration in relation to death) then the results suffer from potential bias. In this analysis, we control for non-independent censoring and the consequent selection bias, i.e. when the same determinants may cause attrition and mortality. We adapted to the context of longitudinal data the two-stage equation model that has originally been developed for the control of endogeneity in cross-sectional data. The attrition (out-migration) risk is modeled using available independent variables, including an instrumental variable, e.g., a variable that affects attrition but not mortality.
The selection (censoring by out-migration) equation takes the form:
$$ {\lambda_{C\left| {Z(t)} \right.}}(\left. t \right|z(t)) = {\lambda_{C0}}(t){\exp^{z(t)\beta }}. $$
The main (mortality) equation takes the form:
$$ {\lambda_{T|x(t)}}\left( {t{|}x(t)} \right) = {\lambda_{T0}}(t){\hbox{ex}}{{\hbox{p}}^{x(t)\beta + {\Lambda_{ - 1}}(t)\alpha }}, $$
where:
$$ {\Lambda_{ - 1}}(t) = \sum {_{(\,j = 1)}^N{\lambda_{C|Z(t)}}(t|z(t)).I({C_j} \leqslant t),} $$
is the cumulative hazard function computed at the observed informative censoring time C only. It is interpreted as a propensity (and not a probability since the cumulative hazard can take value higher than 1) to have out-migrated of the population at risk by censoring time t. The cumulative hazard function is preferred to the inverse of the survival function because of its generalization to renewable event, as is out-migration. The squared propensity term can also be introduced in the model to test non-linear effect of attrition.
The vectors Z and X are the covariates respectively for the selection and main equations that verify \( Z = X + V.V \) is a vector of instrumental covariates (variables that can explain the selection but not the event) typically related to data collection issues or to calendar effects that influenced the selection.
Taking the log of the main equation and rearranging gives:
$$ y(t) = \log \left[ {\frac{{{\lambda_{T|x(t)}}\left( {t{|}x(t)} \right)}}{{{\lambda_{T0}}(t)}}} \right] = x(t)\beta + {\Lambda_{ - 1}}(t)\alpha $$
The equation y(t) is identified if Z≠ X, i.e. when the residuals of y(t) are not correlated with instrumental variables v(t) included in vector of covariates z(t) = x(t) + v(t) used to compute the propensity Λ
-1
(t). Here we use as an instrumental variable v(t), the notice of demolition of household structures under the KPLC electric lines (and to a lesser extent next to the Kenya Railway lines and Kenya Pipelines) that led to massive out-migration of part of the study population in 2004.Footnote 3