Application of random survival forests in understanding the determinants of under-five child mortality in Uganda in the presence of covariates that satisfy the proportional and non-proportional hazards assumption.

BACKGROUND: Uganda just like any other Sub-Saharan African country, has a high under-five child mortality rate. To inform policy on intervention strategies, sound statistical methods are required to critically identify factors strongly associated with under-five child mortality rates. The Cox proportional hazards model has been a common choice in analysing data to understand factors strongly associated with high child mortality rates taking age as the time-to-event variable. However, due to its restrictive proportional hazards (PH) assumption, some covariates of interest which do not satisfy the assumption are often excluded in the analysis to avoid mis-specifying the model. Otherwise using covariates that clearly violate the assumption would mean invalid results.

METHODS: Survival trees and random survival forests are increasingly becoming popular in analysing survival data particularly in the case of large survey data and could be attractive alternatives to models with the restrictive PH assumption. In this article, we adopt random survival forests which have never been used in understanding factors affecting under-five child mortality rates in Uganda using Demographic and Health Survey data. Thus the first part of the analysis is based on the use of the classical Cox PH model and the second part of the analysis is based on the use of random survival forests in the presence of covariates that do not necessarily satisfy the PH assumption.

RESULTS: Random survival forests and the Cox proportional hazards model agree that the sex of the household head, sex of the child, number of births in the past 1 year are strongly associated to under-five child mortality in Uganda given all the three covariates satisfy the PH assumption. Random survival forests further demonstrated that covariates that were originally excluded from the earlier analysis due to violation of the PH assumption were important in explaining under-five child mortality rates. These covariates include the number of children under the age of five in a household, number of births in the past 5 years, wealth index, total number of children ever born and the child's birth order. The results further indicated that the predictive performance for random survival forests built using covariates including those that violate the PH assumption was higher than that for random survival forests built using only covariates that satisfy the PH assumption.

CONCLUSIONS: Random survival forests are appealing methods in analysing public health data to understand factors strongly associated with under-five child mortality rates especially in the presence of covariates that violate the proportional hazards assumption.