The time to event analysis or survival analysis aims at making inferences on the time elapsed between the recruitment of subjects or the onset of observations, until the occurrence of some event of interest. Methods used in general statistical analysis, in particular in regression analysis, are not directly applicable to time to event data due to covariate correlation, censoring and truncation. While analysing time to event data, medical statistics adopts mainly nonparametric methods due to difficulty in finding the adequate distribution of the phenomenon under study. This study reviews non-parametric classical methods of time to event analysis namely Aalen Additive Hazards Model (AAHM) trough counting and martingale processes, Cox Proportional Hazard Model (CPHM) and Cox-Aalen Hazards Model (CAHM) with application to the infant mortality at Kigali University Teaching Hospital (KUTH) in Rwanda. Proportional hazards assumption (PHA) was checked by assessing Kaplan-Meier estimates of survival functions per groups of covariates. Multiple events models were also reviewed and a model suitable to the dataset was selected. The dataset comprises 2117 newborns and socio-economic and clinical covariates for mothers and children. Two events per subject were modeled namely, the death and the occurrence of at least one of the conditions that may also cause long term death to infants. To overcome the instability of models (also known as checking consistence of models) and potential small sample size, re-sampling was applied to both CPHM and appropriate multiple events model. The popular non-parametric re-sampling methods namely bootstrap and jackknife for the available covariates were conducted and then re-sampled models were compared to the non-re-sampled ones. The results in different models reveal significant and non-significant covariates, the relative risk and related standard error and confidence intervals per covariate. Among the results, it was found that babies from under 20 years old mothers were at relatively higher risk and therefore, pregnancy of under 20 years old mothers should be avoided. It was also found that an infant’s abnormality in weight and head increases the risk of infant mortality, clinically recommended ways of keeping pregnancy against any cause of infant abnormality were then recommended.

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