Weibull Accelerated Failure Time (AFT) Model: The Effect of Socioeconomic and Demographic Factors on Survival Time in Kenya
Levis Otieno Oduori *
Department of Basic Sciences, Tharaka University, Marimanti, Kenya.
Daniel Mwangi Muriithi
Department of Basic Sciences, Tharaka University, Marimanti, Kenya.
Patrick M’mwamba
Department of Basic Sciences, Tharaka University, Marimanti, Kenya.
Jomba Jason
Department of Basic Sciences, Tharaka University, Marimanti, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Life expectancy is a fundamental demographic indicator that reflects population health and socio-economic development. However, the effects of socio-economic and demographic covariates on survival time in Kenya have rarely been quantified using fully parametric survival regression models. This study estimated and interpreted the effects of selected covariates on survival time using the Weibull Accelerated Failure Time (AFT) model. Secondary data from the 2022 Kenya Demographic and Health Survey (KDHS), comprising 5,400 adults, were analysed. Candidate predictors were identified through univariable Cox proportional hazards regression and subsequently selected using the Akaike Information Criterion (AIC). Model parameters were estimated using maximum likelihood estimation (MLE). The adequacy of the fitted Weibull AFT model was assessed using Weibull probability plots, Cox-Snell residuals, quantile-quantile (Q-Q) plots, and the Kolmogorov-Smirnov goodness-of-fit test. Regression effects were interpreted using time ratios, where values >1 indicated prolonged survival and values <1 indicated reduced survival time. The fitted model identified educational attainment, household wealth, employment status, sex, and place of residence as statistically significant predictors of survival time (p < 0.05). Higher educational attainment and greater household wealth significantly increased expected survival time, whereas unemployment and male sex significantly accelerated mortality by reducing survival time. Urban residence was associated with a modest increase in survival time relative to rural residence. These findings demonstrate that the Weibull AFT model provides a robust and interpretable parametric framework for quantifying the effects of socio-economic and demographic determinants on life expectancy. The study highlights the utility of time-ratio interpretation in survival modelling and provides empirical evidence to inform policies aimed at reducing health inequalities and improving population longevity in Kenya.
Keywords: Survival analysis, Weibull AFT model, time ratio, socio-economic determinants, household wealth