One of the Millennium Development Goals is the reduction of infant and child mortality by two-thirds of 1990 mortality levels by 2015. Generally, significant progress has been made in reducing mortality in children under five years of age. The global under-five mortality rate declined by 59 per cent, from 93 deaths per 1,000 live births in 1990 to 38 in 2019. In Kenya, the infant mortality rate in 2021 is 32.913 deaths per 1000 live births, a 3.36 per cent decline from 2020. In 2020 it was 34.056 deaths per 1,000 live births, a drop of 3.24 per cent from the year 2019. In Kenya, Nyanza Province has the highest infant mortality rate (133 deaths per 1,000 live births) and the lowest in Central Province (44 deaths per 1,000 live births). Despite this advancement, the world still needs to achieve that Millennium Development Goal, target number four, of reducing child mortality. This study aims at identifying vital risk factors affecting child mortality in Kenya. The paper's main objective is to determine the effect of socioeconomic and demographic variables on child mortality in the presence of dependencies in clusters. We then did a logistic regression and tested the proportionality of the significant covariates. Then, performed a Stratified Cox regression model and, finally, a shared frailty model in survival analysis based on data from the Kenya Demographic and Health Survey (KDHS 2014), which was collected using questionnaires. Child mortality from the KDHS 2014 data was analyzed in an ageing period: mortality from the age of 12 months to the age of 60 months, referred to as "child mortality". The study reveals that clusters (households), maternal age at birth, preceding birth interval length and the number of births in the last five years significantly impacted child mortality.