134 International Journal of Statistics in Medical Research, 2014, 3, 134-144 E-ISSN: 1929-6029/14 © 2014 Lifescience Global Application of Cox’s Proportional Hazard Model and Construction of Life Table for Under-Five Salam Shantikumar Singh * Department of Statistics, Pachhunga University College, Aizawl-Mizoram, India Abstract: A primary data of 836 eligible women in the age group of 15-49 years is used to determine the causal effects of covariates on under-five mortality. The eight covariates viz., number of family members (NHM), type of toilet facility (TTF), total children ever born (TCB), parity (PAR), duration of breastfeeding (DBF), use contraceptive (CMT), DPT and ideal number of girl (ING) are considered as covariates of the study. By applying Cox’s regression analysis, six covariates viz., TTF, NHM, CMT, DBF, DPT and ING have substantially and significantly effect on under-five mortality. Further, a life table of under-five children under study is constructed using the estimate of survival function obtained from Cox’s regression model. Keywords: Under-five, Covariates, Cox’s regression, hazard function and life table. 1. INTRODUCTION The first five years of life are the most crucial to the physical and intellectual development of children and can determine their potential to learn and thrive for a life time. That is why it is specifically stated as one of the goals of the millennium development goals (MDGs) to reduce child mortality by two-thirds by 2015. Although there has been a substantial reduction in infant and child mortality rates in most developing countries in the recent past, it still remains a major public health issue in South Asian countries particularly in India. Mortality and its converse indicator, longevity or life expectancy are among the most important measures of well-being and development in developing countries. Since child mortality has an overwhelming influence on life expectancy, it is important to analyze the determinants of child mortality in India and particularly in the state of Manipur. Moreover, child mortality indicates the health status of not only child but also the health status of mothers as well as society as a whole. The child mortality has received a new momentum of the study since there is a strong association ship between mortality and fertility as high mortality corresponds high fertility and vice-versa. Thus, the study of especially on child has as immense contribution towards the regulation of population growth and enhancing the health status of the society. The general medical definition distinguishes mortality of a child with respect to the child age: death within the first week of life is included with prenatal *Address correspondence to this author at the Department of Statistics, Pachhunga University College, Aizawl, Mizoram, PIN NO. 796001, India; Tel: (+91)8732843655; E-mail: shantikumarsalam@yahoo.co.in mortality (which also includes late foetal mortality) and death within the first month is referred to as neonatal mortality, and death within one year is referred to as infant mortality. The death under five is referred to as child mortality (WHO, (2005) [1]). Since peri and neonatal mortality is heavily influenced by prematurity, fatal genetic conditions of the foetus, and problems associated with delivery. The mortality after first month, which is mostly related to socio-economic and health conditions of the household. It is possible to analysis the determinants of child mortality at various levels of causality (Mosley & Chen (1984) [2]). The biomedical and epidemiological literature typically focuses on the immediate determinants of child mortality, in particular the impact of various diseases and weakened resistance. In contrast, socio-economic, environment & sanitation, medical and health care, demographic, exposure to mass media, etc., are usually focused on underlying determinants of child mortality that make children more vulnerable to the attack of various diseases. Moreover, the child mortality rates vary from countries to countries and even within the country also it is varied in region to region and state to state. In developed countries, the main factor influencing on child mortality is demographic factors whereas socio- economic, health care, etc., are main factors influencing on child mortality in developing countries. Thus, the study of child mortality is different from country to country and region to region. 1.1. Review of Literature From the past research findings, it is known that parity (birth order) is associated with infant and child mortality. Hobcraft et al. (1985) [3] indicate that beyond the first year of the morality of first born children is on average slightly lower than for children of birth orders 2