APPLICATION OF SURVIVAL ANALYSIS IN ESTIMATING LIFE EXPECTANCY IN NIGERIA

CHAPTER ONE

INTRODUCTION

1.1 Background to the Study

Survival analysis is the branch of statistics concerned with the analysis of time-to-event data, in which the outcome variable is the duration until a defined event most commonly death occurs. Its distinguishing feature is its treatment of censoring: observations for which the event has not occurred by the end of observation, or for which the subject is lost to follow-up, contribute the information that survival exceeded a known duration rather than being discarded. The two foundational tools of the field are the Kaplan Meier product-limit estimator, which provides a non-parametric estimate of the survival function from incomplete observations (Kaplan & Meier, 1958), and the Cox proportional hazards regression model, which relates covariates to the hazard of the event without specifying the baseline hazard (Cox, 1972). Parametric alternatives exponential, Weibull, gamma, log-normal and log-logistic models permit direct estimation of expected survival time and are therefore of particular interest where the quantity of interest is life expectancy itself.

Life expectancy at birth is among the most widely used summary indicators of population health. Nigeria's position on this indicator is poor by both global and regional standards. World Bank estimates place life expectancy at birth in Nigeria at approximately 54.6 years in 2024, up marginally from 54.5 years in 2023, against a world average of roughly 73.9 years (World Bank, 2026). Healthy life expectancy the years a person may expect to live in full health is estimated at about 54.9 years (World Health Organization, 2024). Behind these aggregates lies a mortality structure dominated by early-life deaths: Nigeria bears the highest under-five mortality burden in Africa, with an estimated 850,000 under-five deaths from preventable causes reported in 2024, and analysis of the 2024 Nigeria Demographic and Health Survey indicates that nearly half of all under-five deaths occur within the first twenty-eight days of life.

Survival analytic methods have been applied productively to Nigerian mortality data. Okoli, Hajizadeh, Rahman and Khanam (2022), using Kaplan Meier estimates and Cox regression on the 2018 NDHS, found that most under-five mortality occurs within twelve months of birth, that children of fathers with no formal education faced a 36 per cent higher hazard of death than those of tertiary-educated fathers, and that children in the North-West faced a 63.4 per cent higher hazard than those in the South-West. Egbon, Bogoni, Babalola and Louzada (2022) extended this using Bayesian spatial hierarchical hazard models with exponential, gamma, log-normal, Weibull and Cox specifications. Clinical applications have also been reported, including studies of mortality among adults on antiretroviral therapy in south-eastern Nigeria (Odafe et al., 2014) and of paediatric snakebite mortality in the north-east.

What these studies share, however, is a focus on the hazard of death in specific sub-populations rather than on the estimation of life expectancy itself. The conventional route to Nigerian life expectancy figures is the abridged life table constructed from model life tables and indirect demographic estimation, a method necessitated by the incompleteness of vital registration but one which imposes strong assumptions about the age pattern of mortality. Survival analysis offers a complementary route: by fitting parametric survival distributions to observed duration data and integrating the fitted survival function, expected remaining lifetime can be estimated directly, with covariates permitting the disaggregation of life expectancy by sex, region, education, wealth quintile and place of residence. This study pursues that approach.

1.2 Statement of the Problem

Nigeria's official life expectancy estimates are produced largely by international agencies through indirect demographic techniques, because the country's civil registration and vital statistics system captures only a small fraction of deaths. This creates several problems.

First, the resulting national figures are model-dependent and offer limited disaggregation. A single national life expectancy of about 54.6 years conceals differentials between the North-West and the South-West, between rural and urban residence, and across wealth quintiles that survival analyses of the same underlying survey data have shown to be substantial (Okoli et al., 2022).

Second, the reliance on model life tables imposes an assumed age pattern of mortality derived from other populations, which may not describe Nigeria's actual mortality profile one that is unusually concentrated in the neonatal and infant periods.

Third, life expectancy estimates that cannot be disaggregated are of limited use for the two domains that most need them. Public health planners require sub-national estimates to target intervention; life insurers, annuity providers and pension fund administrators require Nigerian mortality tables to price products, and the absence of credible local tables has forced reliance on foreign experience, a deficiency with direct solvency implications for the rapidly growing annuity market.

The problem, therefore, is that Nigeria lacks life expectancy estimates derived directly from observed survival data using methods that accommodate censoring and permit covariate adjustment. This study addresses that gap by applying survival analysis techniques to Nigerian survival data to estimate life expectancy and its determinants.

1.3 Aim and Objectives of the Study

The aim of this study is to apply survival analysis techniques to estimate life expectancy in Nigeria and to identify its principal determinants.

The specific objectives are to:

1. estimate the survival function for the study population using the Kaplan Meier product-limit estimator;

2. compare survival experience across sex, geopolitical zone, place of residence, maternal education and household wealth quintile using the log-rank test;

3. fit and compare parametric survival models (exponential, Weibull, log-normal, log-logistic and gamma) to the survival data;

4. estimate life expectancy from the best-fitting parametric model and compare it with published life table estimates; and

5. identify the significant determinants of survival using the Cox proportional hazards regression model.

1.4 Research Questions

1. What is the estimated survival function for the study population in Nigeria?

2. Are there significant differences in survival experience across sex, geopolitical zone, place of residence, maternal education and household wealth quintile?

3. Which parametric survival distribution best describes Nigerian survival data?

4. What life expectancy is implied by the best-fitting parametric survival model, and how does it compare with published life table estimates?

5. Which covariates significantly influence the hazard of death in Nigeria?

1.5 Research Hypotheses

The following null hypotheses will be tested at the 5% level of significance:

H₀₁: There is no significant difference in survival experience between males and females in Nigeria.

H₀₂: There is no significant difference in survival experience across the six geopolitical zones of Nigeria.

H₀₃: There is no significant difference in survival experience between rural and urban residents.

H₀₄: Maternal education and household wealth have no significant effect on the hazard of death.

H₀₅: There is no significant difference in goodness of fit among the candidate parametric survival distributions.

1.6 Significance of the Study

For public health policy, disaggregated survival estimates identify where in the life course and in which geographies mortality reduction effort yields the greatest gain in life expectancy a question of direct relevance to Nigeria's progress towards Sustainable Development Goal 3. For the National Population Commission and the National Bureau of Statistics, the study offers a methodological complement to indirect estimation, demonstrating what can be recovered from survey survival histories using censoring-aware methods. For life insurers, annuity providers and pension fund administrators, the study contributes towards the construction of Nigerian mortality experience, which is a precondition for prudent annuity pricing and reserving under the risk-based capital regime now in force. For health-care providers and development partners, the identified determinants of survival indicate modifiable risk factors amenable to intervention. For scholarship, the study extends the Nigerian survival analysis literature currently dominated by hazard modelling in specific sub-populations towards the direct estimation of life expectancy, and applies parametric survival distributions where non-parametric and semi-parametric methods have predominated.

1.7 Scope of the Study

The study covers Nigeria, disaggregated by the six geopolitical zones. It uses secondary survival data from the Nigeria Demographic and Health Survey (most recent available round), supplemented where appropriate by hospital-based or institutional records and by published mortality statistics from the World Health Organization, the World Bank and the United Nations World Population Prospects. The covariates examined are sex, age, geopolitical zone, place of residence, maternal and paternal education, household wealth quintile, birth order, birth interval and access to health-care services. Methodologically the study is confined to non-parametric (Kaplan Meier, Nelson Aalen), semi-parametric (Cox proportional hazards) and parametric (exponential, Weibull, log-normal, log-logistic, gamma) survival models. It does not extend to cause-of-death decomposition or to the construction of full period life tables by conventional demographic methods.

1.8 Limitations of the Study

(i) Incomplete vital registration Nigeria's civil registration system records only a minority of deaths, so the study depends on survey-based retrospective survival histories, which are subject to recall error and to the omission of deaths in households that have since dissolved. (ii) Recall and heaping bias reported ages and durations in Nigerian survey data show characteristic heaping at rounded values, which affects the precision of duration estimates. (iii) Right censoring and truncation survival information is censored at the survey date, and adult mortality in particular is incompletely captured by surveys designed primarily around women of reproductive age and their children. (iv) Proportional hazards assumption the Cox model requires that hazard ratios be constant over time, an assumption that must be tested and may not hold for all covariates. (v) Extrapolation estimating full life expectancy from data concentrated in the early years of life requires extrapolation beyond the observed range, which introduces model dependence. (vi) Currency of data survey rounds are conducted at multi-year intervals, so estimates describe the period of the survey rather than the present.

1.9 Operational Definition of Terms

Survival analysis: A set of statistical methods for analysing the expected duration of time until the occurrence of a defined event.

Survival function, S(t): The probability that an individual survives beyond time t.

Hazard function, h(t): The instantaneous rate of occurrence of the event at time t, conditional on survival to that time.

Censoring: The condition in which the exact survival time of a subject is unknown, typically because the event had not occurred by the end of observation or the subject was lost to follow-up.

Kaplan Meier estimator: A non-parametric estimator of the survival function from incomplete (censored) observations.

Cox proportional hazards model: A semi-parametric regression model relating covariates to the hazard function through a multiplicative effect on an unspecified baseline hazard.

Log-rank test: A non-parametric test for the equality of survival distributions across two or more groups.

Hazard ratio (HR): The ratio of the hazard in one group to that in a reference group; values above one indicate elevated risk.

Life expectancy at birth: The average number of years a newborn would live if prevailing age-specific mortality rates at the time of birth remained unchanged throughout its life.

Healthy life expectancy (HALE): The average number of years a person may expect to live in full health, adjusting for years lived with disability or illness.

References

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Egbon, O. A., Bogoni, M. A., Babalola, B. T., & Louzada, F. (2022). Under age five children survival times in Nigeria: A Bayesian spatial modeling approach. BMC Public Health, 22(1), 2207. https://doi.org/10.1186/s12889-022-14660-1

Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457 481. https://doi.org/10.1080/01621459.1958.10501452

Klein, J. P., & Moeschberger, M. L. (2003). Survival analysis: Techniques for censored and truncated data (2nd ed.). Springer.

National Population Commission & ICF. (2019). Nigeria demographic and health survey 2018. NPC and ICF.

Odafe, S., Idoko, O., Badru, T., Aiyenigba, B., Suzuki, C., Khamofu, H., Torpey, K., & Chabikuli, O. N. (2014). Determinants of mortality among adult HIV-infected patients on antiretroviral therapy in a rural hospital in southeastern Nigeria: A 5-year cohort study. AIDS Research and Treatment, 2014, 1 8. https://doi.org/10.1155/2014/682697

Okoli, C. I., Hajizadeh, M., Rahman, M. M., & Khanam, R. (2022). Geographic and socioeconomic inequalities in the survival of children under-five in Nigeria. Scientific Reports, 12, 8389. https://doi.org/10.1038/s41598-022-12621-7

World Bank. (2026). Life expectancy at birth, total (years) Nigeria [Data set]. World Development Indicators. https://data.worldbank.org/indicator/SP.DYN.LE00.IN?locations=NG

World Health Organization. (2024). Nigeria country health profile: Life expectancy and healthy life expectancy. WHO. https://data.who.int/countries/566