Investigating statistical models to handle competing risks with applications to mortality

Abstract

The aim of this thesis is to develop a framework for the modelling of historic cause-specific mortality rates allowing efficient forecasting of the aforementioned rates. Whilst the International Classification of Diseases and Related Health Problems (ICD) has been used to record the underlying cause of death for all reported deaths since the end of the 19th Century, the decennial revisions to the classification require special attention to ensure continuity of the time series for statistical analysis. While these updates have an influence on all causes of death, the greatest impact of the changes in ICD coding rules applies to the number of deaths attributed to pneumonia and bronchopneumonia. While comparability ratios exist for certain groups of causes of death, their application to the data distorts the overall number of deaths in a country. We propose a Multinomial Logistic extension of the classical Lee-Carter model as well as the Li-Lee model to estimate the effect of age and time on cause-specific mortality rates. The Li-Lee model is a multi-country extension of the Lee-Carter model with an additional bilinear term that pools mortality experience across countries and allows us to borrow strength when there are issues with the data for a single country. While the classical Lee-Carter and Li-Lee models are applied to mortality rates, we apply them to survival and death probabilities to take advantage of the sum to one constraint imposed by the logit transformation. This is the first use of the Multinomial Logistic Li-Lee model and also the first application of a Multinomial Logistic Lee-Carter model to cause-specific mortality as far as we are aware. We sort death counts from England & Wales and France during the period 1968 to 2005 into six groups by cause of death and five-year age groups for the majority of ages using mortality data collected by World Health Organization and made available in their Mortality Database. We estimate model coefficients using maximum likelihood and assess their fits using information criteria. We also compare the standard errors of the coefficient estimates obtained via bootstrap and MCMC. We then re-estimate the probabilities of death using the Hamiltonian Monte Carlo (HMC) algorithm and compare the mean squared errors of the in-sample values. We find that the Multinomial Logistic Li-Lee model outperforms the Multinomial Logistic Lee-Carter model when applied to the 1968-2005 mortality data for England & Wales and for France. Finally, we use the above mentioned models to project the cause-specific mortality probabilities using the HMC algorithm for the years 2006 through 2014.

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ORCID for Erengul Dodd: orcid.org/0000-0001-6658-0990

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