Five essays on models and methods for the analysis of survival data with single and multiple causes of failure : With applications in family demography
Abstract: The dissertation consists of five self-contained essays dealing with analytical investigations, simulation studies, and demographic applications of statistical models and associated methods for the analysis of the so-called survival data.Our analytical results in the first paper indicate that models for grouped survival data which, depending on the application, are labeled different names, practically, make use of the same method in the process of parameter estimation and inference. Further, we find, empirically, that estimates of covariate-effects are not always robust to distributional assumptions for the duration variable.The second paper demonstrates, both analytically and empirically, that results of inference concerning covariate-effects as obtained from a dynamic model for the cause-specific hazard rate, and a static logistic regression model for a conditional probability, are generally the same.In the third paper we provide analytical and empirical justification to demonstrate that separate and simultaneous modeling of multiple causes of failure lead to the same estimates of hazard rates, Wedemonstrate further, that simultaneous modeling is based on the assumption of independence among thecauses of failure in which case it is impossible to distinguish between crude and net hazard rates.The fourth paper demonstrates, analytically, that in situations where a covariate interacts with two other covariates in the same multiplicative model, the traditional approach of using two first-order interaction terms leads to estimates of relative hazards that are not identified. A model involving a single second-order interaction term is proposed as a solution.In the fifth paper we examine the effects of differences in sample sizes and heteroscedasticity levels on the power and size of the conventional Chow test for the equality of two log-normal duration models.The main result, on the basis of simulated data, is that the test performs well from both aspects of size and power when the sample sizes from the two models are equal, and the error terms in the two models have the same form of heteroscedasticity.
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