Discrete time-to-event construction for multiple recurrent state transitions.

Abstract

Recent developments in multi-state models have considered discrete time rather than continuous time in the modeling of transition intensities, whose major drawback lies in the possibility of resulting in biased parameter estimates that arise from issues of handling ties. Discrete-time models have included univariate multilevel models to account for possible dependence among specific pairwise recurrent transitions within the same subject. However, in most cases, there would be several specific pairwise transitions of interest. In such cases, there is a need to model the transitions with the aim of identifying those transitions that are correlated. This provides insight into how the transitions are related to each other. In order to investigate the interdependencies between transitions, the unique contribution of this thesis is to propose a multivariate discrete-time multi-state model with multiple state transitions. In this model, each specific recurrent transition is associated with a random effect to capture possible dependence in the transitions of the same type or different types. The random effects themselves were then modeled by a multivariate normal distribution and model parameters were estimated using maximum likelihood methods with Gaussian quadratures numerical integration. A simulation study was done to evaluate the performance of the proposed model. The model yielded satisfactory results for most fixed effects and random effects estimates. This is noticed by near-zero biases and mean square errors of the average estimates as well as high 95% coverage probabilities of the 95% confidence intervals from 1000 replications. The proposed methodology was applied to marriage formation and dissolution data from KwaZulu-Natal province, South Africa. Five transitions were considered, namely: Never Married to Married, Married to Separated, Married to Widowed, Separated to Married and Widowed to Married. The presence of very small unobserved subject-to subject heterogeneity for each transition and a weak positive correlation between transitions were produced. Statistically, the model produced smaller standard errors compared to those from univariate models, hence it is more precise on estimates. The multivariate modeling of discrete time-to-event models provides a better understanding of the evolution of all transitions simultaneously, thus in addition to covariate effects, giving an assessment of how one transition is associated with the other. Empirical results confirmed well known important socio-demographic predictors of entering and exiting a marriage. Age at sexual debut played a positive critical role in most of the transitions. More educated subjects were associated with a lower likelihood of entering a first marriage, experiencing a marital dissolution as well as remarrying after widowhood. Subjects who had a sexual debut at younger ages were more likely to experience a marital dissolution than those who started late. Age at first marriage had a negative association with marital dissolution. We may, therefore, postulate that existing programs that encourage delay in onset of sexual activity for HIV risk reduction for example, may also have a positive impact on lowering rates of marital dissolution, thus ultimately improving psychological and physical health.