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Discrete-time and ordinal logistic regression models for recurrent event data
In the Cox Regression model, the outcome under study is the time to a single event, for example death or the occurrence of disease. Recurrent event data may arise if individuals are followed beyond their first event to subsequent event or censoring times. For example, we may record the times to two or more hospitalizations, seizures, infections, or bleeding incidents for each individual in a cohort. Prentice, Williams and Peterson (PWP, 1981) extended the Cox model to the analysis of continuous recurrent event times using a conditional stratification approach. In this research we adopt the general PWP modelling approach to the analysis of discrete recurrence data using a conditional logistic model (PWPD). We also develop extensions of Person-time (PTLR) and ordinal logistic models (CLR1, CLR2) for the analysis of repeated events. For each model a likelihood function is derived and maximum likelihood methods are used to estimate model parameters. A simulation study was conducted to evaluate the proposed methods. We examined the bias and mean squared error (MSE) of the parameter estimates from each model under a variety of conditions. The factors varied were: the effect size, censoring rate, interval length, and correlation between event times. We also checked model robustness under two types of model misspecification: nonproportional hazards and unobserved subject level random effects. The proposed methods were applied to three real data sets reflecting various censoring patterns and dependence structures. Overall, the continuous PWP type model performed well, having the smallest bias and MSE. The PWPD model yielded slightly larger parameter estimates and standard errors, but provided a reasonable approximation to the continuous time model in most cases. The models were sensitive to both types of misspecification considered. The PTLR, CLR1 and CLR2 models were found to be significantly biased for non-null effect sizes, and, therefore, are not generally recommended for use.
Sciarappa, Kenneth Alan, "Discrete-time and ordinal logistic regression models for recurrent event data" (1996). Doctoral Dissertations Available from Proquest. AAI9709650.