Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring

For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox’s proportional hazard model. We revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size.

Simulation

We carried out a series of simulations to examine the accuracy of the above multiple failure time models in terms of four factors: different sample sizes, censoring levels, numbers of recurrence events and correlation levels. The sample sizes under consideration were $n = (50, 100, 200, 400)$ . Survival times were censored at fixed time determined to yield censoring percentages $p$ of $0\%$, $15\%$, $30\%$ and $50\%$ . The maximum number of recurrent events under consideration were $K=(3,6,9,12)$ . For subject $i$, the recurrence times $t_{i1}$, $t_{i2}$,$\ldots$, $t_{iK}$ were generated as correlated Weibull deviates. The 320 simulated scenarios were defined by crossing all levels of these four factors. Each simulation series consisted of the generation of $m$ = 10000 random samples, each one representing a survival dataset where half of individuals were considered as “control” and half of individuals were considered as “treatment”. This covariate was represented by a binary variable with values $0$ and $1$. The treatment effect was set at $\beta=-1$. For each simulated dataset we adjusted the WLW, AG and PWP models.

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Results

Please select the number of recurrents events, correlation level and percentage of censoring to view the accuracy of each model in terms of relative bias of $\beta$, bias of naive and robust variances and coverage of robust 95% confidence intervals: