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Abstract
Survival regression models allow for consideration of the effects of multiple covariates on the occurrence and timing of events (e.g., the classical survival analysis event of death). In any given data analysis, however, one or more of the assumptions underlying these models may be violated, and the ability to arrive at appropriate estimates and draw meaningful conclusions may correspondingly be adversely impacted. This dissertation investigates the performance of three survival regression models – the highly popular semiparametric Cox model as well as the parametric exponential and Weibull models – in the presence of multiple, simultaneous assumption violations.
Specifically, a simulation study was conducted to evaluate the performance of these models in scenarios with various combinations of non-proportional hazards, informative censoring, and (for the parametric models) misspecification of the event time distribution. Performance was evaluated across the following five outcomes: bias in β estimates, standard errors for the β estimates, Type II inference errors, bias in predictions of median event times, and bias in predictions of five-year survival probabilities. The effects of sample size and censoring percentage on such performance were also considered. The central simulation was complemented by a reduced simulation with a true event time distribution different from those considered in the primary simulation as well as by an illustrative real data analysis in which multiple assumption violations were present.
Results from the simulation studies indicated that violation of the non-informative censoring assumption and a misspecification of the event time distribution (when applying a parametric model) can have marked, often deleterious, effects on the performance of the regression models. While a proportional hazards assumption violation sometimes likewise had a notable effect (e.g., pervasive Type II errors for the covariate effect demonstrating non-proportionality), more often, results were little changed across corresponding conditions with and without a proportional hazards violation. These observations suggest particular attention be given to establishing the non-informativeness of censoring prior to fitting any of these models as well as to extensively checking alignment between the model-assumed event time distribution and the data at hand.
With regard to the number of assumption violations present, performance of the considered regression models was sometimes, but not always, worse in the presence of more violations than in the presence of no or fewer violations. Indeed, in some assumption violation conditions (e.g., when the effects of the considered violations on a particular outcome acted in different directions), performance was better when multiple violations were present than with the singular component violations alone. Thus, anticipating the effects of multiple assumption violations in any given analysis context is not straightforward.
When a misspecification of the event time distribution was not present, performance of the three regression models was generally similar for non-prediction outcomes, with some advantage noted for the parametric models when properly aligned with the true event time distribution (e.g., smaller biases in the β estimates with the Weibull model compared to the Cox model when the event time distribution was truly Weibull). In contrast, when misalignment between the assumed and true event time distributions was present, performance of the parametric models (particularly the exponential model) deteriorated sharply, again emphasizing the importance of the distributional assumption for these models.
The Cox model (with the Breslow estimator for the baseline survival function), on the other hand, often did not yield predictions of the median event times and five-year survival probabilities for the considered covariate profiles in high censoring, small sample size conditions with an exponential event time distribution. The parametric models, in contrast, always produce such predictions, and these predictions were generally good when all assumptions were satisfied or with a singular proportional hazards violation. Though, predictions again often deteriorated when distributional misspecification was present with the parametric models and, for all three models, when the non-informative censoring assumption was violated.
