Purpose: To determine the relation between accuracy of estimated regression coefficients in Cox proportional hazards (PH) models, when unobserved heterogeneity is introduced, and the number of independent variables in the model and the available number of events per variable (EPV). Excess unexplained variability (frailty) will negatively affect the accuracy of estimates of survival model coefficients, in models that do not contain an error term, such as the Cox PH model. It is unclear whether this decrease in accuracy depends on the number of independent variables in the model or the number of available EPV.

Methods: We simulated datasets of survival times, based on known parameters, using exponential, Weibull or Gompertz distributions, extended with covariates. Frailty was defined as a latent multiplicative effect on the hazard function, following a gamma distribution with mean 1 and variance Θ, with Θ representing the level of overdispersion. For different, sufficiently large, EPV values (range 10 to 500) regression was performed on models for different numbers of coefficients and different parameter values. We calculated the average percent relative bias for regression coefficients and determined the proportion of simulations for which the 95% CI did not contain the true (known) parameter value.

Results: Increasing overdispersion resulted in increased shrinking of the estimated model coefficients towards zero (i.e. increasingly negative relative bias), for all datasets and all regression models. Furthermore, the degree of relative bias was similar for the complete EPV range and for all different numbers of parameters. The proportion of simulations for which the 95% CI failed to encompass the true parameter value depended on both the effect size of the parameter and the EPV. Larger values for the EPV resulted in smaller standard deviations (SD) and therefore in CI that excluded the true value more often.

Conclusions: The inaccuracy of estimated model coefficients in the presence of frailty does not depend on the EPV or on the number of covariates in the model. However, for a low number of EPV the bias in model coefficients is masked by the large SDs, while for high numbers of EPV the small SDs provide an incorrect sense of accuracy.