Impact of misspecified residual correlation structure on the parameter estimates in a shared spatial frailty model

ABSTRACT

In practice, survival data are often collected over geographical regions. Shared spatial frailty models have been used to model spatial variation in survival times, which are often implemented using the Bayesian Markov chain Monte Carlo method. However, this method comes at the price of slow mixing rates and heavy computational cost, which may render it impractical for data-intensive application. Alternatively, a frailty model assuming an independent and identically distributed (iid) random effect can be easily and efficiently implemented. Therefore, we used simulations to assess the bias and efficiency loss in the estimated parameters, if residual spatial correlation is present but using an iid random effect. Our simulations indicate that a shared frailty model with an iid random effect can estimate the regression coefficients reasonably well, even with residual spatial correlation present, when the percentage of censoring is not too high and the number of clusters and cluster size are not too low. Therefore, if the primary goal is to assess the covariate effects, one may choose the frailty model with an iid random effect; whereas if the goal is to predict the hazard, additional care needs to be given due to the efficiency loss in the parameter(s) for the baseline hazard.

KEYWORDS:

• Survival data
• shared frailty model
• spatial correlation
• MCMC

MATHEMATICAL SUBJECT CLASSIFICATION 2010:

• 62N01

Acknowledgments

We sincerely thank the referees and the associate editor for their insightful and valuable comments that lead to greatly improved presentation of the work.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Cindy X. Feng http://orcid.org/0000-0003-4030-7413

Longhai Li http://orcid.org/0000-0002-3074-8584

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grants to Feng and Li.