Parametric and semiparametric correlated frailty models for the analysis of multivariate event times

• Applicant: Professor Dr. Andreas Wienke
• Subject Area: Epidemiology and Medical Biometry/Statistics
• Term: from 2008 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 62133860

The event time analysis has developed during the last decades to a major area in biometry. In nearly all areas of medicine methods from event time analysis such as Kaplan-Meier-curves or the Cox model are applied. Often the user is confronted with correlated event times. Correlated event times occur in biometric-epidemiological applications in different types of studies, e.g. with clustered event times in multi-center trials (here patients are clustered in study centers), in data of relatives (here probands are clustered in families) or with the analysis of geographic patterns in mortality (here probands are clustered in geographical regions such as streets, districts, counties). In a meta-analysis of event times the single studies represent the clusters. Recurrent events such as infections, hospitalizations, asthma attacks, stillbirths, nonfatal myocardial infarcts or epileptic seizures consider the individual as a cluster with several event times and imply also correlated event times. Statistical standard models for event time analysis of uncorrelated event times such as the proportional hazards model by Cox (1972) cannot be used directly in this case. The aim of this proposal is in part A) an extension of the log-normal frailty models, which were considered in the first phase of the DFG project to continuous or smooth baseline hazard functions (splines). It will be analyzed whether the better fit of the baseline hazard function also translates into better estimates of the fixed and random effects in the model. Furthermore the exact Gauss quadrature estimation procedure will be compared with the PQL method (penalized quasi likelihood). Part B) contains the modeling of continuous covariates by splines. Part C) will consider the extension of existing possibilities for the modeling of the covariance matrix of the random effects towards very flexible correlation structure. The fourth part D) will consider the choice for the type of confidence intervals in the specific situation of estimation of random effects in event time analysis. In all four parts the equivalence of log-normal frailty models with generalized linear mixed models (GLMM) will be used to transfer or adapt the broad results from GLMM to the area of frailty models. The planned project will serve to popularizes frailty models in the area of medicine and to provide the user with software and guidance.

• DFG Programme: Research Grants
• International Connection: Belgium
• Participating Persons: Professor Dr. Luc Duchateau; Professor Dr. Niel Hens; Professor Dr. Oliver Kuß