Firth’s penalized likelihood for proportional hazards regressions for complex surveys

This article proposes a weight scaling method for Firth’s penalized likelihood for proportional hazards regression models. The method derives a relationship between the penalized likelihood that uses scaled weights and the penalized likelihood that uses unscaled weights, and it shows that the penalized likelihood that uses scaled weights have some desirable properties. A simulation study indicates that the penalized likelihood using scaled weights produces smaller biases in point estimates and standard errors than the biases produced by the penalized likelihood using unscaled weights. The weighted penalized likelihood is applied to estimate hazard rates for heart attacks by using a public-use data set from the National Health and Epidemiology Followup Study (NHEFS). SAS® statements to estimate hazard rates using data from complex surveys are given in the appendix.