A penalized likelihood approach for arbitrarily censored and truncated data: Application to age-specific incidence of dementia

The Cox model is the model of choice when analyzing survival data presenting only right censoring and left truncation. There is a need for methods that can accommodate more complex observation schemes involving general censoring and truncation. In addition, it is important in many epidemiological applications to have a smooth estimate of the hazard function. We show that the penalized likelihood approach gives a solution to these problems. The solution of the maximum of the penalized likelihood is approximated on a basis of splines. The smoothing parameter is estimated using approximate cross-validation; confidence bands can be given. A simulation study shows that this approach gives better results than the smoothed Nelson-Aalen estimator. We apply this method to the analysis of data from a large cohort study on cerebral aging. The age-specific incidence of dementia is estimated and risk factors of dementia studied.