Variable Selection by sNML Criterion in Logistic Regression with an Application to a Risk-Adjustment Model for Hip Fracture Mortality

Abstract

When comparing the performance of health care providers, it is important that the effect of such factors that have an unwanted effect on the performance indicator (eg. mortality) is ruled out. In register based studies randomization is out of question. We develop a risk adjustment model for hip fracture mortality in Finland by using logistic regression. The model is used to study the impact of the length of the register follow-up period on adjusting the performance indicator for a set of comorbidities. The comorbidities are congestive heart failure, cancer and diabetes. We also introduce an implementation of the minimum description length (MDL) principle for model selection in logistic regression. This is done by using the normalized maximum likelihood (NML) technique. The computational burden becomes too heavy to apply the usual NML criterion and therefore a technique based on the idea of sequentially normalized maximum likelihood (sNML) is introduced. The sNML criterion can be evaluated efficiently also for large models with large amounts of data. The results given by sNML are then compared to the corresponding results given by the traditional AIC and BIC model selection criteria. All three comorbidities have clearly an effect on hip fracture mortality. The results indicate that for congestive heart failure all available medical history should be used, while for cancer it is enough to use only records from half a year before the fracture. For diabetes the choice of time period is not as clear, but using records from three years before the fracture seems to be a reasonable choice.