A flexible alternative to the Cox proportional hazards model for assessing the prognostic accuracy of hospice patient survival

Abstract

Prognostic models are often used to estimate the length of patient survival. The Cox proportional hazards model has traditionally been applied to assess the accuracy of prognostic models. However, it may be suboptimal due to the inflexibility to model the baseline survival function and when the proportional hazards assumption is violated. The aim of this study was to use internal validation to compare the predictive power of a flexible Royston-Parmar family of survival functions with the Cox proportional hazards model. We applied the Palliative Performance Scale on a dataset of 590 hospice patients at the time of hospice admission. The retrospective data were obtained from the Lifepath Hospice and Palliative Care center in Hillsborough County, Florida, USA. The criteria used to evaluate and compare the models' predictive performance were the explained variation statistic R(2), scaled Brier score, and the discrimination slope. The explained variation statistic demonstrated that overall the Royston-Parmar family of survival functions provided a better fit (R(2) =0.298; 95% CI: 0.236-0.358) than the Cox model (R(2) =0.156; 95% CI: 0.111-0.203). The scaled Brier scores and discrimination slopes were consistently higher under the Royston-Parmar model. Researchers involved in prognosticating patient survival are encouraged to consider the Royston-Parmar model as an alternative to Cox.

Figure 1. Kaplan-Meier survival curves by initial PPS.

Figure 2. Test of the proportional hazards assumption under CPH for initial PPS.

Figure 3. Test of the probit assumption under RP for initial PPS.

Figure 4. Baseline survival functions under CPH and RP models.

Figure 5. Predicted survival by PPS under RP and CPH compared with the Kaplan-Meier estimates in the validation data.

Figure 6. Difference between Brier scores for RP and CPH models (6a) and between discrimination slopes for RP and CPH models (6b) as a function of patient survival times in the naïve (whole) data set and cross-validated data set.

Both are consistently higher for RP indicating better accuracy and discrimination.