Can’t see the wood for the trees: Using common likelihoods to share information regarding selection of functional form in survival analysis

Abstract

Background The estimation of mean survival is a key consideration when estimating the cost-effectiveness of interventions. Estimation typically requires extrapolation using parametric survival analysis and may be sensitive to choice of functional form. We demonstrate a simple method that allows goodness-of-fit information to be assessed jointly across studies, where such information is believed likely to be exchangeable, to help inform the selection of functional form for parametric survival analysis. Methods Individual patient data for survival was estimated from digitised Kaplan-Meier curves for four trials in advanced soft tissue sarcoma. A range of parametric survival models were fitted. Two approaches were explored for identifying the preferred parametric model: (i) selecting functional forms independently for each study; and (ii) selecting a common functional form across studies. Akaike’s Information Criterion (AIC) or Bayesian Information Criterion (BIC) were used to select optimal functional form. For approach (ii) joint BIC or AIC statistics were calculated for each model by combining the components of the AIC or BIC, respectively, across studies. A bootstrap analysis was conducted to estimate the uncertainty in selection of functional form. Results Estimates of mean survival varied markedly according to choice of functional form. Independent selection led to different functional forms being selected for each study with considerable uncertainty regarding the optimum functional form according to AIC or BIC. In this case study, selecting an optimum functional form based on joint AIC or BIC across studies reduced uncertainty in model selection and variance in mean survival compared to selection of functional form independently. Conclusion Extrapolation of estimates of survival may be sensitive to choice of functional form. If it is believed, a priori, reasonable to share information regarding the choice of functional form for survival analysis across studies, estimating joint goodness-of-fit information across studies could reduce uncertainty and lead to more reliable estimates of mean survival and cost-effectiveness.