title: The extension of total gain (TG) statistic in survival models: properties and applications.
abstract: BACKGROUND
  The results of multivariable regression models are usually summarized in the form of parameter estimates for the covariates, goodness-of-fit statistics, and the relevant p-values. These statistics do not inform us about whether covariate information will lead to any substantial improvement in prediction. Predictive ability measures can be used for this purpose since they provide important information about the practical significance of prognostic factors. R (2)-type indices are the most familiar forms of such measures in survival models, but they all have limitations and none is widely used.
  
  
  METHODS
  In this paper, we extend the total gain (TG) measure, proposed for a logistic regression model, to survival models and explore its properties using simulations and real data. TG is based on the binary regression quantile plot, otherwise known as the predictiveness curve. Standardised TG ranges from 0 (no explanatory power) to 1 ('perfect' explanatory power).
  
  
  RESULTS
  The results of our simulations show that unlike many of the other R (2)-type predictive ability measures, TG is independent of random censoring. It increases as the effect of a covariate increases and can be applied to different types of survival models, including models with time-dependent covariate effects. We also apply TG to quantify the predictive ability of multivariable prognostic models developed in several disease areas.
  
  
  CONCLUSIONS
  Overall, TG performs well in our simulation studies and can be recommended as a measure to quantify the predictive ability in survival models.
authors.affiliation: MRC Clinical Trials Unit at UCL, Aviation House, 125 Kingsway, London, WC2B 6NH, UK. b.choodari-oskooei@ucl.ac.uk.
authors.forename: Babak
authors.initials: B
authors.lastname: Choodari-Oskooei
authors.affiliation: MRC Clinical Trials Unit at UCL, Aviation House, 125 Kingsway, London, WC2B 6NH, UK. j.royston@ucl.ac.uk.
authors.forename: Patrick
authors.initials: P
authors.lastname: Royston
authors.affiliation: MRC Clinical Trials Unit at UCL, Aviation House, 125 Kingsway, London, WC2B 6NH, UK. m.parmar@ucl.ac.uk.
authors.forename: Mahesh K B
authors.initials: MK
authors.lastname: Parmar
mesh_terms: D000465:Algorithms; D035843:Biomedical Research / Q000379:methods*; D001699:Biometry / Q000379:methods*; D006801:Humans; D053208:Kaplan-Meier Estimate; D016015:Logistic Models; D015999:Multivariate Analysis; D017063:Outcome Assessment, Health Care / Q000379:methods / Q000706:statistics & numerical data; D011379:Prognosis; D016016:Proportional Hazards Models; D016019:Survival Analysis