Case-base sampling for fitting and validating prognostic models - PowerPoint PPT Presentation

Case-base sampling for fitting and validating prognostic models Workshop on Statistical Issues in Biomarker and Drug Co-development Fields Institute, Toronto Olli Saarela Dalla Lana School of Public Health, University of Toronto November 8, 2014 Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 1 / 23

Outline Outline Case-base sampling 1 Application: estimation of ROC/AUC from time-to-event data 2 Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 2 / 23

Case-base sampling Motivation: Cox regression and absolute risk Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 3 / 23

Case-base sampling Motivation: Cox regression and absolute risk Time matching/risk set sampling (including Cox partial likelihood) eliminates the baseline hazard from the likelihood expression for the hazard ratios. Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 3 / 23

Case-base sampling Motivation: Cox regression and absolute risk Time matching/risk set sampling (including Cox partial likelihood) eliminates the baseline hazard from the likelihood expression for the hazard ratios. If, however, the absolute risks are of interest, they have to be recovered using the semi-parametric Breslow estimator. Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 3 / 23

Case-base sampling Motivation: Cox regression and absolute risk Time matching/risk set sampling (including Cox partial likelihood) eliminates the baseline hazard from the likelihood expression for the hazard ratios. If, however, the absolute risks are of interest, they have to be recovered using the semi-parametric Breslow estimator. Alternative approaches for fitting flexible hazard models for estimating absolute risks, not requiring this two-step approach? Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 3 / 23

Case-base sampling Motivation: Cox regression and absolute risk Time matching/risk set sampling (including Cox partial likelihood) eliminates the baseline hazard from the likelihood expression for the hazard ratios. If, however, the absolute risks are of interest, they have to be recovered using the semi-parametric Breslow estimator. Alternative approaches for fitting flexible hazard models for estimating absolute risks, not requiring this two-step approach? There is; it originates from Mantel (1973) and Hanley & Miettinen (2009). Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 3 / 23

Case-base sampling An alternative framework for survival analysis Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 4 / 23

Case-base sampling An alternative framework for survival analysis Case-base sampling combined with logistic/multinomial regression provides an alternative to risk set sampling -based semi-parametric survival analysis methods. Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 4 / 23

Case-base sampling An alternative framework for survival analysis Case-base sampling combined with logistic/multinomial regression provides an alternative to risk set sampling -based semi-parametric survival analysis methods. This enables easy fitting of smooth-in-time and non-proportional hazard models with multiple time scales . Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 4 / 23

Case-base sampling An alternative framework for survival analysis Case-base sampling combined with logistic/multinomial regression provides an alternative to risk set sampling -based semi-parametric survival analysis methods. This enables easy fitting of smooth-in-time and non-proportional hazard models with multiple time scales . Provides an alternative to Kaplan-Meier-based methods for estimating discrimination statistics (e.g. ROC, AUC, risk reclassification probabilities) from censored survival data . Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 4 / 23

Case-base sampling Study base 6000 5000 4000 Population 3000 2000 1000 0 0 2 4 6 8 10 Follow−up years Population−time (55243 PY in total) Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 5 / 23

Case-base sampling Case series 6000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 5000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 4000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Population ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 2000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 ● ● ● ● ● 0 2 4 6 8 10 Follow−up years ● Incident CVD event (493 in total) Olli Saarela (University of Toronto) Case-base sampling for prognostic modeling Nov 8, 2014 6 / 23