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Joint modeling of progression‐free and overall survival and computation of correlation measures
Author(s) -
Meller Matthias,
Beyersmann Jan,
Rufibach Kaspar
Publication year - 2019
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8295
Subject(s) - joint probability distribution , statistical inference , nonparametric statistics , inference , econometrics , computer science , statistics , random effects model , statistical model , parametric statistics , mathematics , artificial intelligence , medicine , meta analysis
In this paper, we derive the joint distribution of progression‐free and overall survival as a function of transition probabilities in a multistate model. No assumptions on copulae or latent event times are needed and the model is allowed to be non‐Markov. From the joint distribution, statistics of interest can then be computed. As an example, we provide closed formulas and statistical inference for Pearson's correlation coefficient between progression‐free and overall survival in a parametric framework. The example is inspired by recent approaches to quantify the dependence between progression‐free survival, a common primary outcome in Phase 3 trials in oncology and overall survival. We complement these approaches by providing methods of statistical inference while at the same time working within a much more parsimonious modeling framework. Our approach is completely general and can be applied to other measures of dependence. We also discuss extensions to nonparametric inference. Our analytical results are illustrated using a large randomized clinical trial in breast cancer.