Multi-state models for colon cancer recurrence and death with a cured fraction

Abstract

In cancer clinical trials, patients often experience a recurrence of disease prior to the outcome of interest, overall survival. Additionally, for many cancers, there is a cured fraction of the population who will never experience a recurrence. There is often interest in how different covariates affect the probability of being cured of disease and the time to recurrence, time to death, and time to death after recurrence. We propose a multi-state Markov model with an incorporated cured fraction to jointly model recurrence and death in colon cancer. A Bayesian estimation strategy is used to obtain parameter estimates. The model can be used to assess how individual covariates affect the probability of being cured and each of the transition rates. Checks for the adequacy of the model fit and for the functional forms of covariates are explored. The methods are applied to data from 12 randomized trials in colon cancer, where we show common effects of specific covariates across the trials.

Keywords: Cox-Snell residuals; colon cancer; cure model; deviance residuals; multi-state model.

Figure 1

Multi-state cure model structure: dashed lines represent effect of treatment, solid lines represent transitions between states.

Figure 2

Cox-Snell residual plots for time to death. Results from 12 trials.

Figure 3

Comparison of estimates to recurrence only model. Results from 12 trials. The lower line for each trial is the posterior mean and 95% credible interval for the coefficient from the full multistate cure model. The upper line is the posterior mean and 95% credible interval for the coefficient from the cure model that does not incorporate death times.