Semiparametric Bayesian survival analysis using models with log-linear median

Abstract

We present a novel semiparametric survival model with a log-linear median regression function. As a useful alternative to existing semiparametric models, our large model class has many important practical advantages, including interpretation of the regression parameters via the median and the ability to address heteroscedasticity. We demonstrate that our modeling technique facilitates the ease of prior elicitation and computation for both parametric and semiparametric Bayesian analysis of survival data. We illustrate the advantages of our modeling, as well as model diagnostics, via a reanalysis of a small-cell lung cancer study. Results of our simulation study provide further support for our model in practice.

Figure 1

Plots of residuals versus the age at entry (in years) and versus the estimated median survival time (in months) using parametric TBS model for the lung cancer data.

Figure 2

Q-Q plots of the residuals under parametric TBS model for the lung cancer data

Figure 3

Plots of observed survival times versus Age (z₂) with three estimated quartile functions for two treatment arms. (Solid lines: estimated via TBS model; Dotted straight lines: estimated via Portnoy’s method; △: censored observation)

Figure 4

Plot of the log-ratio of two CPOs obtained from semiparametric TBS and Gaussian TBS model (y-axis), versus Age (x-axis): ○ uncensored from treatment A; △ censored from treatment A; ● uncensored from treatment B; ▲ censored from treatment B)