A Flexible Bayesian Parametric Proportional Hazard Model: Simulation and Applications to Right-Censored Healthcare Data

Abstract

Survival analysis is a collection of statistical techniques which examine the time it takes for an event to occur, and it is one of the most important fields in biomedical sciences and other variety of scientific disciplines. Furthermore, the computational rapid advancements in recent decades have advocated the application of Bayesian techniques in this field, giving a powerful and flexible alternative to the classical inference. The aim of this study is to consider the Bayesian inference for the generalized log-logistic proportional hazard model with applications to right-censored healthcare data sets. We assume an independent gamma prior for the baseline hazard parameters and a normal prior is placed on the regression coefficients. We then obtain the exact form of the joint posterior distribution of the regression coefficients and distributional parameters. The Bayesian estimates of the parameters of the proposed model are obtained using the Markov chain Monte Carlo (McMC) simulation technique. All computations are performed in Bayesian analysis using Gibbs sampling (BUGS) syntax that can be run with Just Another Gibbs Sampling (JAGS) from the R software. A detailed simulation study was used to assess the performance of the proposed parametric proportional hazard model. Two real-survival data problems in the healthcare are analyzed for illustration of the proposed model and for model comparison. Furthermore, the convergence diagnostic tests are presented and analyzed. Finally, our research found that the proposed parametric proportional hazard model performs well and could be beneficial in analyzing various types of survival data.

Figure 1

Visual representation for the different hazard rate shapes of the GLL distribution with different values of the parameters.

Figure 2

Gelman diagnostics from a GLL PH framework with distributional parameters (α=1.5, k=0.75, and η=1.25), covariates β=(0.75, −0.75, 0.5), and n=300 and censoring proportion for 20 percentage.

Figure 3

Trace plots from a GLL PH framework with distributional parameters (α=1.5, k=0.75, and η=1.25), covariates β=(0.75, −0.75, 0.5), and n=300 and censoring proportion for 20 percentage.

Figure 4

Kernel density plots from a GLL PH framework with distributional parameters (α=1.5, k=0.75, and η=1.25) and covariates β=(0.75, −0.75, 0.5), and  n=300 and censoring proportion for 20 percentage.

Figure 5

Autocorrelation plots from a GLL PH framework with distributional parameters (α=1.5, k=0.75, and η=1.25), covariates β=(0.75, −0.75, 0.5), and n=300 and censoring proportion for 20 percentage.

Figure 6

TTT plot, box plot, and the histogram for the survival times of the lung cancer data sets.

Figure 7

The standardized Schoenfeld residuals from the data I—lung cancer data set, taking the test p value for each covariate into account.

Figure 8

Density plots for regression coefficients and distributional parameters from the Veterans lung cancer data set.

Figure 9

The time series plots for the baseline hazard parameters and the regression coefficients for the Veterans lung cancer data.

Figure 10

PSRF of the baseline hazard parameters and the regression coefficients for the Veterans lung cancer data.

Figure 11

The running mean plots for the baseline distributional parameters and regression coefficients for the Veterans lung cancer data set.

Figure 12

Autocorrelation plots for all the baseline distributional parameters and regression coefficients for the Veterans lung cancer data set.

Figure 13

TTT plot, box plot, and the histogram for the survival times of the larynx cancer data set.

Figure 14

The standardized Schoenfeld residuals from the data |—larynx cancer data set, taking the test p value for each covariate into account.

Figure 15

Density plots for the baseline hazard parameters and the regression coefficients for the larynx cancer data.

Figure 16

The time series plots for baseline hazard parameters and the regression coefficients for the larynx cancer.

Figure 17

The Ergodic mean plots for the baseline hazard parameters and regression coefficients for the larynx cancer data.

Figure 18

Autocorrelation plots for all the baseline hazard parameters and regression coefficients for the larynx cancer data.

Figure 19

PSRF of the baseline hazard parameters and the regression coefficients for the larynx cancer data.