APPLICATION OF BIVARIATE CONDITIONAL INVERSE-GAUSSIAN DISTRIBUTION TO CANCER SURVIVAL ANALYSIS

Abstract

This investigation explores the application of the Bivariate Inverse-Gaussian Distribution (BCIGD) to model the time to relapse (TR) and time to death (TD) with sequential medical events. A moderate negative linear correlation between TR and TD was pragmatic in the scatter plot. Thus, the inverse relationship suggests that patients with a longer TR tend to have shorter TD and vice versa. The histogram plot showed that TR has a bimodal distribution with two peaks; while TD has a multimodal distribution. The Kolmogorov-Smirnov tests suggested that both TR and TD data follow a normal dis-tribution for p-values greater than a significance level of 0.05. The prominent peak of the contour plot indicates the region of highest probability density for TR and TD is centred on 0.5. The rapid decay of density values beyond 1.5 for TR and TD aligns with the inverse-Gaussian distribution’s tendency to concentrate values near the mean with a strident drop-off as values diverge from this central region. These findings support the use of the inverse-Gaussian distribution in this area and highlight the potential of numerical integration to understand probability density behaviour in survival analysis and medi-cal event modelling.