Statistical issues in survival analysis (Lindley frailty model)
March 26, 2025 Their primary goal of their paper was to introduce a novel frailty model based on the weighted Lindley (WL) distribution for modeling clustered survival data. They used the weighted Lindley as the frailty distribution. This was a two parameter distribution where the main statistic is always on the positive real line. This distribution allowed lot of flexibility more so than other distributions. It is useful for modeling right-skewed data and bathtub hazard shaped data as well as bimodal data, which lot of other typical frailty distributions cannot handle. The WL distribution can be denoted as a mixture of two gamma distributions with weights. They also showed a version where the mean is fixed at 1 as typically done for the frailty distribution in analyses. They used Laplace transforms for which they had closed form solutions for the derivatives. They also wrote out the univariate and the shared frailty, to allow for clustering, versions of the WL frailty model. They used Kendall’s tau to calculate the product of difference between survival times to calculate that correlation. An alternative transform was based on the Laplace transform of the frailty distribution. They found for a fixed variance for the frailty, the WL provides a greater Kendall’s tau as compared to the gamma or inverse Gaussian