Exploration Of Heterogeneous Treatment Effects With Multivariate Failure Time Data Under Frailty Model

Recently,the concept of precision medicine is deep-rooted and popular,as well as has been widely discussed and studied by many researchers.Understanding heterogeneity between subpopulations is one of crucial parts to develop precision medicine.It's worth noting that heterogeneity may be altered over time and event.For example,some patients may get worse or even deteriorate into another disease over a period of time.Hence,it's important to analyze the relevant time-to-event data.We focus on general frailty survival model with heterogeneity,and aim to identify subgroup structure without information about them in advance,and estimate the parameters of interest.There are two main ingredients to be presented in our work.On the one hand,we present profile and non-profile Minorization-Maximization(MM)algorithms to separate the objective high-dimensional function into a sum of lowdimensional functions so as to simplify computation.Another,we apply a pairwise fusion approach to subgroup analysis based on the proposed MM algorithms together with Alternating Direction Method of Multipliers(ADMM)algorithm which can identify the number of subgroups and estimate all interested parameters automatically and simultaneously.Meanwhile,we prove the convergence properties of the MM algorithm and ADMM algorithm.Simulations illustrate that the proposed approaches perform well on heterogeneity between subgroups.Then the methods are applied to analyze the Alzheimer Disease Neuroimaging Initiative ADNI data.