Implementation of Bayesian Mixture Models in identifying subpopulation of breast cancer patients based on blood test measurements

Abstract

Abstract A complete blood test is one of a series of initial examinations of cancer patients that is relatively easy. The use of blood measurement components in analysing patient conditions is commonly used. However, it is not the case for the ratio and inter-ratio components of blood measurements, and this is what is proposed in this study. The built hypothesis is that the ratio and inter-ratio components of blood tests that can explain the condition of cancer patients are better than the blood test’s own components. An analysis will also be conducted to develop a patient profile based on these measurements, and those that can clearly distinguish between patient groups will be identified. The Finite Mixture Model is a method for modelling heterogeneous data that may originate from different subpopulations, where subpopulations represent groups of patients based on a particular latent condition. This model takes the form of a superposition of several distributions, which in this study, a Gaussian distribution is used. The parameter estimation used in the Bayesian method, which determines the prior distribution of the model parameters, and it is combined with the likelihood which will produce a posterior distribution. Then, the Markov Chain Monte Carlo-Gibbs Sampler is used to draw samples on the parameters of the posterior distribution. By using the breast cancer patient blood test data from the Oncology Department of a hospital in Jakarta, with 100,000 iterations as burn-in, and 200,000 iterations for sampling, based on Deviance Information Criterion values, the optimal grouping is two subpopulations using blood ratio and inter-ratio measurements. Two subpopulations were identified, with the first population is characterized by low distribution value and the second subpopulation with the opposite characteristics. The explanatory factors of ratio data are ratio neutrophils to lymphocytes, ratio platelets to lymphocytes, and ratio lymphocytes to monocytes.