Analyzing the temporal association between health disorders and medical treatments using probability models and Monte Carlo simulation

Statistical analysis is often used in medical studies to provide evidence for an association between a treatment and a patient condition. The work in this paper is motivated by a recent medical study which analyzes the temporal association between a treatment (i.e., an implant procedure) and the rare autoimmune disorders, polymyositis and dermatomyositis (PM/DM). To address this association mathematically, this paper develops a probability model based on the multinomial distribution that can be used to make statistical inferences about the timing of incidences of a treatment/condition pair. This paper details an empirical study of this model using Monte Carlo simulation. It also describes some analytical results developed in subsequent research efforts. Data from the medical study illustrate the application of this model and its results.