A statistical analysis of the effect of a covariate profile on a binary outcome

Abstract

Case control studies are widely used in medicine to analyze the association between the disease status and exposure profile of a group of subjects. It is a “retrospective” study because the Outcome or disease status of a subject is first observed then those subjects are followed “backwards” and the exposure observations are obtained. Case control studies are widely used and are popular in the medical discipline especially in dealing with rare diseases because it saves a lot of time and cost as compared to “prospective” studies where subjects are followed up over time and their disease status is noted. Case control studies usually involve longitudinal observations measured over time for a subject. Usually, the most recent observations are used to estimate the current disease risk of a subject. It is of interest to study whether the past exposure history or a cumulative measure based on the past exposure of a subject would be more useful in predict ing the current disease status of a subject. In this project we try to study the effect of prior exposure data on the current disease status. We begin our analysis by doing a simple linear regression analysis using averages as a summary measure of the expo sure profile and see if it helps in explaining the current disease status. We then take each subject’sprofile into account to develop regression models explaining disease status. Based on the inferences from the visual inspection of scatter plots, we also develop random intercept model and random slope and intercept model dataset. We end our analysis by fitting a longitudinal model predicting the disease status based on the subject’s integrated exposure profile. Based on our study, it can be concluded that longitudinal profile data contains more information about the disease status than only the last observation data and that a better predictive model for disease status can be developed based on past exposure data.