sequential testing multinomial distributiuon

In fact, in real life, we are interested in assessing the concurrent effect of several predictor factors (both continuous and categorical) on a single dichotomous outcome. Similarly, we may wish to know whether the age of patients, a continuous variable, was different in the two treatment arms and whether this difference could have influenced the association between treatment and mortality. Therefore, it would be inappropriate for us to look at the effect of ligation versus sclerotherapy without accounting for beta-blocker administration. From this analysis, it is obvious that ligation increased the risk of death among those receiving beta-blockers but reduced this risk among those not receiving beta-blockers. However, often, we are interested in finding out whether there is any confounding between various predictors, for example, did equal proportion of patients in ligation and sclerotherapy arms receive beta-blockers? This can be done by stratifying the data and making separate tables for two levels of the likely confounder, for example, beta-blocker and no beta-blocker. Each of these analyses assesses the association of the dichotomous outcome variable - death - with one predictor factor these are known as univariate analyses and give us unadjusted ORs. Similarly, we can determine the association of death with other predictors, such as gender, age, and presence of other illnesses. Let us look at the effect of beta-blocker therapy on death by constructing a 2 × 2 table this reveals an OR for death in the “no beta-blocker” arm of 4.1 as compared to the “beta-blocker” arm. These could include age, gender, concurrent beta-blocker therapy, and presence of other illnesses, among others. We, however, know that factors other than the choice of treatment may also influence the risk of death. This means that a person receiving sclerotherapy is nearly twice as likely to die than a patient receiving ligation (please note that these are odds and not actual risks – for more on this, please refer to our article on odds and risk).

A simple (univariate) analysis reveals odds ratio (OR) for death in the sclerotherapy arm of 2.05, as compared to the ligation arm. Let us consider the example of a hypothetical study to compare two treatments, variceal ligation and sclerotherapy, in patients with esophageal varices. In this article, we look at logistic regression, which examines the relationship of a binary (or dichotomous) outcome (e.g., alive/dead, success/failure, yes/no) with one or more predictors which may be either categorical or continuous.

In a previous article in this series, we discussed linear regression analysis which estimates the relationship of an outcome (dependent) variable on a continuous scale with continuous predictor (independent) variables.

Sequential testing multinomial distributiuon