Clinical Trials

❘❙❚■ Chapter 24 | Regression AnalysisIntroductionThe purpose of a clinical trial analysis is to obtain an accurate estimate of anytreatment effect. This is often measured as the difference between treatmentgroups in the primary outcome, based on the assumption of perfect balanceamong baseline characteristics. If important imbalances are found among somevariables, covariate (or a variable related to the outcome) adjustment analysis issometimes employed to estimate adjusted treatment effects with an aim to takeimbalances into account. Furthermore, we might want to assess the associationsbetween patient characteristics measured at baseline (before randomization) andthe primary outcome measured during the follow-up. By doing this, we canidentify factors that have increased or decreased the likelihood of events occurring.These tasks can often be achieved with multiple regression methods.In statistical terminology, the outcome variable in regression analysis is oftencalled the dependent or response variable, and the baseline characteristics of patientsare referred to as independent, explanatory, or predictor variables or covariates.The most simple form of regression analysis, looking at the relationship betweenone outcome variable and only one predictor variable, is called a univariateanalysis (or more accurately bivariate analysis).Suppose that we are interested in estimating the effect of smoking behavior(the predictor) on the occurrence of death among patients with heart failure.We know that, in reality, a number of other variables are potential predictors ofdeath. Even if we are interested only in the effect of smoking behavior, we needto control for the effects of variables such as age, gender, body mass index, cardiacfunction, systolic blood pressure (SBP), and history of previous heart failure orheart attacks. These variables are associated not only with the risk of death,but also with smoking behavior.In order to assess the contribution of smoking status to risk of death, we couldsimply do a univariate analysis and look at the rates of death in smokers andnonsmokers. This would be crude and would not allow us to determine what theexact contribution of smoking was. To answer this more complex question we mustcompare like with like, ie, control for differences in the characteristics of smokersand nonsmokers that might be related to death. For example, if death rates arehigher among obese patients and this group also has a higher proportion ofsmokers than other groups, a simple comparison of smokers and nonsmokersacross all weight groups would distort the true effect of smoking.One approach to the problem would be to split the sample into different weightgroups (eg, lean, normal, obese) and to compare smokers and nonsmokers274