Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘within each. In practice, however, there will be many control variables andrepeatedly splitting the sample can lead to a large number of small subgroups.A more efficient method is to perform a multivariate (multiple) regressionanalysis. This assesses the effect of smoking status on the risk of death, whilesimultaneously taking into account the influence of the other variables chosen tobe in the analysis.Classification of regression methodsRegression methods can be classified according to the measurement of the responsevariable. While several methods exist, the three usual methods used are as follows:• If the response is continuous (eg, blood pressure, or total cholesterol level)then linear regression can be used.• If the response is binary (eg, whether or not an individual has beendiagnosed with lung cancer) then logistic regression is applied.• If the response is time to the occurrence of an event (eg, the timefrom randomization to patient death in a cancer trial) then hazardsregression is an appropriate method.All regression models can handle both continuous and categoricalpredictor variables.Multiple linear regressionThe first step of any regression analysis is to examine the distribution of eachvariable and the bivariate distributions of each pair of variables, particularly theresponse (or outcome) variable paired with each of the predictors. If the responseis a continuous variable with a symmetrical (normal) distribution, multiple linearregression can be used. However, a response with a skewed distribution might firstneed to be transformed. For example, a log transformation can remove a positiveskew. Scatterplots of the response variable versus continuous predictors should beinspected to check that the relationship is linear; a non-linear relationship can behandled by fitting a curve rather than a line, or by categorizing the predictor.Graphical checks of the data can also reveal unusual observations or outliers,which should be investigated further before being retained in the analysis.Let y idenote the value of individual i on the continuous outcome variable, wherei indexes the individuals in the sample (i = 1, 2, …, n). Suppose that there arep predictor variables, which we denote by x 1, x 2, …, x p(they can be continuous,275