Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Using a linear regression modelUsing data from the hypothetical trial in Table 1, a linear regression model canbe applied to illustrate how to evaluate the interaction effect in a trial where theprimary endpoint is a continuous variable. In this example, Y represents thechange in SBP for each patient, X 1represents the treatment variable (X 1= 0 forplacebo, and X 1= 1 for active drug treatment) and X 2represents the smokingstatus variable (X 2= 0 for a nonsmoker, and X 2= 1 for a smoker). A linearregression model that predicts Y based on X 1and X 2can then be expressed as:Y = α + βX 1+ γX 2+ ε (1)Where α is a constant, β and γ represent the effects of the treatment (X 1) andsmoking status (X 2) on SBP (Y), respectively, and ε is a random error. The abovemodel (1) assumes that the effects of X 1and X 2are additive and are independentof each other, and so it is often called the main effect model.The interaction between treatment and smoking status can now be investigated byadding another term into the linear regression model (1):Y = α + βX 1+ γX 2+ δ(X 1X 2) + ε (2)This means that, in addition to the main effect of treatment (X 1) and smokingstatus (X 2), there is an interaction effect (δ) between treatment and smokingstatus (X 1X 2). The value of X 1X 2is 1 for a patient who is a smoker on activetreatment, and 0 otherwise. The model implies that the change in SBP differsaccording to different combinations of treatment and smoking status. In otherwords, the treatment effect differs by the smoking status. If δ is found to bestatistically significantly different from 0 then there is evidence of an interactionbetween treatment and smoking status, suggesting that the effect of the treatmentdepends on the smoking status of patients.Example 1 (continued)Table 2 presents the results from fitting the two regression models described inequations (1) and (2), using the data in Example 1. The main effect model showsthat the difference in mean SBP reduction is statistically significantly different,not only between the antihypertensive drug and placebo groups, but also betweensmokers and nonsmokers. However, whether the drug works differently forsmokers and nonsmokers is uncertain. To address this uncertainty, the interactionterm is introduced.309