13. Randomized Controlled Experiments

In many cases, the presence of confounding factors makes the identification of causal effects rather difficult. One solution to avoid potential bias is to run a randomized controlled experiment, either in the form of a clinical trial or a field experiment (Sect. 13.1). The basic tenet is to assign the subjects to a control group and a treatment group, such that they share similar characteristics on average (Sect. 13.2). The impact of an intervention is then obtained by comparing the average outcomes observed in both groups and testing whether the difference is significant (Sect. 13.3). An important issue is to assess the risks of type I and type II errors, i.e. the probabilities that the statistical test yields the wrong conclusion (Sect. 13.4). Controlling for those risks implies finding the minimum number of subjects to enroll in the experiment to achieve a given statistical power (Sect. 13.5). Another issue is to select an indicator (e.g., absolute risk reduction, relative risk ratio, odds ratio, number needed to treat) in order to point out the number of successes and failures in each group (Sect. 13.6). The analysis can also be extended to a more general framework were the timing of event occurrence is explicitly accounted for, via the estimation of survival curves with the Kaplan-Meier approach (Sect. 13.7) and the implementation of the Mantel-Haenszel test (Sect. 13.8).