Sequential Design

Experimental studies in the social and behavioral sciences typically follow a fixed experimental [Page 1347]design where the sample size and composition (e.g., experimental group allocation) is determined prior to conducting the experiment. In contrast, sequential experimental designs treat the sample size as a random variable by allowing sequential interim analyses and decision making based on cumulative data and previous design decisions while maintaining appropriate control over experiment-wise errors in decision making (i.e., Type I [α] and Type II [β] error rates). Also referred to as adaptive or flexible designs, current design decisions in sequential designs are sequentially selected according to previous design points. Sequential designs rely on the principal of stochastic curtailment to stop the experiment if the given data at an interim analysis are likely to predict the eventual outcome with a high probability. In contrast to a fixed design where the size and composition of the sample is determined prior to conducting the experiment, the number of observations or participants is not predetermined in a sequential design. Thus, the size and composition of the sample is considered random because of decision dependence on previous observations. However, a finite upper limit is often set in practice.

Sequential designs allow for the early termination of experiments if cumulative evidence suggests a clear effect or lack thereof. The capacity for sequential designs to terminate early can be beneficial from an ethical perspective by preventing unnecessary exposure to unsafe experimental conditions in terms of both length of exposure and the number of participants exposed, as well as unnecessarily withholding administration when the experimental condition is clearly beneficial. Popular in medical trials and drug studies, the early termination of prevention or intervention experiments might lead to minimized exposure to potentially harmful or ineffective treatments. Sequential designs can also be beneficial from a logistical perspective as they can save both time and resources. More generally, sequential designs have the potential to lead to financial savings because of reduced sample sizes. Under the null hypothesis of no effect, sequential designs might be stopped for lack of effectiveness at a total sample size smaller than would be the case with a fixed design. Under the alternative hypothesis of efficacious experimental manipulation, a similar savings is observed in the total sample size required, with the sample size savings typically reported as greater under the alternative hypothesis than under the null hypothesis. Actual sample reductions vary by the type of sequential design and certain design decisions but are generally reported to be as large as 10% under the null hypothesis and as large as 50% under the alternative hypothesis. In research contexts where the participant stream might be small or inaccessible, the potential for such substantial sample size savings when implementing a sequential experimental design might be quite beneficial.

This entry discusses the background and design characteristics, along with the benefits and limitations of sequential design.