Sequential Analysis

Sequential analysis refers to a statistical method in which data are evaluated as they are collected, and further sampling is stopped in accordance with a predefined stopping rule as soon as significant results are observed. This contrasts to classical hypothesis testing where the sample size is fixed in advance. On average, sequential analysis will lead to a smaller average sample size compared with an equivalently powered study with a fixed sample size design and, consequently, lower financial and/or human cost.

Sequential analysis methods were first used in the context of industrial quality control in the late 1920s. The intensive development and application of sequential methods in statistics was due to the work of Abraham Wald around 1945. Essentially, the same approach was independently developed by George Alfred Barnard around the same time.

Interestingly, sequential analysis has not been frequently used in epidemiology despite the attractive feature of allowing the researcher to obtain equal statistical power at a lower cost. In 1962, Lila Elveback predicted a great increase in the application of sequential methods to problems in epidemiology in the coming few years; however, the prediction has not come true. The reluctance to apply sequential methods might be attributed to the fact that making a decision following every observation is complicated. Furthermore, in epidemiological studies, complex associations among outcome variable and predictor variables (rather than simply the primary outcome) are often a major interest and need to be determined in a relatively flexible multivariable modeling framework in light of all available data, while sequential analysis usually requires a well-defined and strictly executed design. Nevertheless, sequential analysis could be appropriately applied to some of the epidemiology research problems where the data are monitored continuously, such as in the delivery of social and health services and disease surveillance.