at the data must be determined before the data is collected, and that the looks at the data should be equally spaced (e.g., after 50, 100, 150, and 200 patients). The alpha spending function approach developed by Demets & Lan does not have these restrictions, and depending on the parameters chosen for the spending function, can be very similar to Pocock boundaries or the corrections proposed by O'Brien and Fleming. Applications of sequential analysis Clinical trials In a randomized trial with two treatment groups, group sequential testing may for example be conducted in the following manner: After n subjects in each group are available an interim analysis is conducted. A statistical test is performed to compare the two groups and if the null hypothesis is rejected the trial is terminated; otherwise, the trial continues, another n subjects per group are recruited, and the statistical test is performed again, including all subjects. If the null is rejected, the trial is terminated, and otherwise it continues with periodic evaluations until a maximum number of interim analyses have been performed, at which point the last statistical test is conducted and the trial is discontinued. Other applications Sequential analysis also has a connection to the problem of gambler's ruin that has been studied by, among others, Huygens in 1657. Step detection is the process of finding abrupt changes in the mean level of a time series or signal. It is usually considered as a special kind of statistical method known as change point detection. Often, the step is small and the time series is corrupted by some kind of noise, and this makes the problem challenging because the step may be hidden by the noise. Therefore, statistical and/or signal processing algorithms are often required. When the algorithms are run online as the data is coming in, especially with the aim of producing an alert, this is an application of sequential analysis. Bias Trials that are terminated early because they reject the null hypothesis typically overestimate the true effect size. This is because in small samples, only large effect size estimates will lead to a significant effect, and the subsequent termination of a trial. Methods to correct effect size estimates in single trials have been proposed. Note that this bias is mainly problematic when interpreting single studies. In meta-analyses, overestimated effect sizes due to early stopping are balanced by underestimation in trials that stop late,