Spending Alpha: What Does This Mean For Clinical Studies and Their Statistical Analysis Plans?

 In the context of statistical hypothesis testing, "spending alpha" refers to the risk of making a Type I error, which is the probability of incorrectly rejecting a true null hypothesis. In other words, it's the risk of claiming an effect or association exists when, in reality, it does not. The concept of spending alpha becomes relevant when multiple hypothesis tests are conducted simultaneously, such as when analyzing multiple outcomes in a clinical study.

In this article, I discuss how primary, secondary, and exploratory outcomes differ with respect to spending alpha:

1. Primary Outcomes and Alpha Spending:

Primary outcomes are the main focus of a clinical study, and they are directly tied to the primary research question. The significance level or alpha (often denoted as α) is typically set for the primary outcome before the study begins. The most common value for alpha is 0.05, which means that the researchers are willing to accept a 5% chance of making a Type I error.

When conducting hypothesis tests for the primary outcome, the alpha level is allocated or "spent" for these tests. In the context of spending alpha, the primary outcome results should be interpreted with the pre-defined alpha level in mind. If the p-value (probability value) associated with the primary outcome is less than or equal to the pre-specified alpha, the researchers may reject the null hypothesis and conclude that there is a statistically significant effect for the primary outcome.

2. Secondary Outcomes and Alpha Spending:

For secondary outcomes, the alpha level that was initially set for the primary outcome is usually adjusted to control the overall Type I error rate when conducting multiple hypothesis tests. Since multiple testing increases the risk of obtaining false positive results by chance, adjustments are made to ensure that the overall alpha is appropriately maintained.

One common approach to alpha spending for secondary outcomes is the Bonferroni correction, where the significance level for each secondary outcome is divided by the number of secondary tests conducted. For example, if the Bonferroni correction is applied to a study with 3 secondary outcomes and α=0.05, then the adjusted significance level for each secondary outcome becomes α/3 ≈ 0.017 (approximately). This correction reduces the risk of Type I errors but can increase the risk of Type II errors (false negatives).

3. Exploratory Outcomes and Alpha Spending:

Since exploratory outcomes are not pre-specified and are analyzed after the study is completed, they are particularly susceptible to alpha spending issues. Analyzing multiple exploratory outcomes without proper correction can significantly increase the risk of obtaining false positive results. It is not uncommon to not spend any alpha on exploratory outcome measurements but rather simply use these exploratory measurements to qualitatively look for trends or gather information for future hypotheses to test.

Due to the more hypothesis-generating nature of exploratory outcomes, it is crucial to interpret their results with caution. The focus should be on generating new research hypotheses rather than drawing definitive conclusions. If exploratory findings warrant further investigation, they should be validated through additional studies.

In clinical studies, spending alpha is a crucial consideration when conducting multiple hypothesis tests for primary, secondary, and exploratory outcomes. Proper alpha spending strategies, such as Bonferroni corrections, help control the overall Type I error rate and ensure the reliability of research findings. Primary outcomes receive the most stringent alpha allocation, while secondary outcomes undergo adjustments to maintain the overall statistical integrity of the study. Exploratory outcomes require careful interpretation and should be used to generate new hypotheses for future research.