Challenge of multiple co‐primary endpoints: a new approach

Abstract

There are many disorders where regulatory agencies have required a new treatment to demonstrate efficacy on multiple co-primary endpoints, all significant at the one-sided 2.5 per cent level, before accepting the treatment's effect for the disorder. This requirement, rooted in the intersection-union (IU) test, has led many researchers to increase the study sample size to make up for the reduction in the statistical power at the study level. Unfortunately, the increase in sample size could be substantial when the endpoints are minimally correlated and the treatment effects on the multiple endpoints are comparable. In this paper, we demonstrate that the frequentist concept of controlling the maximum false positive rate, even when applied to a restricted null space, has only limited success in keeping the sample size increase at a reasonable level. We therefore propose an approach that is based on the notion of controlling an average type I error rate. By employing an upper bound for the average type I error rate, the new approach provides an adjustment to the significance level that depends only on the correlation among the endpoints. For the most common case of two or three co-primary endpoints, the adjusted significance level is at most 5 per cent (one-sided) when the endpoints are moderately correlated. We show how sample size could be calculated under the proposed approach and contrast the needed sample size with that required under the IU test. We provide additional comments and discuss why the new approach is consistent with the principle requiring evidence of significance in the drug development and approval process.

Considerations for Endpoint Selection When Designing HIV Clinical Trials

“…& Important components of a composite endpoint may potentially have different or even opposite treatment effects, and it may be desirable to evaluate these separately [30]. In this case a study could be designed with co-primary endpoints, powered to investigate each endpoint separately, and with adjustment for multiple comparisons [40,41]. & The full scope of the treatment impact may be unknown and extend beyond the traditionally reported outcomes (for example, AIDS).…”

A critical assessment of composite and coprimary endpoints: A complex problem

“…While the requirement that all endpoints be positive in order to establish efficacy means that there is no need to adjust the individual alpha significance levels downwards, adjusting significance levels upwards is also considered statistically unacceptable. 4 However, requiring statistical significance in each endpoint, while attractive from a drug safety and efficacy standpoint, can result in an increased type II error (false-negative) rates, because each test carries a probability of type II error and these are combined when there are multiple endpoints (Fig 1). 8 Depending on the number of endpoints and the expected effects on each endpoint, the study power may be decreased, and the study may therefore require a significant and potentially unrealistic increase in sample size to detect a meaningful treatment difference.…”

“…If a disease has multiple manifestations without a consensus on the most important clinical efficacy endpoint, the disease etiology is unknown, or the treatment approach is multifaceted, it may not be possible to choose a single primary endpoint. 3,4 True single primary endpoints may be difficult to find. 5 Psoriasis is an example of a disease without a clear single primary endpoint; to date, there is no consensus on how body surface area involvement, plaque appearance, and quality of life should be integrated in making a clinical assessment.…”

“…This problem has been termed ''reverse multiplicity'' to distinguish it from the multiplicity problem discussed above in regards to the single-sufficient coprimary endpoint, and several statistical solutions in this evolving area have recently been proposed. 4,7 For example, one proposed solution is to adjust significance levels as a function of the number of coprimary endpoints and the correlation between endpoints. Statisticians have An ''event'' is defined as the first occurrence following an intervention of one of several predesignated outcomes Example: Following interferon treatment for melanoma, ''disease-free survival'' is defined as the time from treatment to any of the following outcomes: d Melanoma recurrence d Diagnosis of a second primary melanoma d Any-cause mortality Scale/index Clinical signs and symptoms are synthesized into a single outcome measure.…”

“…Example: Psoriasis Area and Severity Index (PASI) is defined as a composite score for each patient based on erythema, induration, and scale, weighted by body surface area involvement proposed that the drug label specify the statistical method used to analyze the data. 4 Given the problematic coprimary endpoint, the 2005 recommendations of the Multiple Endpoints Expert Team suggest either trying to identify a single primary endpoint or developing a composite endpoint. 7 Although the term ''composite (or compound) endpoint'' has been used to refer to multiple variables that when combined forms the single primary endpoint of a trial, going forward the term should optimally be reserved for the specific circumstance in which multiple outcomes are synthesized to make a single assessment of each patient.…”