Pooling the study center for statistical analysis purpose is rather an old issue. However, we can still see the discussion o f study center pooling strategy or algorithm in the study protocol or the statistical analysis for multi-center clinical trials. When a clinical trial has multiple centers, study center or investigator site is usually included in the statistical analysis either by including as an exploratory variable in the model (for example ANOVA or ANCOVA) or by conducting the categorical analysis adjusted by study center (for example, Mantel-Haenszel test, Elteren's test, Wilcoxon rank sum test stratified by pooled center). However, there could be situation that some study centers have very few subjects and can not be directly included as a stand alone center for the analysis. In this situation, a pooling strategy is often employed to combine the small centers together. The reason for pooling the small centers instead of using center as random effect may be due to the factor that centers in the clinical trial are rarely a random sample of all possible centers. It is not uncommon to find the statistical analysis including pooled center in regulatory submission or in publications, for example, in NDA for Refludan (the analysis was stratified by pooled center) and in FDA advisory committee documents (… were analyzed using Wilcoxon rank sum test stratified by pooled center (centers that entered fewer subjects than a complete block were pooled by country)). Here are some of the example languages describing such pooling strategies:
“Statistical tests will be performed as two-sided tests and will be adjusted to the multi-centric design of the study. A center must have enrolled at least 8 subjects to be a standalone center in the analysis (centers enrolling less than 8 subjects will be pooled – will be done before the study unblinding”
“Study centers were pooled from largest to smallest until the pooled center had more than 5 subjects with post baseline data in each treatment group. No pooled center had more than 15% of the total number of subjects”
“The majority of study centers were small. A small center was defined as any center with <5 patients with postbaseline data in any treatment group, resulting in 5 large and 25 small centers. To avoid loss of information, small centers were pooled from largest to smallest until the pooled center had 5 patients in each treatment group. These centers were grouped into 11 pooled centers for the purpose of analysis."
In one of hypertension clinical trials, the pooling strategy is described as “To avoid loss of information, small centers (<5 per protocol patients) were pooled from largest to smallest until the pooled center had 5 per protocol patients in each treatment group. These centers were grouped into 19 pooled centers for the purpose of analysis. The pooling algorithm was predetermined before unblinding the data, and the pooling algorithm was described in the statistical analysis plan for the study. Considering the subjective nature of the pooling algorithm, albeit prespecified before completion of the study, an exploratory analysis was also performed with actual center as a fixed effect in contrast to pooled centers. This analysis did not change the inference.”
In a type 2 diabetes trial, a different pooling strategy was used “For all center stratified analyses, centers with <24 randomized and treated subjects were pooled on a geographical basis, independently of treatment identification.”
In a recent brief book for PDAC, the sponsor provided the detail pooling strategy for centers “Pooling algorithm for centers: For non-US sites, all investigative sites within a country with fewer than 10 randomized subjects will be combined into a single pooled site for analysis purposes. If a resulting pooled site still has fewer than 10 randomized subjects, then this pooled site will be further combined with the smallest unpooled site within that country. If there is not another unpooled site within that country, then the pooled site will be combined with the smallest pooled site from another country. This pooling process will continue until there are at least 10 randomized subjects in each pooled site. For US sites, all investigative sites within a geographic region with fewer than 10 randomized subjects will be combined into a single pooled site for analysis purposes. If a resulting pooled site still has fewer than 10 randomized subjects, then this pooled site will be further combined with the smallest unpooled site within that region. If there is not another unpooled site within that region, then the pooled site will be combined with the smallest pooled site from another region within the US. This pooling process will continue until there are at least 10 randomized subjects in each pooled site.”
As we can see from the examples above, the cut point for center pooling (5, 8, 10, or 24) is really arbitrary and there is no scientific basis for choosing one or another. The decision on the cut point may be based on the distribution of the number of subjects across centers.
Center pooling strategy could sometimes be questioned by the regulatory reviewers. For example, in BLA review of Rebif, FDA reviewer had concerns about the pooling strategy “The sponsor’s study center pooling strategy: Per the pre-specified strategy in the sponsor’s statistical analysis plan (SAP), pooling of study centers for inclusion of center as a main effect in analyses was to have been based on geographic considerations for small centers. In fact, the pooling strategy actually used was data driven which is problematic. NOTE: There were 56 participating centers from 9 countries. The smallest recruiting center had 3 subjects, 2 centers contributed 4 subjects, and 5 centers contributed 6 subjects each. The remaining centers contributed between 6 – 24 subjects each (CSR, Table 3, pp. 65-66). This reviewer performed analyses of major efficacy endpoints based on strict geographic pooling of centers into 3 groups (US, Canada, and Europe) as well as un-pooled analyses (not including the center effect). In addition, descriptive analyses for individual centers were also performed for the primary and major secondary efficacy endpoints. The sponsor’s positive statistical findings were found to be robust based on these analyses.”
In Biopharmaceutical Report (Summer 1998), Paul Gallo wrote an article titled “Practical Issues in Linear Models Analyses in Multicenter Clinical Trials” which contained a section discussing “construction of composite centers”. The caveats of using the composite centers are also discussed in the paper.
“In performing unweighted analyses, a practice of defining artificial “pooled” or “composite” centers is often employed; that is, data from different centers are treated in the analysis as if they came from the same center. A number of small centers may be combined, or one or more small centers may be combined with a larger center. This practice attempts to minimize the large variance inflation and data instability of unweighted analyses when there are very small centers. Composites may be constructed to the extent of eliminating empty cells to ensure that treatment effects are estimable in models containing interaction terms. More commonly, this is done to achieve some minimum cell size felt to appropriately limit the influence of individual observations; values around 5 are often chosen. ”
Arbitrarily pooling the centers sometimes does not make sense at all. This is exactly true when the centers with small number of enrolled subjects are pooled even though these centers are scattered in totally unrelated geographic regions or countries. When pooled center is used and the statistically significant center effect is detected, the interpretation of the results is difficult. Instead of the center pooling purely based on the number of enrollees, the geographic distribution of centers should be considered. In many cases, instead of pooling centers by the number of enrollees, we could use country and geographic region in the analysis. In one of our multi-national clinical trials, we grouped centers by geographic region as North American, South American, Eastern Europe, Western Europe, and Eastern Asia. The strategy worked very well.
If possible, we could use the random effect model to include the study site / center as random effect to avoid the center pooling. We could also use a center weighting strategy that is similar to the Meta analysis where centers with more subjects are given more weights.