**Influence of large strata/site calculator**

Calculators are provided here to compute the expected inflation in influence due to large sites/strata which are likely to differ in efficacy from the rest of the site/strata in a clinical study. A likely application of these calculators are to provide caps to the size of sites in a clinical trial. Calculators are provided for binomial, survival and continuous endpoints.

The calculations are based on research that has been published. (Shankar Srinivasan and Arlene Swern. Measures of Expected Influence Provide Useful Constraints to Enrollment in Randomized Multi-Center Clinical Trials for Binomial, Continuous and Time-to-Event Endpoints, Journal of Statistical Science and Application, April 2015, Vol. 3, No. 3-4, 39-49). The influence of a site on the final statistical analysis is a function of the size of the site/strata and a function of the extent to which it is likely to differ from other sites/strata in a clinical trial. Two measures of influence are computed. One is the scaled inflation in the influence which is the increase in mean influence divided the square root of the variance of influence. The other measure is the percent increase in influence. Formulae for the calculations of these measures of inflation of influence of aberrant large sites are in this document. Following Cohen’s (*Statistical power analysis for the behavioral sciences*. Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1988) classification of scaled measures, we will consider a scaled inflation as mild if it is between 0.2 and 0.5, moderate if it is between 0.5 and 0.8 and large if it is larger than 0.8.

There are three tabs to the calculator with the three kinds of endpoints. Each calculator has two boxes with calculators. The first box contains the inputs to the calculation and the second box contains the resulting computations.

For the survival calculator, we have as a default in the first box, a 1:1 randomized study with a total of 434 patients. It is a fixed follow-up study meaning all patients will be observed for the same fixed amount of time. Time from the end of enrollment to analysis is 18 months. No censoring due to drop-outs is assumed. A drop-out hazard rate can easily be entered using the calculator in this page. The percent randomized to potentially influential site/strata is 15%. The influential site differs from the rest of the study – the median time to event is expected to be worse at 12 months compared to a median of 14 months for other sites in the study. The box with the calculations provides the hazard ratios and sample sizes of the influential cohort and the remaining cohort. Also calculated are the scaled inflation in influence, the percent inflation in expected influence and the percent inflation in the variance of inflation. Using the Cohen result, the scaled inflation in the influence of such a site of 0.159 indicates that the inclusion of such a site may not be overly detrimental to the analysis. In the absence of estimates of treatment control effects at some influential site, it is recommended that a null effect is assumed at the influential site when using this calculator to obtains caps on the size of sites in a clinical trial.

The other two calculator tabs are similar. For the binomial calculator, one would need to enter the proportions expected to respond in the influential cohort and remaining study cohort. A colleague kindly pointed out that since the binomial distribution is associated with very low variance for very low or very high proportions, using a null effect with the extreme proportion for both treatment and control in the potentially influential site/strata may lead to an assessment of a large influence at the site. The user could use the average of the non-influential proportions instead, in such a context. The continuous tab requires means and standard deviations.

**Edit the blue cells in the spreadsheet and enter your data and the calculations in the bottom box of the spreadsheet will refresh. **

Clay surface contour models of covariance mixtures of three dimensional elliptically symmetric distributions.