# Estimating Clinical Trial Enrollment Eligible Subsets in Oncology

## Starting Estimates to help Enrollment Assessments

Cancer Clinical Trials often involve initiation of therapy at diagnosis or at a second, third or subsequent relapse. These are the usual core inclusion criteria in clinical trials. The calculator at this page will help provide rough starting estimates of the proportions of patients at sites who are likely to meet the core inclusion criteria of having had a relapse during an enrollment period or starting therapy on diagnosis during the period. The calculator here provides an upper bound to help those in operations make realistic assessments on the number and size of clinical trial sites and the enrollment time frames that might be needed to complete planned total patient enrollment. Usually additional inclusion/exclusion criteria such as co-morbidity exclusions, requirement of certain biomarkers, specified risk profiles and other criteria apply and the starting estimates computed here would need to be further fractionated by the subgroup proportions meeting these additional criteria.

## Some Calculator Details

This calculator uses the median times to next PFS and subsequent OS measured from diagnosis and after relapses/progressions under exponential distribution assumptions. These medians correspond to patients on a mixed set of standard of therapy options and should typically be assessed by observational studies allowing for a latitude of patient consented clinician choices of therapy. The disease prognosis is presumed stable, with the assessed medians holding true over a medium time frame. This would not hold if there is a breakthrough therapy in that time frame with marked efficacy compared to previous standards, and having considerable market penetration. Further the calculations assume a uniform incidence rate of the disease over time. For further details on the computations please refer to Srinivasan S., Lihua Y., Weiyuan C. 2019. “Estimation of Cancer Progression Based Clinical Trial Subgroups” Journal of Mathematics and System Science 9: 124-9. Brief details on the computations are also in the attached hyperlinked document.

## Calculator Example

In the default example we consider a disease condition where the median survival from diagnosis is 4 years and the median time from diagnosis to next (first) progression/Death is 1.5 years. Corresponding medians from first relapse are 0.75 years (9 months) and 2 years respectively. In a salvage setting (after second or higher relapse) the medians are 0.5 years (6 months) and 1 year respectively. The period considered is 0.5 years (6 months).

The first column estimates the likely breakdown of patients having the disease as a multiple of the number of newly diagnosed patients. For every newly diagnosed patient during a 6 month enrollment time-frame, a 3.85 multiple are ongoing diagnosed patients without a relapse, 0.6 have a first relapse, 0.58 are previously relapsed having a relapse again and 1.6 are previously relapsed ongoing without relapse, all in the same 6 month period. This implies a 2.04 multiple eligible for clinical trials and a 5.45 ineligible if trials are to start on relapse or at diagnosis.

These are converted to percentages in the second column. In addition to some bias when the assumptions noted earlier do not hold, these percentages are associated with error. This error works out to about +/- 5% (95% Confidence Intervals) when considering about a 100 patients and is generally proportional to the inverse of the square root of the number of patients.  For every 100 patients in the sites being considered, about 73 are likely doing reasonably well through the 6 month period and are likely coming in for scheduled visits and possibly just picking their prescriptions or undergoing any therapies at the site without a disease progression, unless there is a decision to draw down therapy with patient consent to allow a patient to consider possible safer or more efficacious alternatives in clinical trials.  These patients would not typically volunteer or be considered for clinical trials. Further for those 100 patients about 13 patients would be newly diagnosed during the period, about 8 would have had their first relapse and another 6 would have had a subsequent relapse, leading to only about 27 eligible for a clinical trial. The last column computes these trial eligible proportions as a percent of the total eligible.

Often regulatory agencies request separate study of therapies in the newly diagnosed and the relapsed settings and licensing is restricted to the setting studied. For the hypothetical example considered, only about 13 in a 100 patients at clinics and hospitals would qualify for a trial by a sponsor pursuing a newly diagnosed indication for their therapy. Often sponsors consider approvals for patients difficult to treat such as those with 1 or more relapses. For the default example in this calculator, this would be about 14 patients among 100 visiting clinics and hospitals over a 6 month period. As noted earlier there would be additional attrition in the available patient pools as one applies inclusion and exclusion criteria. For instance, a requirement of refractoriness to a class of medications in addition to being relapsed would further restrict enrollment.

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