Enrollment Rate Prediction in Clinical Trials based on CDF Sketching and Tensor Factorization tools

Patient enrollment is critical to the success of a clinical trial. In practice, before launching a trial, one of the top priorities is to predict the enrollment rate for different countries, so that one can select clinical sites from the countries with the highest enrollment rates to accelerate patient recruitment. However, based on the limited trial information, estimating the enrollment rate is still a challenge. To deal with this problem, we adopt a very recent tensor factorization approach that aims to approximate the joint Cumulative Distribution Function (CDF) of trial enrollment data. We can always sketch a multivariate CDF in terms of a multidimensional empirical cumulative probability array, i.e., a finite grid-sampled CDF tensor, and introduce a low-rank parametrization by a Canonical Polyadic Decomposition (CPD) model. The proposed model is unassuming of the structure of the data and identifiable under mild conditions by virtue of the uniqueness of CPD. At the same time, it affords both efficient sample likelihood estimation and closed-form inference. Such model can be leveraged for reliable enrollment estimation, delivering probability estimates of a specific trial meeting an expected enrollment rate or probability estimates of being within a certain interval, as well as country recommendation. Experimental results demonstrate an improved performance of the proposed method in the enrollment rate prediction task over the best baselines by up to 12.2% in mean squared error on a real country-level trial dataset, while also offering direct means of quantifying uncertainty in the predictions based on the fitted model. The improved performance and versatility highlight the societal and financial benefits of the proposed approach, which could be transformational in modern healthcare.