The path toward generalizable clinical prediction models

The peaking phenomenon refers to the observation that, after a point, the performance of prediction models starts to decrease as the number of predictors (p) increases. This issue is commonly encountered in small datasets (colloquially known as “small n, large p” datasets or high-dimensional data). It was recently reported based on analysis of data from five placebo-controlled trials that clinical prediction models in schizophrenia showed poor performance (average balanced accuracy, BAC, 0.54). This was interpreted to suggest that prediction models in schizophrenia have poor generalizability. In this paper we demonstrate that this outcome more likely reflects the peaking phenomenon in a small n, large p dataset (n=1513 participants, p=217) and generalize this to a set of illustrative cases using simulated data. We then demonstrate that an ensemble of supervised learning models trained using more data (18 placebo-controlled trials, n=4634 participants), but fewer predictors (p=33), achieves better prediction (average BAC = 0.64) which generalizes to out-of-sample studies as well as to data from active-controlled trials (n=1463, average BAC = 0.67). Based on these findings, we argue that the achievable prediction accuracy for treatment response in schizophrenia— and likely for many other medical conditions—is highly dependent on sample size and the number of included predictors, and, hence, remains unknown until more data has been analyzed. Finally, we provide recommendations for how researchers and data holders might work to improve future data analysis efforts in clinical prediction. ### Competing Interest Statement F.H has received speakers fees from Janssen Pharmaceuticals. SDO received the 2020 Lundbeck Foundation Young Investigator Prize. SDO owns/has owned units of mutual funds with stock tickers DKIGI, IAIMWC, SPIC25KL and WEKAFKI, and owns/has owned units of exchange traded funds with stock tickers BATE, TRET, QDV5, QDVH, QDVE, SADM, IQQH, USPY, EXH2, 2B76, IS4S, OM3X and EUNL. The remaining authors report no conflicts of interest. ### Clinical Protocols ### Funding Statement This study was supported by the Swedish Research Council and The Lundbeck Foundation. No funding source had any role in the study design, data collection, data analysis, data interpretation, writing, or submission of this report. All trials were originally funded by Janssen Research and Development. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: All data used in this study comes from the Yale University Open Data Access Project (YODA Project 2019-394). Data access was approved by YODA. No local ethics review was required in the jurisdictions where the research was carried out (Denmark and Sweden). I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data can be requested from the Yale University Open Data Access Project. Accession numbers for the included studies are provided in the Supplement. The code necessary to replicate all analyses is archived with Zenodo (DOI: 10.5281/zenodo.10976022).