Sequential sample size calculations and learning curves safeguard the robust development of a clinical prediction model for individuals
Bibliographic record
Abstract
BACKGROUND AND OBJECTIVES: When recruiting participants to a new study developing a clinical prediction model (CPM), sample size calculations are typically conducted before data collection based on sensible assumptions. This leads to a fixed sample size, but if the assumptions are inaccurate, the actual sample size required to develop a reliable model may be higher or even lower. To safeguard against this, adaptive sample size approaches have been proposed, based on sequential evaluation of (changes in) a model's predictive performance. The objective of the study was to illustrate and extend sequential sample size calculations for CPM development by (i) proposing stopping rules for prospective data collection based on minimizing uncertainty (instability) and misclassification of individual-level predictions and (ii) showcasing how it safeguards against inaccurate fixed sample size calculations. METHODS: Using the sequential approach repeats the predefined model development strategy every time a chosen number (eg, 100) of participants are recruited and adequately followed up. At each stage, CPM performance is evaluated using bootstrapping, leading to prediction and classification stability statistics and plots, alongside optimism-adjusted measures of calibration and discrimination. Learning curves display the trend of results against sample size and recruitment is stopped when a chosen stopping rule is met. RESULTS: Our approach is illustrated for model development of acute kidney injury using (penalized) logistic regression CPMs. Before recruitment based on perceived sensible assumptions, the fixed sample size calculation suggests recruiting 342 patients to minimize overfitting; however, during data collection, the sequential approach reveals that a much larger sample size of 1100 is required to minimize overfitting (targeting a bootstrap-corrected calibration slope ≥0.9). If the stopping rule criteria also target small uncertainty and misclassification probability of individual predictions, the sequential approach suggests an even larger sample size of about 1800. CONCLUSION: For CPM development studies involving prospective data collection, a sequential sample size approach allows users to dynamically monitor individual-level prediction and classification instability. This helps determine when enough participants have been recruited and safeguards against using inaccurate assumptions in a sample size calculation before data collection. Engagement with patients and other stakeholders is crucial to identify sensible context-specific stopping rules for robust individual predictions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.136 | 0.337 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".