Sample size estimation using a latent variable model for mixed outcome co‐primary, multiple primary and composite endpoints
Bibliographic record
Abstract
Mixed outcome endpoints that combine multiple continuous and discrete components are often employed as primary outcome measures in clinical trials. These may be in the form of co-primary endpoints, which conclude effectiveness overall if an effect occurs in all of the components, or multiple primary endpoints, which require an effect in at least one of the components. Alternatively, they may be combined to form composite endpoints, which reduce the outcomes to a one-dimensional endpoint. There are many advantages to joint modeling the individual outcomes, however in order to do this in practice we require techniques for sample size estimation. In this article we show how the latent variable model can be used to estimate the joint endpoints and propose hypotheses, power calculations and sample size estimation methods for each. We illustrate the techniques using a numerical example based on a four-dimensional endpoint and find that the sample size required for the co-primary endpoint is larger than that required for the individual endpoint with the smallest effect size. Conversely, the sample size required in the multiple primary case is similar to that needed for the outcome with the largest effect size. We show that the empirical power is achieved for each endpoint and that the FWER can be sufficiently controlled using a Bonferroni correction if the correlations between endpoints are less than 0.5. Otherwise, less conservative adjustments may be needed. We further illustrate empirically the efficiency gains that may be achieved in the composite endpoint setting.
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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 | 0.065 | 0.205 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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".