Estimators of the local false discovery rate designed for small numbers of tests
Bibliographic record
Abstract
Histogram-based empirical Bayes methods developed for analyzing data for large numbers of genes, SNPs, or other biological features tend to have large biases when applied to data with a smaller number of features such as genes with expression measured conventionally, proteins, and metabolites. To analyze such small-scale and medium-scale data in an empirical Bayes framework, we introduce corrections of maximum likelihood estimators (MLEs) of the local false discovery rate (LFDR). In this context, the MLE estimates the LFDR, which is a posterior probability of null hypothesis truth, by estimating the prior distribution. The corrections lie in excluding each feature when estimating one or more parameters on which the prior depends. In addition, we propose the expected LFDR (ELFDR) in order to propagate the uncertainty involved in estimating the prior. We also introduce an optimally weighted combination of the best of the corrected MLEs with a previous estimator that, being based on a binomial distribution, does not require a parametric model of the data distribution across features. An application of the new estimators and previous estimators to protein abundance data illustrates the extent to which different estimators lead to different conclusions about which proteins are affected by cancer. A simulation study was conducted to approximate the bias of the new estimators relative to previous LFDR estimators. Data were simulated for two different numbers of features (N), two different noncentrality parameter values or detectability levels (dalt), and several proportions of unaffected features (p0). One of these previous estimators is a histogram-based estimator (HBE) designed for a large number of features. The simulations show that some of the corrected MLEs and the ELFDR that corrects the HBE reduce the negative bias relative to the MLE and the HBE, respectively. For every method, we defined the worst-case performance as the maximum of the absolute value of the bias over the two different dalt and over various p0. The best worst-case methods represent the safest methods to be used under given conditions. This analysis indicates that the binomial-based method has the lowest worst-case absolute bias for high p0 and for N = 3, 12. However, the corrected MLE that is based on the minimum description length (MDL) principle is the best worst-case method when the value of p0 is more uncertain since it has one of the lowest worst-case biases over all possible values of p0 and for N = 3, 12. Therefore, the safest estimator considered is the binomial-based method when a high proportion of unaffected features can be assumed and the MDL-based method otherwise. A second simulation study was conducted with additional values of N. We found that HBE requires N to be at least 6-12 features to perform as well as the estimators proposed here, with the precise minimum N depending on p0 and dalt.
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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 | 0.125 | 0.416 |
| Meta-epidemiology (narrow) | 0.004 | 0.003 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.008 | 0.004 |
| Research integrity | 0.006 | 0.009 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".