Standard error estimation in meta-analysis of studies reporting medians
Bibliographic record
Abstract
We consider the setting of an aggregate data meta-analysis of a continuous outcome of interest. When the distribution of the outcome is skewed, it is often the case that some primary studies report the sample mean and standard deviation of the outcome and other studies report the sample median along with the first and third quartiles and/or minimum and maximum values. To perform meta-analysis in this context, a number of approaches have recently been developed to impute the sample mean and standard deviation from studies reporting medians. Then, standard meta-analytic approaches with inverse-variance weighting are applied based on the (imputed) study-specific sample means and standard deviations. In this article, we illustrate how this common practice can severely underestimate the within-study standard errors, which results in poor coverage for the pooled mean in common effect meta-analyses and overestimation of between-study heterogeneity in random effects meta-analyses. We propose a straightforward bootstrap approach to estimate the standard errors of the imputed sample means. Our simulation study illustrates how the proposed approach can improve the estimation of the within-study standard errors and consequently improve coverage for the pooled mean in common effect meta-analyses and estimation of between-study heterogeneity in random effects meta-analyses. Moreover, we apply the proposed approach in a meta-analysis to identify risk factors of a severe course of COVID-19.
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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 | 0.354 | 0.702 |
| Meta-epidemiology (narrow) | 0.003 | 0.003 |
| Meta-epidemiology (broad) | 0.012 | 0.021 |
| Bibliometrics | 0.014 | 0.015 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.008 | 0.007 |
| Open science | 0.008 | 0.006 |
| Research integrity | 0.006 | 0.008 |
| 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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".