grad-meta-analysis
用後設分析合併多項研究的效果量，檢查異質性和發表偏誤
中文翻譯
--- name: "grad-meta-analysis" description: "用後設分析整合多項研究的效果量、評估異質性，並檢查發表偏誤。當使用者需要彙整既有研究的發現、比較固定效果與隨機效果模型、計算合併效果量，或問到「整體證據怎麼說」「怎麼合併多項研究的結果」「有沒有發表偏誤」時，就用這個 skill。" metadata: category: "WP-31 量化方法" tags: ["meta-analysis", "effect-size", "heterogeneity", "publication-bias", "I-squared", "systematic-review"] --- # 後設分析 (Meta-Analysis) ## Overview 後設分析用統計方法合併多個獨立研究的效果量，得到精確度和概化性都更高的合併估計。它量化研究之間的異質性，並檢驗發表偏誤，提供比敘事性文獻回顧更嚴謹的證據綜合。 ## When to Use - 彙整針對同一個研究問題的多項研究的量化發現 - 化解各研究之間互相衝突的結果 - 用更窄的信賴區間估計整體效果量 - 找出能解釋研究間異質性的調節變數 ## When NOT to Use - 研究在構念、測量或母群體上差異太大，無法有意義地合併 - 可用的研究少於 5 個（合併估計變得不可靠） - 原始研究的設計根本不同（把 RCT 和觀察性研究混在一起） - 研究問題是質性或概念性的，不是量化的 ## Assumptions ``` IRON LAW: A meta-analysis is only as good as the studies it includes — garbage in, garbage out. Publication bias inflates pooled effect sizes because non-significant findings go unpublished. ``` 關鍵假設： 1. 各研究估計的是同一個底層構念（概念上的同質性） 2. 效果量在統計上獨立（每個研究一個效果，或用多層次模型） 3. 研究層級的調節變數編碼可靠而且沒有偏誤 4. 搜尋策略涵蓋了相關的研究母群體（沒有系統性的遺漏） ## Methodology ### Step 1 — Extract and Code Effect Sizes 把各研究的發現轉換成共同的效果量指標（Cohen's d、Hedges' g、r、OR）。為研究層級的調節變數編碼（樣本數、設計、脈絡）。轉換公式見 `references/`。 ### Step 2 — Choose Fixed-Effect vs Random-Effects Model 固定效果假設只有一個真實效果；隨機效果假設效果會因研究而異。如果各研究橫跨不同的母群體或脈絡，幾乎都該用隨機效果。 ### Step 3 — Assess Heterogeneity 計算 Q 統計量（同質性檢定）、I²（由異質性造成的變異比例）和 τ²（研究間變異數）。I² > 75% 表示有相當大的異質性，值得做調節變數分析。 ### Step 4 — Test for Publication Bias and Report 使用漏斗圖、Egger 迴歸檢定和 trim-and-fill 法。報告合併效果、信賴區間、預測區間，以及偏誤評估的結果。 ## Output Format ```markdown ## Meta-Analysis: [Research Question] ### Study Inclusion | Criterion | Value | |-----------|-------| | Studies included (k) | xx | | Total sample size (N) | xxxx | | Effect size metric | [d / r / OR] | ### Pooled Effect Size | Model | Effect | 95% CI | z | p-value | |-------|--------|--------|---|---------| | Fixed-effect | x.xx | [x.xx, x.xx] | x.xx | x.xx | | Random-effects | x.xx | [x.xx, x.xx] | x.xx | x.xx | ### Heterogeneity | Statistic | Value | Interpretation | |-----------|-------|----------------| | Q | x.xx (p = x.xx) | [significant/not] | | I² | x.xx% | [low/moderate/high] | | τ² | x.xx | [between-study variance] | ### Publication Bias | Test | Result | Interpretation | |------|--------|----------------| | Funnel plot | [symmetric/asymmetric] | [bias suspected?] | | Egger's test | p = x.xx | [significant?] | | Trim-and-fill | adjusted effect = x.xx | [studies imputed: x] | ### Limitations - [Note any assumption violations] ``` ## Gotchas - 拿蘋果和橘子一起比：統計上做得到，但如果構念不同，概念上沒有意義 - 隨機效果模型會給小型研究更多權重，而小型研究的品質常常比較低 - I² 取決於納入研究的精確度，不精確的研究帶來低 I²，不代表同質 - 漏斗圖不對稱可能由發表偏誤以外的因素造成（小研究效應） - 檔案抽屜問題：未發表的虛無結果會系統性地缺漏 - 子群很多、每個子群研究很少的調節變數分析，檢定力不足而且不可靠 ## References - Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). *Introduction to Meta-Analysis*. Wiley. - Higgins, J. P. T., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. *Statistics in Medicine*, 21(11), 1539-1558. - Rothstein, H. R., Sutton, A. J., & Borenstein, M. (2005). *Publication Bias in Meta-Analysis*. Wiley.
英文原文
--- name: "grad-meta-analysis" description: "Apply meta-analysis to synthesize effect sizes across multiple studies, assess heterogeneity, and evaluate publication bias. Use this skill when the user needs to combine findings from prior research, compare fixed-effect vs random-effects models, compute pooled effect sizes, or when they ask 'what does the overall evidence say', 'how do I combine results across studies', or 'is there publication bias'." metadata: category: "WP-31 量化方法" tags: ["meta-analysis", "effect-size", "heterogeneity", "publication-bias", "I-squared", "systematic-review"] --- # 後設分析 (Meta-Analysis) ## Overview Meta-analysis statistically combines effect sizes from multiple independent studies to produce a pooled estimate with greater precision and generalizability. It quantifies between-study heterogeneity and tests for publication bias, providing a rigorous evidence synthesis that goes beyond narrative literature reviews. ## When to Use - Synthesizing quantitative findings from multiple studies on the same research question - Resolving conflicting results across studies - Estimating an overall effect size with tighter confidence intervals - Identifying moderators that explain heterogeneity across studies ## When NOT to Use - Studies are too heterogeneous in constructs, measures, or populations to combine meaningfully - Fewer than 5 studies are available (pooled estimates become unreliable) - Primary studies have fundamentally different research designs (mixing RCTs with observational) - The research question is qualitative or conceptual rather than quantitative ## Assumptions ``` IRON LAW: A meta-analysis is only as good as the studies it includes — garbage in, garbage out. Publication bias inflates pooled effect sizes because non-significant findings go unpublished. ``` Key assumptions: 1. Studies estimate the same underlying construct (conceptual homogeneity) 2. Effect sizes are statistically independent (one effect per study, or use multilevel models) 3. Study-level moderators are coded reliably and without bias 4. The search strategy captures the relevant population of studies (no systematic omission) ## Methodology ### Step 1 — Extract and Code Effect Sizes Convert study findings to a common effect size metric (Cohen's d, Hedges' g, r, OR). Code study-level moderators (sample size, design, context). See `references/` for conversion formulas. ### Step 2 — Choose Fixed-Effect vs Random-Effects Model Fixed-effect assumes one true effect; random-effects assumes effects vary across studies. If studies span different populations or contexts, random-effects is almost always appropriate. ### Step 3 — Assess Heterogeneity Compute Q statistic (test of homogeneity), I² (proportion of variance due to heterogeneity), and τ² (between-study variance). I² > 75% indicates substantial heterogeneity warranting moderator analysis. ### Step 4 — Test for Publication Bias and Report Use funnel plot, Egger's regression test, and trim-and-fill method. Report pooled effect, CI, prediction interval, and results of bias assessment. ## Output Format ```markdown ## Meta-Analysis: [Research Question] ### Study Inclusion | Criterion | Value | |-----------|-------| | Studies included (k) | xx | | Total sample size (N) | xxxx | | Effect size metric | [d / r / OR] | ### Pooled Effect Size | Model | Effect | 95% CI | z | p-value | |-------|--------|--------|---|---------| | Fixed-effect | x.xx | [x.xx, x.xx] | x.xx | x.xx | | Random-effects | x.xx | [x.xx, x.xx] | x.xx | x.xx | ### Heterogeneity | Statistic | Value | Interpretation | |-----------|-------|----------------| | Q | x.xx (p = x.xx) | [significant/not] | | I² | x.xx% | [low/moderate/high] | | τ² | x.xx | [between-study variance] | ### Publication Bias | Test | Result | Interpretation | |------|--------|----------------| | Funnel plot | [symmetric/asymmetric] | [bias suspected?] | | Egger's test | p = x.xx | [significant?] | | Trim-and-fill | adjusted effect = x.xx | [studies imputed: x] | ### Limitations - [Note any assumption violations] ``` ## Gotchas - Combining apples and oranges: statistically possible but conceptually meaningless if constructs differ - Random-effects models give more weight to small studies, which are often lower quality - I² depends on precision of included studies; low I² with imprecise studies does not mean homogeneity - Funnel plot asymmetry can be caused by factors other than publication bias (small-study effects) - File-drawer problem: unpublished null results are systematically missing - Moderator analyses with many subgroups and few studies per subgroup are underpowered and unreliable ## References - Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). *Introduction to Meta-Analysis*. Wiley. - Higgins, J. P. T., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. *Statistics in Medicine*, 21(11), 1539-1558. - Rothstein, H. R., Sutton, A. J., & Borenstein, M. (2005). *Publication Bias in Meta-Analysis*. Wiley.