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後設分析 (Meta-Analysis)

元分析 (Meta-Analysis)

Overview

概述

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.

元分析通过统计学方法整合多项独立研究的效应量，生成合并估计值，具备更高的精确性和普适性。它量化研究间的异质性并检验发表偏倚，提供了比叙述性文献综述更严谨的证据整合方式。

When to Use

适用场景

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

针对同一研究问题，整合多项研究的量化结果
解决不同研究间的结果冲突
估计具有更窄置信区间的整体效应量
识别可解释研究间异质性的调节变量

When NOT to Use

不适用场景

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

研究在概念、测量方法或研究人群上差异过大，无法进行有意义的整合
可用研究数量少于5项（合并估计值会变得不可靠）
原始研究的设计存在本质差异（如将随机对照试验与观察性研究混合）
研究问题为定性或概念性，而非定量

Assumptions

假设前提

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because non-significant findings go unpublished.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:

Studies estimate the same underlying construct (conceptual homogeneity)
Effect sizes are statistically independent (one effect per study, or use multilevel models)
Study-level moderators are coded reliably and without bias
The search strategy captures the relevant population of studies (no systematic omission)

铁律：元分析的质量取决于纳入研究的质量——输入垃圾，输出垃圾。发表偏倚会夸大合并效应量，因为无显著性结果的研究往往不会被发表。

核心假设：

所有研究均估计同一潜在概念（概念同质性）
效应量在统计学上相互独立（每项研究仅提取一个效应量，或使用多水平模型）
研究层面的调节变量编码可靠且无偏倚
检索策略覆盖了相关研究群体（无系统性遗漏）

Methodology

方法流程

Step 1 — Extract and Code Effect Sizes

步骤1 — 提取并编码效应量

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.

将研究结果转换为通用的效应量指标（Cohen's d、Hedges' g、r、OR）。编码研究层面的调节变量（样本量、研究设计、研究场景）。转换公式可参考

references/

目录。

Step 2 — Choose Fixed-Effect vs Random-Effects Model

步骤2 — 选择Fixed-effect模型 vs Random-effects模型

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.

Fixed-effect模型假设存在唯一真实效应；Random-effects模型假设效应在不同研究间存在差异。若研究涵盖不同人群或场景，Random-effects模型几乎总是更合适的选择。

Step 3 — Assess Heterogeneity

步骤3 — 评估异质性

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.

计算Q统计量（同质性检验）、I²（异质性导致的方差占比）和τ²（研究间方差）。I² > 75%表明存在显著异质性，需进行调节变量分析。

Step 4 — Test for Publication Bias and Report

步骤4 — 检验发表偏倚并撰写报告

Use funnel plot, Egger's regression test, and trim-and-fill method. Report pooled effect, CI, prediction interval, and results of bias assessment.

使用漏斗图、Egger回归检验和剪补法（trim-and-fill）。报告合并效应量、置信区间（CI）、预测区间以及偏倚评估结果。

Output Format

输出格式

markdown

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markdown

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Meta-Analysis: [Research Question]

元分析：[研究问题]

Study Inclusion

研究纳入情况

Criterion	Value
Studies included (k)	xx
Total sample size (N)	xxxx
Effect size metric	[d / r / OR]

标准	数值
纳入研究数量(k)	xx
总样本量(N)	xxxx
效应量指标	[d / r / OR]

Pooled Effect Size

合并效应量

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

模型	效应值	95% CI	z	p值
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

异质性分析

Statistic	Value	Interpretation
Q	x.xx (p = x.xx)	[significant/not]
I²	x.xx%	[low/moderate/high]
τ²	x.xx	[between-study variance]

统计量	数值	解释
Q	x.xx (p = x.xx)	[显著/不显著]
I²	x.xx%	[低/中/高]
τ²	x.xx	[研究间方差]

Publication Bias

发表偏倚检验

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]

检验方法	结果	解释
漏斗图	[对称/不对称]	[是否怀疑存在偏倚？]
Egger检验	p = x.xx	[是否显著？]
剪补法	调整后效应值 = x.xx	[填补研究数量: x]

Limitations

局限性

[Note any assumption violations]

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[注明任何违反假设的情况]

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Gotchas

注意事项

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

不当整合：若研究概念不同，即使统计上可行，概念层面也毫无意义
Random-effects模型会赋予小样本研究更高权重，而这类研究通常质量较低
I²的大小取决于纳入研究的精确性；若研究本身精度低，I²值小并不代表同质性
漏斗图不对称可能由发表偏倚以外的因素导致（小样本效应）
文件抽屉问题：未发表的无效结果被系统性遗漏
若调节变量分析包含多个亚组且每个亚组的研究数量较少，统计效力不足，结果不可靠

References

参考文献

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.

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.