5 亚组分析

亚组分析只是meta回归的一个特例

先验定义

在亚组分析中，我们假设荟萃分析中的研究不是来自一个总体人群。相反，我们假设它们属于不同的子组，每个子组都有自己的真实整体效应。目的是拒绝亚组之间效应大小没有差异的零假设。

5.1 固定效应（复数）模型

The Fixed-Effects (Plural) Model

固定效应（复数）模型包含随机效应（子组内）和固定效应（因为子组被假设为固定的），因此在文献中也称为混合效应模型。

添加“复数”一词是因为我们必须将其与标准固定效应模型区分开来。固定效应（复数）模型可以看作是一种混合生物，包括固定效应模型和随机效应模型的特征。与随机效应模型一样，我们假设存在多个真实效应大小，因为我们的数据中有子组。

子组分析的计算由两部分组成：首先，我们将每个子组中的效应合并。随后，使用统计测试来比较亚组的效果

Pooling the Effect in Subgroups

a pooled effect \(\hat μ_g\) for each subgroup \(g\) .
share a common estimate of the between-study heterogeneity \(\tau^2\) that was pooled across subgroups

Comparing the Subgroup Effects using a statistical test

Q test ：自由度为G-1的卡方分布

Caution

子组分析：注意事项

子组分析取决于统计功效，因此它通常当研究数量很少时进行一次研究是没有意义的（即K< 10）。
如果未发现子组之间的效应大小存在差异，这并不意味着子组产生等效的结果。
亚组分析纯粹是观察性的，因此，我们应该始终牢记，效果差异也可能是由混杂变量引起的
在亚组分析中使用汇总研究信息是一个坏主意，因为这可能会引入系统偏差。

5.2 R

Show the code

# Show first entries of study name and 'RiskOfBias' column
head(dmetar::ThirdWave[,c("Author", "RiskOfBias")])
#>            Author RiskOfBias
#> 1     Call et al.       high
#> 2 Cavanagh et al.        low
#> 3   DanitzOrsillo       high
#> 4  de Vibe et al.        low
#> 5  Frazier et al.        low
#> 6  Frogeli et al.        low

Show the code

library(meta)
m.gen <- metagen(TE = TE,
                 seTE = seTE,
                 studlab = Author,
                 data = dmetar::ThirdWave,
                 sm = "SMD",
                 common = FALSE,
                 random = TRUE,
                 method.tau = "REML",
                 method.random.ci = "HK",
                 prediction = TRUE,
                 title = "Third Wave Psychotherapies")

Show the code

update(m.gen, 
       subgroup = RiskOfBias, 
       tau.common = FALSE)
#> Review:     Third Wave Psychotherapies
#> 
#> Number of studies: k = 18
#> 
#>                              SMD            95%-CI    t  p-value
#> Random effects model (HK) 0.5771 [ 0.3782; 0.7760] 6.12 < 0.0001
#> Prediction interval              [-0.0542; 1.2084]              
#> 
#> Quantifying heterogeneity (with 95%-CIs):
#>  tau^2 = 0.0820 [0.0295; 0.3533]; tau = 0.2863 [0.1717; 0.5944]
#>  I^2 = 62.6% [37.9%; 77.5%]; H = 1.64 [1.27; 2.11]
#> 
#> Test of heterogeneity:
#>      Q d.f. p-value
#>  45.50   17  0.0002
#> 
#> Results for subgroups (random effects model (HK)):
#>                     k    SMD           95%-CI  tau^2    tau     Q   I^2
#> RiskOfBias = high   7 0.8126 [0.2835; 1.3417] 0.2423 0.4922 25.89 76.8%
#> RiskOfBias = low   11 0.4300 [0.2770; 0.5830] 0.0099 0.0997 13.42 25.5%
#> 
#> Test for subgroup differences (random effects model (HK)):
#>                   Q d.f. p-value
#> Between groups 2.84    1  0.0917
#> 
#> Details of meta-analysis methods:
#> - Inverse variance method
#> - Restricted maximum-likelihood estimator for tau^2
#> - Q-Profile method for confidence interval of tau^2 and tau
#> - Calculation of I^2 based on Q
#> - Hartung-Knapp adjustment for random effects model (df = 17)
#> - Prediction interval based on t-distribution (df = 17)

Show the code

update(m.gen, subgroup = RiskOfBias, tau.common = TRUE)
#> Review:     Third Wave Psychotherapies
#> 
#> Number of studies: k = 18
#> 
#>                              SMD            95%-CI    t  p-value
#> Random effects model (HK) 0.5771 [ 0.3782; 0.7760] 6.12 < 0.0001
#> Prediction interval              [-0.0542; 1.2084]              
#> 
#> Quantifying heterogeneity (with 95%-CIs):
#>  tau^2 = 0.0820 [0.0295; 0.3533]; tau = 0.2863 [0.1717; 0.5944]
#>  I^2 = 62.6% [37.9%; 77.5%]; H = 1.64 [1.27; 2.11]
#> 
#> Quantifying residual heterogeneity (with 95%-CIs):
#>  tau^2 = 0.0691 [0.0208; 0.3268]; tau = 0.2630 [0.1441; 0.5717]
#>  I^2 = 59.3% [30.6%; 76.1%]; H = 1.57 [1.20; 2.05]
#> 
#> Test of heterogeneity:
#>      Q d.f. p-value
#>  45.50   17  0.0002
#> 
#> Results for subgroups (random effects model (HK)):
#>                     k    SMD           95%-CI  tau^2    tau     Q   I^2
#> RiskOfBias = high   7 0.7691 [0.2533; 1.2848] 0.0691 0.2630 25.89 76.8%
#> RiskOfBias = low   11 0.4698 [0.3015; 0.6382] 0.0691 0.2630 13.42 25.5%
#> 
#> Test for subgroup differences (random effects model (HK)):
#>                    Q d.f. p-value
#> Between groups  1.79    1  0.1814
#> Within groups  39.31   16  0.0010
#> 
#> Details of meta-analysis methods:
#> - Inverse variance method
#> - Restricted maximum-likelihood estimator for tau^2
#>   (assuming common tau^2 in subgroups)
#> - Q-Profile method for confidence interval of tau^2 and tau
#> - Calculation of I^2 based on Q
#> - Hartung-Knapp adjustment for random effects model (df = 17)
#> - Prediction interval based on t-distribution (df = 17)