比例的荟萃分析
Meta-analysis of proportion
我试图对单一比例进行荟萃分析。这是 R 代码：
# Packages
library(metafor)
# Data
dat <- dat.debruin2009 #from metafor package
# Metafor package ----
dat <- escalc(measure = "PLO", xi = xi, ni = ni, data = dat)
## Calculate random effect
res <- rma(yi, vi, data = dat)
res
predict(res, transf = transf.ilogit)
这是 res 对象的原始结果 (logit)：
Random-Effects Model (k = 13; tau^2 estimator: REML)
tau^2 (estimated amount of total heterogeneity): 0.4014 (SE = 0.1955)
tau (square root of estimated tau^2 value): 0.6336
I^2 (total heterogeneity / total variability): 90.89%
H^2 (total variability / sampling variability): 10.98
Test for Heterogeneity:
Q(df = 12) = 95.9587, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.1121 0.1926 -0.5821 0.5605 -0.4896 0.2654
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
这是 predict() 的结果：
pred ci.lb ci.ub pi.lb pi.ub
0.4720 0.3800 0.5660 0.1962 0.7660
所以，我的问题是我从原始结果 (p = 0.5605) 得到了一个不显着的结果。但是，来自 predict() 的 CI 不会过零 (CI = 0.3800, 0.5660 )，这表明结果很重要。我是否误解了某些内容或遗漏了 R 代码中的某个步骤？或任何解释为什么结果自相矛盾？
============================================= ======
编辑：
我尝试使用 meta 包，我得到了与 metafor 类似的矛盾结果。
meta_pkg <- meta::metaprop(xi, ni, data = dat)
meta_pkg$.glmm.random
这是结果（与上面的 predict() 类似的结果）：
> meta_pkg
Number of studies combined: k = 13
Number of observations: o = 1516
Number of events: e = 669
proportion 95%-CI
Common effect model 0.4413 [0.4165; 0.4664]
Random effects model 0.4721 [0.3822; 0.5638]
Quantifying heterogeneity:
tau^2 = 0.3787; tau = 0.6154; I^2 = 87.5% [80.4%; 92.0%]; H = 2.83 [2.26; 3.54]
Test of heterogeneity:
Q d.f. p-value Test
95.96 12 < 0.0001 Wald-type
108.77 12 < 0.0001 Likelihood-Ratio
Details on meta-analytical method:
- Random intercept logistic regression model
- Maximum-likelihood estimator for tau^2
- Logit transformation
与 metafor 中类似的原始结果：
> meta_pkg$.glmm.random
Random-Effects Model (k = 13; tau^2 estimator: ML)
tau^2 (estimated amount of total heterogeneity): 0.3787
tau (square root of estimated tau^2 value): 0.6154
I^2 (total heterogeneity / total variability): 90.3989%
H^2 (total variability / sampling variability): 10.4155
Tests for Heterogeneity:
Wld(df = 12) = 95.9587, p-val < .0001
LRT(df = 12) = 108.7653, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.1118 0.1880 -0.5946 0.5521 -0.4804 0.2567
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
p值是检验平均logit变换比例是否显着不同于0。这与检验比例是否显着不同于0是不一样的。事实上，transf.ilogit(0)给出0.5，所以这是被测比例的对应值。你会注意到 0.5 在反向转换后落在置信区间内。所以一切都是完全一致的。
我试图对单一比例进行荟萃分析。这是 R 代码：
# Packages
library(metafor)
# Data
dat <- dat.debruin2009 #from metafor package
# Metafor package ----
dat <- escalc(measure = "PLO", xi = xi, ni = ni, data = dat)
## Calculate random effect
res <- rma(yi, vi, data = dat)
res
predict(res, transf = transf.ilogit)
这是 res 对象的原始结果 (logit)：
Random-Effects Model (k = 13; tau^2 estimator: REML)
tau^2 (estimated amount of total heterogeneity): 0.4014 (SE = 0.1955)
tau (square root of estimated tau^2 value): 0.6336
I^2 (total heterogeneity / total variability): 90.89%
H^2 (total variability / sampling variability): 10.98
Test for Heterogeneity:
Q(df = 12) = 95.9587, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.1121 0.1926 -0.5821 0.5605 -0.4896 0.2654
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
这是 predict() 的结果：
pred ci.lb ci.ub pi.lb pi.ub
0.4720 0.3800 0.5660 0.1962 0.7660
所以，我的问题是我从原始结果 (p = 0.5605) 得到了一个不显着的结果。但是，来自 predict() 的 CI 不会过零 (CI = 0.3800, 0.5660 )，这表明结果很重要。我是否误解了某些内容或遗漏了 R 代码中的某个步骤？或任何解释为什么结果自相矛盾？
============================================= ======
编辑： 我尝试使用 meta 包，我得到了与 metafor 类似的矛盾结果。
meta_pkg <- meta::metaprop(xi, ni, data = dat)
meta_pkg$.glmm.random
这是结果（与上面的 predict() 类似的结果）：
> meta_pkg
Number of studies combined: k = 13
Number of observations: o = 1516
Number of events: e = 669
proportion 95%-CI
Common effect model 0.4413 [0.4165; 0.4664]
Random effects model 0.4721 [0.3822; 0.5638]
Quantifying heterogeneity:
tau^2 = 0.3787; tau = 0.6154; I^2 = 87.5% [80.4%; 92.0%]; H = 2.83 [2.26; 3.54]
Test of heterogeneity:
Q d.f. p-value Test
95.96 12 < 0.0001 Wald-type
108.77 12 < 0.0001 Likelihood-Ratio
Details on meta-analytical method:
- Random intercept logistic regression model
- Maximum-likelihood estimator for tau^2
- Logit transformation
与 metafor 中类似的原始结果：
> meta_pkg$.glmm.random
Random-Effects Model (k = 13; tau^2 estimator: ML)
tau^2 (estimated amount of total heterogeneity): 0.3787
tau (square root of estimated tau^2 value): 0.6154
I^2 (total heterogeneity / total variability): 90.3989%
H^2 (total variability / sampling variability): 10.4155
Tests for Heterogeneity:
Wld(df = 12) = 95.9587, p-val < .0001
LRT(df = 12) = 108.7653, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.1118 0.1880 -0.5946 0.5521 -0.4804 0.2567
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
p值是检验平均logit变换比例是否显着不同于0。这与检验比例是否显着不同于0是不一样的。事实上，transf.ilogit(0)给出0.5，所以这是被测比例的对应值。你会注意到 0.5 在反向转换后落在置信区间内。所以一切都是完全一致的。