比例的Meta分析

Question

我试着做一个单一比例的meta分析。以下是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)

下面是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

这是来自predict()的结果

   pred  ci.lb  ci.ub  pi.lb  pi.ub 
 0.4720 0.3800 0.5660 0.1962 0.7660 

因此，我的问题是，我从原始结果(p = 0.5605)中得到了一个不重要的结果。但是，来自predict()的CI不会超过零(CI = 0.3800，0.5660 )，这表明结果很重要。我是不是误解了什么，或者在R代码中遗漏了一个步骤？或者解释为什么结果是矛盾的？

===

编辑:我尝试使用meta包，我得到了一个类似于metafor的矛盾结果。

meta_pkg <- meta::metaprop(xi, ni, data = dat)
meta_pkg$.glmm.random

下面是结果(与上面的predict()结果类似)：

> 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

Answer 1

P值是测试平均logit转换比例是否显着不同于0。这与测试该比例是否与0有显着差异不同。事实上，transf.ilogit(0)是0.5，所以这是正在测试的比例的对应值。您将注意到，在反向转换后，0.5落在置信区间内。所以一切都是完全一致的。