Load data
# Load and display the data
rawdata<-read.csv("./data2021.csv", header=TRUE)
rawdata
## study n male female age_mean age_sd mg_mean mg_sd
## 1 Asker (2015) 61 42 19 48.20 9.10 1.41 0.49
## 2 Jiao (2016) 39 15 24 49.57 11.03 2.04 0.17
## 3 Karamanli (2017) 68 46 22 47.20 1.20 1.71 0.21
## 4 Xu (2017) 33 23 10 NA NA 1.71 0.21
## 5 Cakir (2018) 70 70 0 47.57 12.15 2.00 0.12
## 6 Zota (2019) (a) 18 NA NA 55.83 7.05 2.09 0.36
## 7 Zota (2019) (b) 23 NA NA 57.34 7.05 1.90 0.36
# Use metamean to pool the mean from all studies
m1 <- meta::metamean(n,mg_mean,mg_sd, studlab = study, title = "Meta Analysis of Serum Mg Levels in OSA patients")
m1
## Review: Meta Analysis of Serum Mg Levels in OSA patients
##
## Number of studies combined: k = 7
## Number of observations: o = 312
##
## mean 95%-CI
## Common effect model 1.9156 [1.8951; 1.9362]
## Random effects model 1.8363 [1.6598; 2.0129]
##
## Quantifying heterogeneity:
## tau^2 = 0.0541 [0.0208; 0.2795]; tau = 0.2326 [0.1443; 0.5287]
## I^2 = 97.3% [96.0%; 98.2%]; H = 6.08 [4.98; 7.42]
##
## Test of heterogeneity:
## Q d.f. p-value
## 221.54 6 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
## - Untransformed (raw) means
meta::forest.meta(m1, comb.fixed=FALSE, xlim= c(1.2,2.5), plotwidth= unit(8, "cm"), colgap=unit(2, "mm"), prediction = FALSE)
m2 <- meta::metamean(n,mg_mean,mg_sd, exclude = c(1), studlab = study, title = "Meta Analysis of Serum Mg Levels in OSA patients")
m2
## Review: Meta Analysis of Serum Mg Levels in OSA patients
##
## Number of studies combined: k = 6
## Number of observations: o = 312
##
## mean 95%-CI
## Common effect model 1.9302 [1.9093; 1.9511]
## Random effects model 1.9032 [1.7691; 2.0373]
##
## Quantifying heterogeneity:
## tau^2 = 0.0257 [0.0088; 0.1631]; tau = 0.1603 [0.0937; 0.4038]
## I^2 = 96.8% [94.9%; 98.0%]; H = 5.56 [4.42; 7.00]
##
## Test of heterogeneity:
## Q d.f. p-value
## 154.71 5 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
## - Untransformed (raw) means
meta::forest.meta(m2, xlim= c(1.2,2.5), plotwidth= unit(8, "cm"), colgap=unit(2, "mm"), comb.fixed = FALSE)
# m1, m2: the sample means
# s1, s2: the sample standard deviations
# n1, n2: the same sizes
# m0: the null value for the difference in means to be tested for. Default is 0.
# equal.variance: whether or not to assume equal variance. Default is FALSE.
t.test2 <- function(m1,m2,s1,s2,n1,n2,m0=0,equal.variance=FALSE)
{
if( equal.variance==FALSE )
{
se <- sqrt( (s1^2/n1) + (s2^2/n2) )
# welch-satterthwaite df
df <- ( (s1^2/n1 + s2^2/n2)^2 )/( (s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1) )
} else
{
# pooled standard deviation, scaled by the sample sizes
se <- sqrt( (1/n1 + 1/n2) * ((n1-1)*s1^2 + (n2-1)*s2^2)/(n1+n2-2) )
df <- n1+n2-2
}
t <- (m1-m2-m0)/se
dat <- c(m1-m2, se, t, 2*pt(-abs(t),df))
names(dat) <- c("Difference of means", "Std Error", "t", "p-value")
return(dat)
}
t.test2(1.84, 2.07, 1.30674,15.40134,312, 15820)
## Difference of means Std Error t p-value
## -0.2300000 0.1430620 -1.6076945 0.1079854
t.test2(1.90, 2.07, 1.09,15.40134, 251 ,15820)
## Difference of means Std Error t p-value
## -0.1700000 0.1404536 -1.2103638 0.2262157