| Title: | BLUE for Combining Location and Scale Information in a Meta-Analysis |
|---|---|
| Description: | The sample mean and standard deviation are two commonly used statistics in meta-analyses, but some trials use other summary statistics such as the median and quartiles to report the results. Therefore, researchers need to transform those information back to the sample mean and standard deviation. This package implemented sample mean estimators by Luo et al. (2016) <arXiv:1505.05687>, sample standard deviation estimators by Wan et al. (2014) <arXiv:1407.8038>, and the best linear unbiased estimators (BLUEs) of location and scale parameters by Yang et al. (2018, submitted) based on sample quantiles derived summaries in a meta-analysis. |
| Authors: | Xin Yang [cre, aut], Alan Hutson [aut], Dongliang Wang [aut] |
| Maintainer: | Xin Yang <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0.0 |
| Built: | 2024-12-01 08:04:02 UTC |
| Source: | CRAN |
To obtain the global or overall best linear unbiased estimator (BLUE) of location and scale parameters (Yang et al., 2018).
BLUE_c(alpha_c, B_c, X_c)BLUE_c(alpha_c, B_c, X_c)
alpha_c |
the expectation of a combined standardized vector of ordered summary statistics, i.e. equation (3.21) in Yang et al. (2018). |
B_c |
the variance-covariance matrix of a combined standardized vector of ordered summary statistics, i.e. equation (3.22) in Yang et al. (2018). |
X_c |
a combined vector of ordered summary statistics. |
Yang X, Hutson AD, and Wang D. (2018). A generalized BLUE approach for combining location and scale information in a meta-analysis (Submitted).
n1<-30 # sample sizes of three included studies n2<-45 n3<-67 X1<-c(3,1.2) # the mean and standard deviation X2<-c(1,4,10) # the sample mean, minimum and maximum values X3<-c(1.5,3,5.5,8,12) # the sample mean, first and third quartiles, and minimum and maximum values X_c<-c(X1[1],X2,X3) alpha1<-0 #Approximate by the CLT. B1<-1/sqrt(n1) alpha2<-BLUE_s(X2,n2,"S1")$alpha B2<-BLUE_s(X2,n2,"S1")$B alpha3<-BLUE_s(X3,n3,"S3")$alpha B3<-BLUE_s(X3,n3,"S3")$B alpha_c<-c(alpha1,alpha2,alpha3) B_c<-Matrix::bdiag(B1,B2,B3) BLUE_c(alpha_c,B_c,X_c)n1<-30 # sample sizes of three included studies n2<-45 n3<-67 X1<-c(3,1.2) # the mean and standard deviation X2<-c(1,4,10) # the sample mean, minimum and maximum values X3<-c(1.5,3,5.5,8,12) # the sample mean, first and third quartiles, and minimum and maximum values X_c<-c(X1[1],X2,X3) alpha1<-0 #Approximate by the CLT. B1<-1/sqrt(n1) alpha2<-BLUE_s(X2,n2,"S1")$alpha B2<-BLUE_s(X2,n2,"S1")$B alpha3<-BLUE_s(X3,n3,"S3")$alpha B3<-BLUE_s(X3,n3,"S3")$B alpha_c<-c(alpha1,alpha2,alpha3) B_c<-Matrix::bdiag(B1,B2,B3) BLUE_c(alpha_c,B_c,X_c)
To obtain the best linear unbiased estimator (BLUE) of location and scale parameters based on any set of order statistics (Yang et al., 2018), where the underlying distribution is assumed to be normal.
BLUE_s(X, n, type)BLUE_s(X, n, type)
X |
a vector of ordered summary statistics |
n |
the sample size |
type |
a character string indicating which type of summary statistics is reported. The options for the type argument are:
|
Yang X, Hutson AD, and Wang D. (2018). A generalized BLUE approach for combining location and scale information in a meta-analysis (Submitted).
X<-c(1,4,10) n<-30 type<-"S1" BLUE_s(X,n,type) X<-c(5,8) n<-45 type<-"tertiles" BLUE_s(X,n,type)X<-c(1,4,10) n<-30 type<-"S1" BLUE_s(X,n,type) X<-c(5,8) n<-45 type<-"tertiles" BLUE_s(X,n,type)
Use Luo et al.'s methods (Luo et al., 2016) to estimate the sample mean based on sample quantiles derived summaries for a single study.
Luo.mean(X, n, type)Luo.mean(X, n, type)
X |
a vector of ordered summary statistics |
n |
the sample size |
type |
a character string indicating which type of summary statistics is reported. The options for the type argument are:
|
Luo D, Wan X, Liu J, and Tong T. (2016). Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range. Statistical Methods in Medical Research, arXiv:1505.05687.
X<-c(1,4,10) n<-30 type<-"S1" Luo.mean(X,n,type)X<-c(1,4,10) n<-30 type<-"S1" Luo.mean(X,n,type)
Use Wan et al.'s methods (Wan et al., 2014) to estimate the sample standard deviation based on sample quantiles derived summaries for a single study.
Wan.std(X, n, type)Wan.std(X, n, type)
X |
a vector of ordered summary statistics |
n |
the sample size |
type |
a character string indicating which type of summary statistics is reported. The options for the type argument are:
|
Wan X,Wang W, Liu J, and Tong T. (2014). Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Medical Research Methodology, 14:135.
X<-c(1,4,10) n<-30 type<-"S1" Wan.std(X,n,type)X<-c(1,4,10) n<-30 type<-"S1" Wan.std(X,n,type)