Title:	Transforms Statistical Measures Commonly Used for Meta-Analysis
Version:	1.0.0
Description:	Helps calculate statistical values commonly used in meta-analysis. It provides several methods to compute different forms of standardized mean differences, as well as other values such as standard errors and standard deviations. The methods used in this package are described in the following references: Altman D G, Bland J M. (2011) <doi:10.1136/bmj.d2090> Borenstein, M., Hedges, L.V., Higgins, J.P.T. and Rothstein, H.R. (2009) <doi:10.1002/9780470743386.ch4> Chinn S. (2000) <doi:10.1002/1097-0258(20001130)19:22%3C3127::aid-sim784%3E3.0.co;2-m> Cochrane Handbook (2011) https://handbook-5-1.cochrane.org/front_page.htm Cooper, H., Hedges, L. V., & Valentine, J. C. (2009) https://psycnet.apa.org/record/2009-05060-000 Cohen, J. (1977) https://psycnet.apa.org/record/1987-98267-000 Ellis, P.D. (2009) https://www.psychometrica.de/effect_size.html Goulet-Pelletier, J.-C., & Cousineau, D. (2018) <doi:10.20982/tqmp.14.4.p242> Hedges, L. V. (1981) <doi:10.2307/1164588> Hedges L. V., Olkin I. (1985) <doi:10.1016/C2009-0-03396-0> Murad M H, Wang Z, Zhu Y, Saadi S, Chu H, Lin L et al. (2023) <doi:10.1136/bmj-2022-073141> Mayer M (2023) https://search.r-project.org/CRAN/refmans/confintr/html/ci_proportion.html Stackoverflow (2014) https://stats.stackexchange.com/questions/82720/confidence-interval-around-binomial-estimate-of-0-or-1 Stackoverflow (2018) https://stats.stackexchange.com/q/338043.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.2
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	3
Imports:	magrittr, stats, confintr
URL:	https://github.com/RobertEmprechtinger/metaHelper
BugReports:	https://github.com/RobertEmprechtinger/metaHelper/issues
Date:	2024-07-22
NeedsCompilation:	no
Packaged:	2024-07-24 13:59:05 UTC; Robert
Author:	Robert Emprechtinger [aut, cre], Guido Schwarzer [aut], Ulf Tölch [aut], Günther Schreder [aut], Gerald Gartlehner [aut]
Maintainer:	Robert Emprechtinger <emprechtinger@stateofhealth.at>
Repository:	CRAN
Date/Publication:	2024-07-28 20:40:02 UTC

Absolute Risk Difference

Description

Calculates the Absolute Risk Difference (ARD) from a Risk Ratio and baseline risk using simulations. The result is ARD as a decimal. The number of replications is fixed at 100,000.

Usage

ARD_from_RR(BR, BRLL, BRUL, RR, RRLL, RRUL, seed = 1)

Arguments

Value

Named numeric vector containing median ARD, the lower and upper CI of the ARD.

References

Murad M H, Wang Z, Zhu Y, Saadi S, Chu H, Lin L et al. Methods for deriving risk difference (absolute risk reduction) from a meta-analysis BMJ 2023; 381 :e073141 doi:10.1136/bmj-2022-073141

Examples

# Input : Baseline risk and 95% CI (BR BRLL and BRUL), risk ratio and 95% CI (RR, RRLL, RRUL)
BR <- 0.053; BRLL <- 0.039; BRUL <- 0.072
RR <- 0.77; RRLL <- 0.63; RRUL <- 0.94
ARD_from_RR(BR, BRLL, BRUL, RR, RRLL, RRUL)

Confidence Interval for Proportions

Description

Calculates a confidence interval for proportions. For a discussion on the differences between methods to calculate confidence intervals, see the Stack Overflow discussion under References. This method uses the R package "confintr" to calculate the confidence intervals.

Usage

CI_from_proportions(events, n, method = "Clopper-Pearson")

Arguments

Value

List of confidence interval of proportions if input length > 1. If input length = 1 Lower CI and Upper CI.

References

Confintr Function Description Stackoverflow Method Discussion

Examples

# CI for 9 events in a sample of 10
CI_from_proportions(9, 10)

Combined Standard Deviation for Multiple Groups

Description

Computes the pooled standard deviation for multiple groups.

Usage

SD_M_n_pooled_from_groups(M, SD, n)

Arguments

Details

This function also returns the combined mean and the total sample size across all groups. Requires also the mean for all individual groups. If there are only two groups and the mean is not available SDp_from_SD() can be used instead.

Value

Within standard deviation

References

Cochrane Handbook

Rücker G, Cates CJ, Schwarzer G. Methods for including information from multi-arm trials in pairwise meta-analysis. Res Synth Methods. 2017 Dec;8(4):392-403. doi: 10.1002/jrsm.1259. Epub 2017 Aug 25. PMID: 28759708.

Examples

# Compute the Standard deviation for the following grouped data
M <- c(1, 1.5, 2) # Means
SD <- c(2, 3, 2.5) # SDs
n <- c(72, 80, 55) # sample sizes
SD_M_n_pooled_from_groups(M, SD, n)

Standard Deviation from Confidence Interval

Description

Computes the standard deviation from the confidence interval and sample size. This method is valid only for single groups and assumes the confidence interval is symmetrical around the mean. For two groups (e.g., intervention effects), use SDp_from_CIp(). For sample sizes smaller than 60, the t-distribution (parameter "t-dist") is typically used to calculate the confidence interval.

Usage

SD_from_CI(CI_low, CI_up, n, sig_level = 0.05, two_sided = TRUE, t_dist = TRUE)

Arguments

Value

Standard deviation single group

References

Cochrane Handbook

See Also

SDp_from_CIp() for two groups (e.g. intervention effects).

Examples

# lower CI = -0.5, upper CI = 2, sample size = 100
SD_from_CI(-05, 2, 100)

Standard Deviation from Standard Error (Single Group)

Description

IMPORTANT: When there are two groups, use the method for calculating the pooled standard error provided by the function SDp_from_SEp()! Calculates the standard deviation from the standard error for a single group.

Usage

SD_from_SE(SE, n)

Arguments

Value

Single group standard deviation

References

Cochrane Handbook

See Also

SDp_from_SEp() in case of two groups.

Examples

# Standard error = 2 and sample size = 100
SE <- 2
n <- 100
SD_from_SE(SE, n)

Within-Group Standard Deviation for Matched Groups

Description

Computes the within-group standard deviation for matched groups. This within-group standard deviation can be used to calculate standardized mean differences for matched groups. This method requires a correlation coefficient r.

Usage

SD_within_from_SD_r(SD_diff, r)

Arguments

Value

Within standard deviation

References

Borenstein, M., Hedges, L.V., Higgins, J.P.T. and Rothstein, H.R. (2009). Effect Sizes Based on Means . In Introduction to Meta-Analysis (eds M. Borenstein, L.V. Hedges, J.P.T. Higgins and H.R. Rothstein). https://doi.org/10.1002/9780470743386.ch4

Examples

# SD_diff is the standard deviation of the group difference
SD_diff <- 2
# r is the correlation coefficient between the groups
r <- 0.5
SD_within_from_SD_r(SD_diff, r)

Pooled Standard Deviation from Confidence Interval

Description

Computes the pooled standard deviation (e.g., standard deviation of an intervention effect) from confidence intervals and sample sizes. According to the Cochrane Handbook (see references), this standard deviation is referred to as the "within-group standard deviation." This method is valid only if the confidence interval is symmetrical around the mean and if either the t-distribution or normal distribution (when "t_dist = FALSE") was used to calculate the confidence interval.

Usage

SDp_from_CIp(
  CI_low,
  CI_up,
  n1,
  n2,
  sig_level = 0.05,
  two_sided = TRUE,
  t_dist = TRUE
)

Arguments

Value

Pooled standard deviation

References

Cochrane Handbook

See Also

SD_from_CI() for single group standard deviation.

Examples

#lower CI = 0.5, upper CI = 0.7, N1 = 50, N2 = 70
SDp_from_CIp(0.5, 0.7, 50, 70)

Pooled Standard Deviation from Two Standard Deviations

Description

Calculates the pooled standard deviation.

Usage

SDp_from_SD(SD1, SD2, n1 = NA, n2 = NA, method = "hedges")

Arguments

Details

The method according to Hedges requires the sample sizes. If only standard deviations are available, the simpler equation provided by Cohen (1988) can be used. If there are more than two groups, SD_M_n_pooled_from_groups() should be used. Note: The use of the names "Cohen" and "Hedges" for the methods can be inconsistent in the literature. It is somewhat unusual because Cohen (1977) outlined both estimators for the pooled standard deviation before Hedges (1981) discussed them.

Value

Pooled standard deviation

References

Borenstein, M., Hedges, L.V., Higgins, J.P.T. and Rothstein, H.R. (2009). Converting Among Effect Sizes. In Introduction to Meta-Analysis (eds M. Borenstein, L.V. Hedges, J.P.T. Higgins and H.R. Rothstein). https://doi.org/10.1002/9780470743386.ch7

Cohen, J. (1977). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ, US: Lawrence Erlbaum Associates, Inc.

Ellis, P.D. (2009), "Effect size equations". Link

Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6, 107-128.

Difference between Cohen's d and Hedges' g for effect size metrics. Stackoverflow. Link

See Also

SD_within_from_SD_r() for matched groups

Examples

# Standard deviation according to Cohen:
SDp_from_SD(2, 3, method = "cohen")

# Standard deviation according to Hedges needs sample sizes:
SDp_from_SD(2, 3, 50, 50)

Standard Deviation from the Pooled Standard Error

Description

IMPORTANT: For a single group, use SD_from_SE()! Calculates the standard deviation from the pooled standard error and sample sizes of two groups (e.g., for intervention effects). This method is the reverse of SEp_from_SDp().

Usage

SDp_from_SEp(SEp, n1, n2)

Arguments

Value

Pooled standard deviation

References

Cochrane Handbook

See Also

SD_from_SE() for a single group. SEp_from_SDp() if the standard error should be computed instead.

Examples

#pooled standard error, sample size 1 and sample size 2
SE <- 0.12
n1 <- 140
n2 <- 140

SDp_from_SEp(SE, n1, n2)

Standard Error of from Confidence Intervals of Odds Ratio

Description

Calculates the standard error from an odds ratio confidence interval.

Usage

SE.SMD_from_OR.CI(CI_low, CI_up, sig_level = 0.05, two_tailed = TRUE)

Arguments

Details

This method uses multiple steps in the background: 1 Takes odds ratio (OR) limits and transforms them to log(OR) 2 Calculates the standard error for the log(OR) 3 Transforms the log(OR) standard error to standardized mean differences (SMD) standard error by multiplying it with sqrt(3)/pi

Value

Standard Error

References

Chinn S. A simple method for converting an odds ratio to effect size for use in meta-analysis. Stat Med. 2000 Nov 30;19(22):3127-31. doi: 10.1002/1097-0258(20001130)

Examples

# lower CI = 0.6, upper CI = 0.9
SE.SMD_from_OR.CI(0.6, 0.9)

Standard Error from Sample Sizes and SMD

Description

Approximates SMD standard error from sample sizes and SMD.

Usage

SE.SMD_from_SMD(SMD, n1, n2, method = "hedges")

Arguments

Value

Standard error of SMD (e.g. standard error of intervention effect)

References

Cooper, H., Hedges, L. V., & Valentine, J. C. (Eds.). (2009). Link

Examples

# SMD = 0.6, sample size group_1 = 50, sample size group_2 = 75
SE.SMD_from_SMD(0.6, 50, 75)

Standard Error for a Single Group

Description

IMPORTANT: For cases involving two groups (e.g., intervention effects), use SEp_from_SDp() instead.#' Calculates the standard error for a single group. This method is only valid for single groups

Usage

SE_from_SD(SD, n)

Arguments

Value

Single group standard error

References

Cochrane Handbook

See Also

SEp_from_SDp() for two groups

Examples

# Standard deviation = 2, group size = 50
SE_from_SD(2, 50)

Standard Error from Confidence Interval for Differences of Means

Description

Calculates the standard error from the confidence interval limits for differences of means (and can also be used for the confidence intervals of standardized mean differences, SMD). This method is valid only when the confidence interval is symmetrical around the mean and is applicable for t-distributions or normal distributions (as specified by the t_dist argument). For sample sizes less than 60, it is generally recommended to use the t-distribution.

Usage

SEp_from_CIp(
  CI_low,
  CI_up,
  n1 = NA,
  n2 = NA,
  sig_level = 0.05,
  two_tailed = TRUE,
  t_dist = TRUE
)

Arguments

Value

Pooled standard error (e.g. intervention effect)

References

Cochrane Handbook

Examples

# lower CI = -1.5, upper CI = 0.5
SEp_from_CIp(-1.5, 0.5)

Standard Error (Pooled)

Description

IMPORTANT: When there is only one group, the following method has to be used: SE_from_SD() Calculates the pooled standard error for two groups (e.g., intervention effect).

Usage

SEp_from_SDp(SDp, n1, n2)

Arguments

Value

Pooled standard error for two groups (e.g. standard error of intervention effect)

References

Cochrane Handbook

See Also

SE_from_SD() for a single group

Examples

# Pooled standard deviation = 2, sample size group a = 50, sample size group b = 75
SEp_from_SDp(2, 50, 75)

Standard Error from Treatment Effect and p-Value

Description

Calculates the pooled standard error using the treatment effect and p-value. To avoid an infinitive return when p-value = 1, the p-value is automatically adjusted to 0.99999

Usage

SEp_from_TE.p(TE, p, two_tailed = TRUE)

Arguments

Value

Pooled standard error (e.g. standard error of intervention effect)

References

Altman D G, Bland J M. How to obtain the confidence interval from a P value BMJ 2011; 343 :d2090 doi:10.1136/bmj.d2090 Cochrane Handbook

Examples

# TE = 1.5, p = 0.8
SEp_from_TE.p(1.5, 0.8)

Standardized Mean Difference from Odds Ratio

Description

Approximates SMD from OR.

Usage

SMD_from_OR(OR)

Arguments

Value

Standardized Mean Difference

References

Borenstein, M., Hedges, L.V., Higgins, J.P.T. and Rothstein, H.R. (2009). Converting Among Effect Sizes. In Introduction to Meta-Analysis (eds M. Borenstein, L.V. Hedges, J.P.T. Higgins and H.R. Rothstein). https://doi.org/10.1002/9780470743386.ch7

Examples

# Transform an OR of 0.3 to SMD
SMD_from_OR(0.3)

Standardized Mean Differences from Group Data

Description

Calculates SMD directly from group data. Method "hedges" needs sample size data and returns Hedges' g. Method "cohen" returns Cohen's d.

Usage

SMD_from_group(M1, M2, SD1, SD2, n1 = NA, n2 = NA, method = "hedges")

Arguments

Value

Standardized Mean Differences

References

Borenstein, M., Hedges, L.V., Higgins, J.P.T. and Rothstein, H.R. (2009). Converting Among Effect Sizes. In Introduction to Meta-Analysis (eds M. Borenstein, L.V. Hedges, J.P.T. Higgins and H.R. Rothstein). https://doi.org/10.1002/9780470743386.ch7

Hedges L. V., Olkin I. (1985). Statistical methods for meta-analysis. San Diego, CA: Academic Press

Goulet-Pelletier, J.-C., & Cousineau, D. (2018). A review of effect sizes and their confidence intervals, Part 1: The Cohen’s d family. The Quantitative Methods for Psychology, 14(4), 242–265. https://doi.org/10.20982/tqmp.14.4.p242

Examples

# Mean control = 23, Mean intervention = 56, SD control = 30,
#    SD intervention = 35, sample size control = 45, sample size intervention = 60
SMD_from_group(23, 56, 30, 35, 45, 60)

Standardized Mean Difference (SMD) from Means and Pooled Standard Deviation

Description

Calculates the SMD. It needs to be provided with the pooled standard deviation. If the pooled standard deviation is not available SMD_from_group() provides a direct method to calculate the SMD and also offers different forms like Hedges' g or Cohen's d.

Usage

SMD_from_mean(M1, M2, SD_pooled)

Arguments

Details

CAVE: If you want to get Hedges' g it is insufficient to simply pool the standard deviation with SDp_from_SD(). The resulting SMD needs to be further multiplied with the hedges factor. This is done automatically when you use SMD_from_group().

Value

Standardized Mean Differences

References

https://handbook-5-1.cochrane.org/chapter_9/9_2_3_2_the_standardized_mean_difference.htm

Examples

# Mean control = 153, Mean intervention = 136, pooled SD = 25
SMD_from_mean(153, 136, 25)

Calculates SMD from Matched Groups

Description

Calculates the standardized mean differences for matched groups. Needs either the mean of the groups or the difference between groups. SD_within is usually not reported but can be calculated by the use of SD_within_from_SD_r().

Usage

SMD_from_mean_matched(M_diff = NA, M1 = NA, M2 = NA, SD_within)

Arguments

Value

Standardized Mean Differences

References

M., Hedges, L.V., Higgins, J.P.T. and Rothstein, H.R. (2009). Converting Among Effect Sizes. In Introduction to Meta-Analysis (eds M. Borenstein, L.V. Hedges, J.P.T. Higgins and H.R. Rothstein). https://doi.org/10.1002/9780470743386.ch7

Examples

# Calcuation with group means
SMD_from_mean_matched(M1 = 103, M2 = 100, SD_within = 7.1005)

# Calculation with group difference
SMD_from_mean_matched(M_diff = 3, SD_within = 7.1005)

# Calculation with standard deviation between
# Correlation Coefficient between groups
r <- 0.7

# SD between groups
SD_between <- 5.5

SMD_from_mean_matched(M_diff = 3,
    SD_within = SD_within_from_SD_r(SD_between, r))