Help for package boutliers

Type:

Package

Title:

Outlier Detection and Influence Diagnostics for Meta-Analysis

Version:

2.1-1

Date:

2025-09-20

Maintainer:

Hisashi Noma <noma@ism.ac.jp>

Description:

Computational tools for outlier detection and influence diagnostics in meta-analysis (Noma et al. (2025) <doi:10.1101/2025.09.18.25336125>). Bootstrap distributions of influence statistics are computed, and explicit thresholds for identifying outliers are provided. These methods can also be applied to the analysis of influential centers or regions in multicenter or multiregional clinical trials (Aoki and Noma (2021) <doi:10.1080/24709360.2021.1921944>, Nakamura and Noma (2021) <doi:10.5691/jjb.41.117>).

Imports:

stats, metafor, MASS

License:

GPL-3

Encoding:

UTF-8

LazyData:

true

NeedsCompilation:

Packaged:

2025-09-20 03:00:25 UTC; nomah

Author:

Hisashi Noma [aut, cre], Kazushi Maruo [aut], Masahiko Gosho [aut]

Repository:

CRAN

Date/Publication:

2025-09-20 23:10:02 UTC

The 'boutliers' package.

Description

Computational tools for outlier detection and influence diagnostics in meta-analysis. Bootstrap distributions of influence statistics are computed, and explicit thresholds for identifying outliers are provided. These methods can also be applied to the analysis of influential centers or regions in multicenter or multiregional clinical trials.

References

Aoki, M., Noma, H., and Gosho, M. (2021). Methods for detecting outlying regions and influence diagnosis in multi-regional clinical trials. Biostatistics & Epidemiology. 5(1): 30-48. doi:10.1080/24709360.2021.1921944

Hedges, L. V., and Olkins, I. (1985). Statistical Methods for Meta-Analysis. New York: Academic Press.

Nakamura, R., and Noma, H. (2021). Detection of outlying centers and influence diagnostics for the analysis of multicenter clinical trials (in Japanese). Japanese Journal of Biometrics. 41(2): 117-136. doi:10.5691/jjb.41.117

Noma, H., Gosho, M., Ishii, R., Oba, K., and Furukawa, T. A. (2020). Outlier detection and influence diagnostics in network meta-analysis. Research Synthesis Methods. 11(6): 891-902. doi:10.1002/jrsm.1455

Noma, H., Maruo, K., and Gosho, M. (2025). boutliers: R package of outlier detection and influence diagnostics for meta-analysis. medRxiv. doi:10.1101/2025.09.18.25336125

Viechtbauer, W., and Cheung, M. W. (2010). Outlier and influence diagnostics for meta-analysis. Research Synthesis Methods. 1(2): 112-125. doi:10.1002/jrsm.11

Likelihood ratio test using a mean-shifted model

Description

Implementing the likelihood ratio tests using the mean-shifted model. The bootstrap p-values are provided.

Usage

LRT(y, v, model="RE", data, B=2000, alpha=0.05, seed=123456)

Arguments

y

A vector of the outcome measure estimates (e.g., MD, SMD, log OR, log RR, RD)

v

A vector of the variance estimate of y

model

A logical value specifying the pooling model (RE: random-effects model, FE: fixed-effect model)

data

An optional data frame containing the variables y and v.

B

The number of bootstrap resampling (default: 2000)

alpha

The significance level (default: 0.05)

seed

A numeric value that determines the random seed for reproducibility (default: 123456).

Value

Results of the likelihood ratio tests involving bootstrap p-values. The outputs are ordered by the p-values.

id: ID of the study.
LR: The likelihood ratio statistic for based on the mean-shifted model.
Q: 1-alphath percentile for the bootstrap distribution of the likelihood ratio statistic.
P: The bootstrap p-value for the likelihood ratio statistic.

Examples

require(metafor)
data(SMT)

edat2 <- escalc(m1i=m1,sd1i=s1,n1i=n1,m2i=m2,sd2i=s2,n2i=n2,measure="MD",data=SMT)

LRT(yi, vi, data=edat2, B=10)
# Random-effects model.
# This is an example command for illustration. B should be >= 1000.

LRT(yi, vi, data=edat2, model="FE", B=10)
# Fixed-effect model.
# This is an example command for illustration. B should be >= 1000.

Crocker et al. (2018)'s patient and public involvement (PPI) intervention data

Description

ID: Study ID
d1: Number of events in PPI intervention group
n1: Number of observations in PPI intervention group
d2: Number of events in non-PPI intervention group
n2: Number of observations in non-PPI intervention group

Usage

data(PPI)

Format

A data frame with 21 rows and 5 variables

References

Crocker, J. C., Ricci-Cabello, I., Parker, A., Hirst, J. A., Chant, A., Petit-Zeman, S., Evans, D., Rees, S. (2018). Impact of patient and public involvement on enrolment and retention in clinical trials: systematic review and meta-analysis. BMJ. 363: k4738. doi:10.1136/bmj.k4738

Rubinstein et al. (2019)'s chronic low back pain data

Description

ID: Study ID
Souce: First author name and year of publication
m1: Estimated mean in experimental group
s1: Standard deviation in experimental group
n1: Number of observations in experimental group
m2: Estimated mean in control group
s2: Standard deviation in control group
n2: Number of observations in control group

Usage

data(SMT)

Format

A data frame with 23 rows and 8 variables

References

Rubinstein, S. M,, de Zoete, A., van Middelkoop, M., Assendelft, W. J. J., de Boer, M. R., van Tulder, M. W. (2019). Benefits and harms of spinal manipulative therapy for the treatment of chronic low back pain: systematic review and meta-analysis of randomised controlled trials. BMJ. 364: l689. doi:10.1136/bmj.l689

Studentized residuals by leave-one-out analysis

Description

Calculating the studentized residuals by leave-one-out analysis (studentized deleted residuals) and the percentiles of their bootstrap distributions.

Usage

STR(y, v, method="REML", data, B=2000, alpha=0.95, seed=123456)

Arguments

y

A vector of the outcome measure estimates (e.g., MD, SMD, log OR, log RR, RD)

v

A vector of the variance estimate of y

method

A logical value specifying the estimation method (default: REML). The same options as those available for the method argument of the rma function in the metafor package can be used (e.g., FE for the fixed-effect model, SJ for the Sidik–Jonkman method, and PM for the Paule–Mandel method).

data

An optional data frame containing the variables y and v.

B

The number of bootstrap resampling (default: 2000)

alpha

The bootstrap percentiles to be outputted; 0.5(1-alpha)th and (1-0.5(1-alpha))th pecentiles. Default is 0.95; 2.5th and 97.5th percentiles are calculated.

seed

A numeric value that determines the random seed for reproducibility (default: 123456).

Value

The studentized residuals by leave-one-out analysis. The outputs are ordered by the sizes of the studentized residuals.

id: ID of the study.
psi: The studentized residuals by leave-one-out analysis (studentized deleted residuals).
Q1: 0.5(1-alpha)th percentile for the bootstrap distribution of the studentized residual (default: 2.5th percentile).
Q2: 1-0.5(1-alpha)th percentile for the bootstrap distribution of the studentized residual (default: 97.5th percentile).

Examples

require(metafor)
data(PPI)

edat1 <- escalc(ai=d1,n1i=n1,ci=d2,n2i=n2,measure="OR",data=PPI)

STR(yi, vi, data=edat1, B=10)
# Random-effects model (REML estimation).
# This is an example command for illustration. B should be >= 1000.

STR(yi, vi, data=edat1, method="SJ",B=10)
# Random-effects model (Sidik–Jonkman method).
# This is an example command for illustration. B should be >= 1000.

STR(yi, vi, data=edat1, method="FE",B=10)
# Fixed-effects model.
# This is an example command for illustration. B should be >= 1000.

Variance ratio influential statistics

Description

Calculating the variance ratio influential statistics by leave-one-out analysis and the percentiles of their bootstrap distributions.

Usage

VRATIO(y, v, method="REML", data, B=2000, alpha=0.05, seed=123456)

Arguments

y

A vector of the outcome measure estimates (e.g., MD, SMD, log OR, log RR, RD)

v

A vector of the variance estimate of y

method

data

An optional data frame containing the variables y and v.

B

The number of bootstrap resampling (default: 2000)

alpha

The bootstrap percentile to be outputted (default: 0.05)

seed

A numeric value that determines the random seed for reproducibility (default: 123456).

Value

The variance ratio influential statistics by leave-one-out analysis and their bootstrap percentiles. The outputs are ordered by the sizes of the variance ratio statistics.

id: ID of the study.
VR: The VRATIO statistic (relative change of the variance of the overall estimator) by leave-one-out analysis.
Q1: alphath percentile for the bootstrap distribution of the VRATIO statistic.
TR: The TAU2RATIO statistic (relative change of the heterogeneity variance) by leave-one-out analysis.
Q2: alphath percentile for the bootstrap distribution of the TAU2RATIO statistic.

Examples

require(metafor)
data(finasteride)

edat3 <- escalc(m1i=m1,sd1i=s1,n1i=n1,m2i=m0,sd2i=s0,n2i=n0,
measure="MD",data=finasteride)

VRATIO(yi, vi, data=edat3, B=10)
# This is an example command for illustration. B should be >= 1000.

A multicenter clinical trial data assessing the treatment effect of finasteride for benign prostatic hyperplasia

Description

center: Center ID
n1: Number of observations in finasteride group
m1: Mean of the change of Boyarsky score from baseline in finasteride group
s1: SD of the change of Boyarsky score from baseline in finasteride group
n0: Number of observations in placebo group
m0: Mean of the change of Boyarsky score from baseline in placebo group
s0: SD of the change of Boyarsky score from baseline in placebo group

Usage

data(PPI)

Format

A data frame with 29 rows and 7 variables

References

Gormley, G. J., Stoner, E., Bruskewitz, R. C., et al. (1992). The effect of finasteride in men with benign prostatic hyperplasia. The Finasteride Study Group. New England Journal of Medicine. 327: 1185-1191. doi:10.1056/nejm199210223271701

Gould, A. L. (1998). Multi-centre trial analysis revisited. Statistics in Medicine. 17: 1779-1797.