The function meta-analyzes one-group or two-group studies where each study reports one of the following summary measures:

S1: median, minimum and maximum values, and sample size

S2: median, first and third quartiles, and sample size

S3: median, minimum and maximum values, first and third quartiles, and sample size

S4: mean, standard deivation, and sample size.

This function estimates the study-specific means and their standard errors from the S1, S2, S3, or S4 summary data. When studies report S1, S2, or S3 summary data, a number of approaches can be applied to estimate the study-specific means and their standard errors. Then, this function estimates the pooled mean (for one-group studies) or the pooled difference of means (for two-group studies) based on the standard inverse variance method via the `rma.uni`

function. The convention used for calculating differences of means in two-group studies is: mean in group 1 minus mean in group 2.

```
metamean(
data,
mean_method = "mln",
se_method,
sd_method,
nboot = 1000,
pool_studies = TRUE,
...
)
```

an object of class "rma.uni". See documentation of `rma.uni`

.

- data
data frame containing the study-specific summary data. For one-group studies, this data frame can contain the following columns:

`min.g1`

minimum value. `q1.g1`

first quartile. `med.g1`

median. `q3.g1`

third quartile. `max.g1`

maximum value. `n.g1`

sample size. `mean.g1`

sample mean. `sd.g1`

sample standard deviation. For two group studies, this data frame can also contain the following columns for the summary data of the second group:

`min.g2`

,`q1.g2`

,`med.g2`

,`q3.g2`

,`max.g2`

,`n.g2`

,`mean.g2`

, and`sd.g2`

.- mean_method
character string specifying the approach used to estimate the study-specific means. The options are the following:

`'hozo/wan/bland'`

Method recommended by Wan et al. (2014), i.e., the method of Hozo et al. (2005) in scenario S1, method of Wan et al. (2014) in scenario S2, and method of Bland (2015) in scenario S3. `'luo'`

Method of Luo et al. (2018). `'shi_lognormal'`

Method of Shi et al. (2020b). `'qe'`

Quantile Matching Estimation method (McGrath et al. 20220). `'bc'`

Box-Cox method (McGrath et al. 2020). `'mln'`

Method for Unknown Non-Normal Distributions (Cai et al. 2021). `'yang'`

Method of Yang et al. (2022) under the assumption of normality. - se_method
character string specifying the approach used to estimate the standard errors of the study-specific means estimators in scenarios S1, S2, and S3. The options are the following:

`'naive'`

Uses the estimated standard deviation divided by the square root of the sample size as the estimate of the standard error of the mean estimator. This is the default option when `mean_method`

is set to`'wan'`

,`'luo'`

, or`'shi_lognormal'`

. The approach used to estimate the standard deviation is specified by the`sd_method`

argument.`'bootstrap'`

Parametric bootstrap approach described by McGrath et al. (2023). This option is only available (and is the default option) when `mean_method`

is set to`'qe'`

,`'bc'`

, or`'mln'`

.`'plugin'`

Uses the analytically derived standard error of the mean estimator, and plugs in the estimated standard deviation in place of the distributional standard deviation. This option is only available (and is the default option) when `mean_method`

is set to`'yang'`

.- sd_method
character string specifying the approach used to estimate the study-specific standard deviations when applying the naive standard error estimator (if applicable). The options are the following:

`'wan'`

Method of Wan et al. (2014). This is the default option when `mean_method`

is set to`'hozo/wan/bland/hozo'`

.`'wan/shi_normal'`

Method recommended by Shi et al. (2020a), i.e., the method of Wan et al. (2014) in scenarios S1 and S2 and the method of Shi et al. (2020a) in scenario S3. This is the default option when `mean_method`

is set to`'luo'`

.`'shi_lognormal'`

Method of Shi et al. (2020b). This is the default option when `mean_method`

is set to`'shi_lognormal'`

.`'qe'`

Quantile Matching Estimation method (McGrath et al. 20220). This is the default option when `mean_method`

is set to`'qe'`

.`'bc'`

Box-Cox method (McGrath et al. 2020). This is the default option when `mean_method`

is set to`'bc'`

.`'mln'`

Method for Unknown Non-Normal Distributions (Cai et al. 2021). This is the default option when `mean_method`

is set to`'mln'`

.`'yang'`

Method of Yang et al. (2022) under the assumption of normality. This is the default option when `mean_method`

is set to`'yang'`

.- nboot
integer specifying the number of bootstrap samples to use when using parametric bootstrap to estimate the study-specific standard errors in scenarios S1, S2, and S3. The default is

`1000`

.- pool_studies
logical scalar specifying whether to meta-analyze the studies. If this argument is set to

`FALSE`

, function will not meta-analyze the studies and will return a list with components`yi`

containing the study-specific outcome measure estimates and`sei`

containing the study-specific within-study standard error estimates. The default is`TRUE`

.- ...
optional arguments that are passed into the

`rma.uni`

function for pooling. See documentation of`rma.uni`

.

Hozo S.P., Djulbegovic B., and Hozo I. (2005). Estimating the mean and variance from the median, range, and the size of a sample. *BMC Medical Research Methodology*. **5**(1):1-10.

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**(1):1-13.

Bland M. (2015). Estimating mean and standard deviation from the sample size, three quartiles, minimum, and maximum. *International Journal of Statistics in Medical Research*. **4**(1):57-64.

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*. **27**(6):1785-805.

Shi J., Luo D., Weng H., Zeng X.T., Lin L., Chu H., and Tong T. (2020a). Optimally estimating the sample standard deviation from the five-number summary. *Research synthesis methods*. **11**(5):641-654.

Shi J., Tong T., Wang Y., and Genton M.G. (2020b). Estimating the mean and variance from the five-number summary of a log-normal distribution. *Statistics and Its Interface*. **13**(4):519-531.

McGrath S., Zhao X., Steele R., Thombs B.D., Benedetti A., and the DEPRESsion Screening Data (DEPRESSD) Collaboration. (2020). Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis. *Statistical Methods in Medical Research*. **29**(9):2520-2537.

Cai S., Zhou J., and Pan J. (2021). Estimating the sample mean and standard deviation from order statistics and sample size in meta-analysis. *Statistical Methods in Medical Research*. **30**(12):2701-2719.

Yang X., Hutson A.D., and Wang D. (2022). A generalized BLUE approach for combining location and scale information in a meta-analysis. *Journal of Applied Statistics*. **49**(15):3846-3867.

McGrath S., Katzenschlager S., Zimmer A.J., Seitel A., Steele R., Benedetti A. (2023). Standard error estimation in meta-analysis of studies reporting medians. *Statistical Methods in Medical Research*. **32**(2):373-388.

```
# \donttest{
## Method for Unknown Non-Normal Distributions
metamean(data = dat.age, mean_method = "mln", se_method = "bootstrap", nboot = 50)
## Box-Cox method
metamean(data = dat.age, mean_method = "bc", se_method = "bootstrap", nboot = 50)
## Quantile Matching Estimation method
metamean(data = dat.age, mean_method = "qe", se_method = "bootstrap", nboot = 50)
# }
```

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