mln.mean.sd: Method for unknown non-normal distributions (MLN) approach...

In estmeansd: Estimating the Sample Mean and Standard Deviation from Commonly Reported Quantiles in Meta-Analysis

Method for unknown non-normal distributions (MLN) approach for estimating the sample mean and standard deviation

Description

This function applies the Method for Unknown Non-Normal Distributions (MLN) approach to estimate the sample mean and standard deviation from a study that presents one of the following sets of summary statistics:

• 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

Usage

mln.mean.sd(min.val, q1.val, med.val, q3.val, max.val, n)

Arguments

min.val	numeric value giving the sample minimum.
q1.val	numeric value giving the sample first quartile.
med.val	numeric value giving the sample median.
q3.val	numeric value giving the sample third quartile.
max.val	numeric value giving the sample maximum.
n	numeric value giving the sample size.

Details

Like the Box-Cox method of McGrath et al. (2020), the MLN method of Cai et al. (2021) assumes that the underlying distribution is normal after applying a suitable Box-Cox transformation with power parameter \lambda. Specifically, the MLN method consists of the following steps, outlined below.

First, a maximum likelihood approach is used to estimate the power parameter \lambda, where the methods of Luo et al. (2016) and Wan et al. (2014) are applied to estimate the mean and standard deviation of the distribution of the transformed data. Then, a second round estimate of the mean and standard deviation of the distribution of the transformed data is obtained by maximum likelihood estimation conditional on the estimated power parameter. Finally, the inverse transformation is applied to estimate the sample mean and standard deviation of the original, untransformed data.

Value

A object of class mln.mean.sd. The object is a list with the following components:

est.mean	Estimated sample mean.
est.sd	Estimated sample standard deviation.
location	Estimated mean of the Box-Cox transformed data.
scale	Estimated standard deviation of the Box-Cox transformed data.
shape	Estimated transformation parameter \lambda.
bc.norm.rvs	The random variables generated by the Box-Cox (or, equivalently, power-normal) distribution during the Monte Carlo simulation.
...	Some additional elements.

The results are printed with the print.mln.mean.sd function.

References

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.

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.

Box G.E.P., and D.R. Cox. (1964). An analysis of transformations. Journal of the Royal Statistical Society Series B. 26(2):211-52.

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

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.

Examples

## Generate S2 summary data
set.seed(1)
n <- 100
x <- stats::rlnorm(n, 2.5, 1)
quants <- stats::quantile(x, probs = c(0.25, 0.5, 0.75))
obs.mean <- mean(x)
obs.sd <- stats::sd(x)

## Estimate the sample mean and standard deviation using the MLN method
mln.mean.sd(q1.val = quants[1], med.val = quants[2], q3.val = quants[3],
    n = n)

estmeansd documentation built on May 29, 2024, 7:11 a.m.