Page 36 - JCTR-9-4

252 Shuster | Journal of Clinical and Translational Research 2023; 9(4): 246-252
Biostatisticians accept the fact that an unlucky dataset can yield of Myocardial Infarction and Death from Cardiovascular
misleading results, but they cannot accept misleading results Causes. N Engl J Med 2007;356:2457-71.
caused by the use of off-label statistical methodology. [4] Neto AS, Cardosa SO, Manetta JA, Pereira VG,
Acknowledgments Esposito DC, de Oliveira Prado Pasqualucci M, et al.
Association Between Use of Lung-Protective Ventilation
The author wishes to thank Editor, Dr. Michal Heger for his with Lower Tidal Volumes and Clinical Outcomes Among
critically important assistance in the write-up. Patients Without Acute Respiratory Distress Syndrome:
A Meta-Analysis. JAMA 2012;308:1651-9.
Funding
[5] Diamond GA, Kaul S. Rosiglitazone and Cardiovascular
This paper was entirely self-funded. The author has personal Risk. N Engl J Med 2007;357:938-9.
licenses for all software used. [6] Shuster JJ, Guo JD, Skyler JS. Meta-Analysis of Safety
Conflicts of Interest for Low Event-Rate Binomial Trials. Res Synth Methods
2012;3:30-50.
None. [7] Shuster JJ, Walker MA. Low-Event-Rate Meta-Analyses
References of Clinical Trials: Implementing Good Practices. Stat Med
2016;35:2467-78.
[1] Shuster JJ. Meta-Analysis 2020: A Dire Alert and a Fix. [8] Borenstein M, Hedges LV, Rothstein HR, Higgins JP.
Biostat Biom Open Access J 2021;10:73-8. Introduction to Meta-Analysis. New York, NY: John Wiley
[2] Borenstein M. Common Mistakes in Meta-Analysis and and Sons; 2009.
How to Avoid Them. Englewood, NJ: Biostat Inc.; 2019. [9] Shuster JJ. Nonparametric Optimality of the Sample Mean
[3] Nissen SE, Wolski K. Effect of Rosiglitazone on the Risk and Sample Variance. Am Stat 1982;36:176-8.

APPENDIX

(A) How to obtain free software: between-study variance (minimum variance unbiased) per Shuster
[9]. It is superior to (less random) than the mainstream estimate
To obtain free quality assured software to help you analyze a of σ . It follows from Assumptions A1 and A2 that (M-1) S /σ
2
2
2
collection of randomized clinical trials, download, and save the are independent and have Chi-square distributions with degrees of
j
three files from the Website freedom (M-1) where M is the number of studies being combined.
https://biostat.ufl.edu/research/faculty-developed-software/ The ratio F = S /S has a central F-distribution with degrees of
2
2
2
1
There is a user-friendly User’s Guide and two Excel templates, one freedom M-1 for both the numerator and denominator.
for relative risk and one for differences in means and proportions. A meta-analysis of eight studies would have a 61% chance
There are two real worked examples that guide you through the that the larger of the two sample variances would be at least 50%
data input and interpretation of the results. larger than the smaller. The between-study variance is therefore a
seriously random variable making the mainstream weights, which
(B) This part of the appendix is for readers with some rely heavily on the between-study variance, seriously random
statistical training:
variables. The mainstream reliance on the weights being near
Quantification of the randomness of the between-study variance, constants is not supportable.
a key component of the weights Why the ratio estimates are expected to perform well in their
Suppose we look at the true between-study variance in the urn
(Assumption A1) denoted by σ and suppose “an informer” had the target population
2
true study-specific effect sizes for the completed studies in the meta- The relative risk and difference of means and proportions are
analysis. Suppose she denotes the unweighted sample variance of calculated as the ratio of sample means. Both the numerator and
two independent repetitions of these true study-specific effect sizes denominator are optimal (i.e., nonparametric minimum variance
by S (j = 1,2) and provides us only with this value. Absent additional unbiased estimators per Shuster [9]) for their corresponding
2
j
extraneous information, S (j = 1,2) are each optimal estimates of its population parameter.
2
j

Publisher’s note
AccScience Publishing remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.
DOI: http://dx.doi.org/10.18053/jctres.09.202304.22-00019