Review Article
Imputing variance estimates do not alter the conclusions of a meta-analysis with continuous outcomes: a case study of changes in renal function after living kidney donation

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Abstract

Objective

To assess how different imputation methods used to account for missing variance data in primary studies influence tests of heterogeneity and pooled results from a meta-analysis with continuous outcomes.

Study Design and Setting

Point and variance estimates for changes in serum creatinine, glomerular filtration rate, systolic blood pressure, and diastolic blood pressure were variably reported among 48 primary longitudinal studies of living kidney donors (71%–78% of point estimates were reported, 8%–13% of variance data were reported). We compared the results of meta-analysis, which either were restricted to available data or used four methods to impute missing variance data. These methods used reported P-values, reported nonparametric summaries, results from other similar studies using multiple imputation, or results from estimated correlation coefficients.

Results

Significant heterogeneity was present in all four outcomes regardless of the imputation methods applied. The random effects point estimates and 95% confidence intervals varied little across imputation methods, and the differences were not clinically significant.

Conclusions

Different methods to impute the variance data in the primary studies did not alter the conclusions from this meta-analysis of continuous outcomes. Such reproducibility increases confidence in the results. However, as with most meta-analyses, there was no gold standard of truth, and results must be interpreted judiciously. The generalization of these findings to other meta-analyses, which differ in outcomes, missing data, or between-study heterogeneity, requires further consideration.

Introduction

In a meta-analysis of continuous outcomes, both a point estimate of effect size and an estimate of its variance are required from each of the primary studies. The inverse of the variance estimate is used to provide the weight each study exerts in determining the fixed pooled estimate, and the sum of the weights is used to calculate the standard error and hence the confidence interval of the pooled estimate. When summarizing all the relevant literature for any given question, it is almost certain that the variance estimate for the estimated effect of interest will not be reported in some of the primary studies. Attempts to obtain relevant data from the primary authors are often not fruitful, and excluding such studies from all main or supplementary analyses may introduce bias [1]. There are several methods to impute variance estimates when they are missing [1], [2], [3], [4], [5]. However, it is unclear how the use of these various imputation methods influences the results of meta-analysis. Here in a review of live kidney donors, we examined how these imputation methods influenced tests of heterogeneity, and the pooled point estimate and 95% confidence interval derived from a random effects model.

Section snippets

Clinical context of case study

Despite its advantages, living kidney donation remains a complex moral, medical, and economic issue. The premise for accepting living donors is that the “minimal” risk of short- and long-term medical harm realized by the donor is outweighed by the definite advantages to the recipient and potential psychosocial benefits of altruism to the donor. The short-term medical consequences of living donation are well established. The immediate medical risk of the operative procedure is a mortality rate

No imputation: limit meta-analysis to studies with complete data

Studies that reported the change variance estimate were pooled, although there were very few such studies. As predicted by Follmann et al. [3], the results from studies with reported estimates varied from the pooled estimates, which also used imputed variance estimates (Fig. 2, Fig. 3). In addition, the confidence intervals of the pooled estimates calculated only from reported estimates were much larger than those calculated from imputation methods in all outcomes except for the decrement in

Discussion

In a case study exploring the influence of imputation methods on a meta-analysis of the changes in renal function in living kidney donors, random effects point and variance estimates varied slightly across imputation methods. Over 85% of primary authors were contacted, but in most cases they did not provide the requested data. If one only considered those few studies where complete data were reported, then the pooled results obtained appeared unrepresentative of the total available evidence.

Acknowledgments

We thank investigators in the Donor Nephrectomy Outcomes Research Network who abstracted data for the original meta-analysis: Bob Yang, Greg Knoll, Ramesh Prasad, Neil Boudville, Norman Muirhead, Patricia Rosas-Arellano, and Abdulrahman Housawi. We acknowledge the work of Jan Challis, MLIS who provided administrative help. Finally, we thank the 30 authors of the included studies who generously confirmed and provided information and performed additional analyses for this review.

This review was

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