Method for Calculating Point Estimates and Standard Errors for Meta‐Analysis from Reported Point Estimates, 95% Confidence Intervals, and P‐Values

Abstract

BackgroundThe quality of a meta‐analysis depends on accurate estimates from original publications. Existing back‐calculation methods for point estimates [e.g., odds ratios (ORs), log(ORs), or means] and standard errors (SEs) from reported point estimates and 95% confidence intervals (CIs) can create estimates that, when forward‐calculated, do not round to the originally reported values. This can be particularly true for ORs. A new method is proposed that incorporates information from the upper and lower CIs and point estimates, with examples of data encountered in a meta‐analysis of the associations between quick service restaurant foods and obesity.MethodsLog(ORs) and SEs are calculated using one of four methods: using the lower CI and the OR; the upper CI and the OR; the average SE from SEs calculated from the lower and upper CIs; and a new method that proposes to use the centroid of a region of values that satisfies the originally reported, rounded OR and CI (herein referred to as the Centroid Method). The methods are compared by simulating 10,000 2×2 tables, rounding the true OR and CI to 1 or 2 decimal places, and calculating the residuals between the log(OR) and SE determined through the four methods compared to the true log(OR) and SE. Extensions of the method are demonstrated for continuous data and under different distributional assumptions. The methods are compared using real examples from data extracted for a meta‐analysis of the associations between quick service restaurants and obesity.ResultsAll methods appear unbiased, but the proposed Centroid Method results in log(ORs) and SEs that deviate less from the simulated true log(ORs) and SEs. The improvement in estimates drops precipitously as the number of decimal places reported for ORs and CIs increases. The method can successfully restrict the region of possible values based on z or t distributional assumptions for the back‐calculation of CIs, and can further restrict the legal region by including reported p‐values. The Centroid Method allows for valid estimates of point estimates where the other methods failed, such as the case where a study reported an OR and 95% CI of 1.3 [1.1,1.7].ConclusionsThe proposed Centroid Method provides tighter estimates of log ORs and SEs for meta‐analyzing data reported as odds ratios with 95% confidence intervals; provides valid estimates where other methods fail; and can be used with different distributional assumptions and data types.Support or Funding InformationAWB was supported in part by NIDDK grant P30 DK056336. JAD was supported by startup funds provided by Texas Tech University through his department (Nutritional Sciences, College of Human Sciences) and the President Cluster Hire in Biostatistics and Bioinformatics (Center for Biotechnology and Genomics). The content is solely the responsibility of the authors and does not necessarily represent the official views of any organization.