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Empirical Assessment of Within-Arm Correlation Imputation in Trials of Continuous Outcomes
Methods Research Reports
Investigators: Ethan M Balk, MD, MPH, Amy Earley, BS, Kamal Patel, MPH, MBA, Thomas A Trikalinos, MD, PhD, and Issa J Dahabreh, MD, MS.
Author Information and AffiliationsStructured Abstract
Objectives:
To better understand how to impute within-arm correlation for meta-analyses of continuous outcomes when data are missing, this study describes the range of correlation values in a representative set of studies with sufficient data reported, and simulates the effect of using different correlation values on meta-analysis summary estimates when imputing missing data.
Background:
It is common that studies do not report sufficient data to allow meta-analysis of continuous outcomes. The standard error (SE) of the within-group differences is often not reported and cannot be calculated because the within-group correlation is unknown. For meta-analysis of net-changes, one must thus estimate the SE based on an arbitrarily chosen correlation.
Methods:
From articles available to us from previous systematic reviews and from trials registered at ClinicalTrials.gov, we selected those that prospectively compared two or more interventions for continuous outcomes and reported all three of: baseline means and SEs (or equivalent), final means and SEs, and within-group changes and SEs. From these data we back-calculated correlation values for each study group. We described these data and tested for patterns based on study characteristics. We assessed the bias on estimates of within-group change SEs by comparing reported SEs with imputed SEs using arbitrarily chosen correlation values. We simulated meta-analyses, assessing the bias, coverage, and accuracy of the summary estimates derived from studies with missing correlation data.
Results:
We analyzed 811 within-group correlation values from 123 studies with 281 study groups. The median (interquartile range) within-group correlation values across all studies was 0.59 (0.40, 0.81). Active treatment groups had lower correlation values (median 0.54) than no treatment groups (median 0.73, P<0.001). There was heterogeneity of correlation values across both outcome types and clinical domains. There was no apparent association with followup duration, but correlation values were lower with increasing sample size among no treatment groups. In the empiric dataset, imputing low correlation values (0 or 0.25) yielded an overestimation of the within-group SE in more than 85 percent of cases; imputing a correlation of 0.5 yielded values closer to those actually reported. Imputation had similar effects on the net-change SE. Simulation studies informed by the empirical results, demonstrated that imputation of values does not introduce bias in the meta-analysis estimate. Imputing values higher than the true correlation resulted in coverage probabilities that were lower than those in analyses using the complete data. However, coverage probabilities were generally lower than nominal (<0.95 even with complete data) in the presence of moderate to substantial between study heterogeneity, despite using random effects models (DerSimonian-Laird).
Conclusions:
Negative within-group correlation values are very uncommon in clinical studies. Imputing values in meta-analyses where some or all within-group correlation estimates are not reported does not introduce bias in the summary estimate of the treatment effect. However, imputation can affect the SE of the summary estimate when the imputed value is different from the “true.” In such cases, sensitivity analyses using alternative imputation values, possibly informed by studies reporting relevant information, are recommended.
Contents
- Preface
- Introduction
- Methods
- Results
- Aim 1 In a Representative Sample of Trials, Describe the Range of Correlation Values, r
- Aim 2 In a Representative Sample of Trials, Compare Values of the Net-Change SEs Derived From Reported Within-Group SEs, With the Net-Change SEs Derived From Estimating the Correlation Values, r
- Aim 3 By Simulation, Explore the Impact of Imputing a Range of Correlation Values, r, on Fixed and Random Effects Model Meta-Analyses
- Summary of Key Findings
- Discussion
- References
- Appendix A Detailed Simulation Methods
- Appendix B Additional Simulation Results
- Appendix C Included Studies
Prepared for: Agency for Healthcare Research and Quality, U.S. Department of Health and Human Services1, Contract No. 290-2007-10055-I Prepared by: Tufts Evidence-based Practice Center, Tufts Medical Center, Boston, MA
Suggested citation:
Balk EM, Earley A, Patel K, Trikalinos TA, Dahabreh IJ. Empirical Assessment of Within-Arm Correlation Imputation in Trials of Continuous Outcomes. Methods Research Report. (Prepared by the Tufts Evidence-based Practice Center under Contract No. 290-2007-10055-I.) AHRQ Publication No. 12(13)-EHC141-EF. Rockville, MD: Agency for Healthcare Research and Quality. November 2012. www.effectivehealthcare.ahrq.gov/reports/final.cfm.
This report is based on research conducted by the Tufts Evidence-based Practice Center (EPC) under contract to the Agency for Healthcare Research and Quality (AHRQ), Rockville, MD (Contract No. 290-2007-10055-I). The findings and conclusions in this document are those of the author(s), who are responsible for its contents; the findings and conclusions do not necessarily represent the views of AHRQ. Therefore, no statement in this report should be construed as an official position of AHRQ or of the U.S. Department of Health and Human Services.
The information in this report is intended to help health care decisionmakers—patients and clinicians, health system leaders, and policymakers, among others—make well-informed decisions and thereby improve the quality of health care services. This report is not intended to be a substitute for the application of clinical judgment. Anyone who makes decisions concerning the provision of clinical care should consider this report in the same way as any medical reference and in conjunction with all other pertinent information, i.e., in the context of available resources and circumstances presented by individual patients.
This report may be used, in whole or in part, as the basis for development of clinical practice guidelines and other quality enhancement tools, or as a basis for reimbursement and coverage policies. AHRQ or U.S. Department of Health and Human Services endorsement of such derivative products may not be stated or implied.
None of the investigators have any affiliations or financial involvement that conflicts with the material presented in this report.
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