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A simple method for analyzing data from a randomized trial with a missing binary outcome.

ABSTRACT: BACKGROUND: Many randomized trials involve missing binary outcomes. Although many previous adjustments for missing binary outcomes have been proposed, none of these makes explicit use of randomization to bound the bias when the data are not missing at random. METHODS: We propose a novel approach that uses the randomization distribution to compute the anticipated maximum bias when missing at random does not hold due to an unobserved binary covariate (implying that missingness depends on outcome and treatment group). The anticipated maximum bias equals the product of two factors: (a) the anticipated maximum bias if there were complete confounding of the unobserved covariate with treatment group among subjects with an observed outcome and (b) an upper bound factor that depends only on the fraction missing in each randomization group. If less than 15% of subjects are missing in each group, the upper bound factor is less than.18. RESULTS: We illustrated the methodology using data from the Polyp Prevention Trial. We anticipated a maximum bias under complete confounding of.25. With only 7% and 9% missing in each arm, the upper bound factor, after adjusting for age and sex, was.10. The anticipated maximum bias of.25 x.10 =.025 would not have affected the conclusion of no treatment effect. CONCLUSION: This approach is easy to implement and is particularly informative when less than 15% of subjects are missing in each arm.

SUBMITTER: Baker SG

PROVIDER: S-EPMC194902 | biostudies-literature | 2003 May

REPOSITORIES: biostudies-literature

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A simple method for analyzing data from a randomized trial with a missing binary outcome.

Baker Stuart G SG Freedman Laurence S LS

BMC medical research methodology 20030506

<h4>Background</h4>Many randomized trials involve missing binary outcomes. Although many previous adjustments for missing binary outcomes have been proposed, none of these makes explicit use of randomization to bound the bias when the data are not missing at random.<h4>Methods</h4>We propose a novel approach that uses the randomization distribution to compute the anticipated maximum bias when missing at random does not hold due to an unobserved binary covariate (implying that missingness depends ...[more]

PMID: 12734019

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Project description:BackgroundMissing participant outcome data (MOD) are ubiquitous in systematic reviews with network meta-analysis (NMA) as they invade from the inclusion of clinical trials with reported participant losses. There are available strategies to address aggregate MOD, and in particular binary MOD, while considering the missing at random (MAR) assumption as a starting point. Little is known about their performance though regarding the meta-analytic parameters of a random-effects model for aggregate binary outcome data as obtained from trial-reports (i.e. the number of events and number of MOD out of the total randomised per arm).MethodsWe used four strategies to handle binary MOD under MAR and we classified these strategies to those modelling versus excluding/imputing MOD and to those accounting for versus ignoring uncertainty about MAR. We investigated the performance of these strategies in terms of core NMA estimates by performing both an empirical and simulation study using random-effects NMA based on electrical network theory. We used Bland-Altman plots to illustrate the agreement between the compared strategies, and we considered the mean bias, coverage probability and width of the confidence interval to be the frequentist measures of performance.ResultsModelling MOD under MAR agreed with exclusion and imputation under MAR in terms of estimated log odds ratios and inconsistency factor, whereas accountability or not of the uncertainty regarding MOD affected intervention hierarchy and precision around the NMA estimates: strategies that ignore uncertainty about MOD led to more precise NMA estimates, and increased between-trial variance. All strategies showed good performance for low MOD (<5%), consistent evidence and low between-trial variance, whereas performance was compromised for large informative MOD (>?20%), inconsistent evidence and substantial between-trial variance, especially for strategies that ignore uncertainty due to MOD.ConclusionsThe analysts should avoid applying strategies that manipulate MOD before analysis (i.e. exclusion and imputation) as they implicate the inferences negatively. Modelling MOD, on the other hand, via a pattern-mixture model to propagate the uncertainty about MAR assumption constitutes both conceptually and statistically proper strategy to address MOD in a systematic review.

Project description:BackgroundA number of strategies have been proposed to handle missing binary outcome data (MOD) in systematic reviews. However, none of these have been evaluated empirically in a series of published systematic reviews.MethodsUsing published systematic reviews with network meta-analysis (NMA) from a wide range of health-related fields, we evaluated comparatively the most frequently described Bayesian modelling strategies for MOD in terms of log odds ratio (log OR), between-trial variance, inconsistency factor (i.e. difference between direct and indirect estimates for a comparison), surface under the cumulative ranking (SUCRA) and rankings. We extended the Bayesian random-effects NMA model to incorporate the informative missingness odds ratio (IMOR) parameter, and applied the node-splitting approach to investigate inconsistency locally. We considered both pattern-mixture and selection models, different structures for prior distribution of log IMOR, and different scenarios for MOD. To illustrate level of agreement between different strategies and scenarios, we used Bland-Altman plots.ResultsAddressing MOD using extreme scenarios and ignoring the uncertainty about the scenarios led to systematically different and more precise log ORs compared to modelling MOD under the missing at random (MAR) assumption. Hierarchical structure of log IMORs led to lower between-trial variance, especially in the case of substantial MOD. Assuming common-within-network or trial-specific log IMORs yielded similar posterior results for all NMA estimates, whereas intervention-specific structure systematically inflated uncertainty around log ORs and SUCRAs. Pattern-mixture model agreed with selection model, particularly under the trial-specific structure; however, selection model systematically reduced precision around log IMORs. Overall, different strategies and scenarios mostly had good agreement in the case of low MOD.ConclusionsAddressing MOD using extreme scenarios and/or ignoring the uncertainty about the scenarios may negatively affect NMA estimates. Modelling MOD via the IMOR parameter can ensure bias-adjusted estimates and offer valuable insights into missingness mechanisms. The researcher should seek an expert opinion in order to decide on the structure of log IMOR that best aligns to the condition and interventions studied and to define a proper prior distribution for log IMOR. Our findings also apply to pairwise meta-analyses.

Project description:BackgroundTrials with binary outcomes can be synthesised using within-trial exact likelihood or approximate normal likelihood in one-stage or two-stage approaches, respectively. The performance of the one-stage and the two-stage approaches has been documented extensively in the literature. However, little is known about how these approaches behave in the presence of missing outcome data (MOD), which are ubiquitous in clinical trials. In this work, we compare the one-stage versus two-stage approach via a pattern-mixture model in the network meta-analysis using Bayesian methods to handle MOD appropriately.MethodsWe used 29 published networks to empirically compare the two approaches concerning the relative treatment effects of several competing interventions and the between-trial variance (?2), while considering the extent and level of balance of MOD in the included trials. We additionally conducted a simulation study to compare the competing approaches regarding the bias and width of the 95% credible interval of the (summary) log odds ratios (OR) and ?2 in the presence of moderate and large MOD.ResultsThe empirical study did not reveal any systematic bias between the compared approaches regarding the log OR, but showed systematically larger uncertainty around the log OR under the one-stage approach for networks with at least one small trial or low event risk and moderate MOD. For these networks, the simulation study revealed that the bias in log OR for comparisons with the reference intervention in the network was relatively higher in the two-stage approach. Contrariwise, the bias in log OR for the remaining comparisons was relatively higher in the one-stage approach. Overall, bias increased for large MOD. For these networks, the empirical results revealed slightly higher ?2 estimates under the one-stage approach irrespective of the extent of MOD. The one-stage approach also led to less precise log OR and ?2 when compared with the two-stage approach for large MOD.ConclusionsDue to considerable bias in the log ORs overall, especially for large MOD, none of the competing approaches was superior. Until a more competent model is developed, the researchers may prefer the one-stage approach to handle MOD, while acknowledging its limitations.

Project description:BACKGROUND:Randomised controlled trials (RCTs) need to be reported so that their results can be unambiguously and robustly interpreted. Binary outcomes yield unique challenges, as different analytical approaches may produce relative, absolute, or no treatment effects, and results may be particularly sensitive to the assumptions made about missing data. This review of recently published RCTs aimed to identify the methods used to analyse binary primary outcomes, how missing data were handled, and how the results were reported. METHODS:Systematic review of reports of RCTs published in January 2019 that included a binary primary outcome measure. We identified potentially eligible English language papers on PubMed, without restricting by journal or medical research area. Papers reporting the results from individually randomised, parallel-group RCTs were included. RESULTS:Two hundred reports of RCTs were included in this review. We found that 64% of the 200 reports used a chi-squared-style test as their primary analytical method. Fifty-five per cent (95% confidence interval 48% to 62%) reported at least one treatment effect measure, and 38% presented only a p value without any treatment effect measure. Missing data were not always adequately described and were most commonly handled using available case analysis (69%) in the 140 studies that reported missing data. Imputation and best/worst-case scenarios were used in 21% of studies. Twelve per cent of articles reported an appropriate sensitivity analysis for missing data. CONCLUSIONS:The statistical analysis and reporting of treatment effects in reports of randomised trials with a binary primary endpoint requires substantial improvement. Only around half of the studied reports presented a treatment effect measure, hindering the understanding and dissemination of the findings. We also found that published trials often did not clearly describe missing data or sensitivity analyses for these missing data. Practice for secondary endpoints or observational studies may differ.

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A simple method for analyzing data from a randomized trial with a missing binary outcome.

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A simple method for analyzing data from a randomized trial with a missing binary outcome.

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