β-Blockers in Congestive Heart Failure: A Bayesian Meta-Analysis

Congestive heart failure has reached pan-epidemic proportions in industrialized countries and is responsible for vast patient morbidity and mortality (1-4). Mortality associated with moderate to severe congestive heart failure may exceed that associated with many neoplasms, and the 1-year survival rate is as dismal as 50% (5). Quality of life is also adversely affected, and congestive heart failure is the most common cause of hospital admission in elderly persons in North America (6). Clearly, additional therapies are urgently needed. Randomized clinical trials are the gold standard for comparative research and have been used to investigate both new and old therapies for congestive heart failure. For example, trials have clearly demonstrated the beneficial effect of angiotensin-converting enzyme inhibitors on patient mortality (7), the neutral effect of digitalis (8), and the deleterious effects of other inotropic agents in congestive heart failure (9-11). Although conventional medical education previously viewed congestive heart failure as a contraindication for the use of -blockers because of their potential short-term negative inotropic effects, benefits of -blocker treatment in this condition have been sporadically reported since 1975 (12). Initially, these studies had only modest samples, thereby limiting definite conclusions. Subsequently, at least four meta-analyses of the cumulative experience of randomized trials with -blockers in heart failure were published (13-16). It is legitimate, therefore, to question whether another summary article is necessary. The answer appears to be affirmative for two reasons. First, results of the largest published trials of -blockers in congestive heart failure (17, 18) have not been included in previously published meta-analyses. With the new larger studies, we can provide a narrower confidence interval, so that clinical benefit is better estimated. Second, unlike previous meta-analyses, we used a Bayesian hierarchical random-effects model. Such a model has several advantages, including the ability to account for possible between-study variation, which may be an important consideration in a meta-analysis of trials covering 15 years and using a variety of -blockers. Methods Randomized trials of -blockers in congestive heart failure were identified by performing a systematic electronic review of the literature. The MEDLINE database was searched from 1966 to July 2000 by using the key words adrenergic -antagonists, congestive heart failure, and trial. This search produced 105 articles, which were hand searched for original randomized clinical trials that compared -blockers with placebo and had mortality as an outcome. Trials were excluded if they involved crossover designs, -blockers with intrinsic sympathomimetic activity, follow-up of less than 3 months, or patients admitted for acute myocardial infarction. This procedure identified 17 trials (17-34). The four meta-analyses (13-16) published in 1997 and 1998 were examined and yielded another 5 eligible trials (35-39). Finally, the Cochrane and the Web of Science databases were searched; no further trials were discovered. Patient variability and differences in trial design, inclusion and exclusion criteria, and target populations make it unrealistic to assume that the effects of -blockers estimated from each of these trials will be identical, as implied by a fixed-effects meta-analysis model. We therefore used a Bayesian hierarchical (random-effects) meta-analytic model (40) to analyze these 22 studies. Bayesian analysis produces direct probability statements calculated from the areas under probability distribution function curves, providing clear clinical interpretations of the accumulated data. In our Bayesian hierarchical model, we assume first that each arm of each study independently estimates the probability p ij of an event (death or hospitalization), where i indexes each study (so that i ranges from 1 to 22) and j indexes the study group (j = 0 for the placebo control group and 1 for the -blocker group). Since the follow-up period varied greatly among trials, we initially used the odds ratio as a measure of the effect size. The odds ratio for trial i is defined as or (i) = p (i1)/(1 p [i1])/p (i0)/(1 p [i0]). The collection of the logarithms of the odds ratios across the different trials is assumed to follow a normal distribution with mean and variance 2. Hence, represents the overall mean effect (odds ratios in probabilities) across studies, and 2 represents study-to-study variation. If 2 = 0, the model reduces to a fixed-effects model, whereas larger values of 2 represent increasing evidence of heterogeneity between the studies. We used diffuse prior distributions for and 2, so that all parameter estimates are almost entirely determined by the observed data. Histograms of log(or[i]) estimates across studies for both death and hospitalization outcomes showed that our normality assumptions were reasonable. Reporting results about allows us to estimate an overall average effect from all studies combined. Study-to-study variation can be considered by predicting what the odds ratio or (i) might be for the next study by selecting a rate from the normal distribution with mean and variance 2. In a random-effects model, we assume that the effect of the treatment varies from setting to setting. Clinicians must therefore understand that the mean effect does not necessarily apply to their individual practices, because their setting may not be like the average setting. By including both the between-study variability and the usual random variability, the clinician can interpret posterior densities and credible intervals (the Bayesian analogue to confidence intervals) as these findings apply to their clinics. Odds ratios are an attractive means of combining studies that have differing follow-up times; however, as a relative measure, odds ratios do not take into account absolute differences and may thereby obscure the clinical importance of an intervention. We therefore converted our results into probability distributions of the differences in survival at 1 year between patients receiving -blockers and placebo. To reliably estimate the contemporary annual baseline mortality rate among placebo recipients, we performed a hierarchical meta-analysis of the baseline rates in the three most recent and largest trials (17, 18, 28). Similar results were obtained by using the placebo arms from all trials published from 1993 onward (data not shown). In creating posterior distributions, we focused on the distribution of the next predicted study. The standard deviation of this distribution is larger than that of the posterior distribution of the mean difference between using -blockers or placebo because it includes between-study variation. The means of both distributions are, however, equal. Parameters from our models were estimated by using FAST*PRO software, version 1.0 (41, 42). Probability density distributions, although unfamiliar to most clinicians, are clinically friendly and supply simple, direct probability estimates to pertinent questions by measuring the area under the curve. This approach permits probability calculations not only relating to any interval null or alternative hypotheses but also to any range of clinically meaningful differences. Results Table 1 shows all of the included trials, along with pertinent patient and study characteristics. Earlier trials focused on patients with idiopathic cardiomyopathy, whereas recent trials have included a preponderance of patients with ischemic cardiomyopathy (Table 1). Overall, the different causes of congestive heart failure have been adequately represented (4127 patients with nonischemic causes and 6005 patients with ischemic causes). As in most cardiovascular clinical trials, more men (78%) than women were studied, and the average age was younger than is generally seen in routine clinical practice. Although most studies had broad eligibility criteria for functional class, patients with New York Heart Association (NYHA) class IV disease have been underrepresented (typically <5% of study samples). Most patients were receiving triple therapy for congestive heart failure; in particular, in recent studies, angiotensin-converting enzymes were used in more than 95% of patients. Table 1. Randomized, Controlled Clinical Trials Comparing -Blockers with Placebo in Stable Patients with Congestive Heart Failure Various -blockers have been studied, but most patients received metoprolol or bisoprolol (up to 200 mg/d); 1-selective agents (up to 10 mg/d); or carvedilol, a nonselective agent (up to 25 mg twice daily). Fifteen studies used a run-in period to assess drug tolerability and patient adherence. The overall rate of adverse events in the run-in periods was 5.3%. The overall quality of the trials was high; each followed a double-blinded protocol, and only one study had possible irregularities in the randomization process (22). Follow-up of randomly assigned patients was almost complete. The only minor methodologic flaw was lack of description of the randomization process in 18 of the 22 trials. Figures 1 and 2 show the original data on total mortality and need for hospital readmission for congestive heart failure. The obvious difference from earlier meta-analyses is the inclusion of data from the Cardiac Insufficiency Bisoprolol Study II (17) and the Metoprolol CR/XL Randomized Intervention Trial in congestive Heart Failure (18), which tripled the available evidence on which to base our conclusions. Before 1999, 3071 patients had undergone randomization in trials of -blockers in heart failure, but by July 2000, this number had increased to 10 135. There were 624 deaths among 4862 patients receiving placebo and 444 deaths among 5273 patients receiving -blocker therapy. Of the 10 135 patients studied, 85% have been enrolled in trials reporting since 1996; most of these trials were ended pre