Confidence intervals meta-analysis

A more recent area of application for meta-analysis is in the choice of the noninferiority margin, A. As mentioned in Section 12.8, A is often chosen as some proportion of the established treatment effect (over placebo) and meta-analysis can be used to obtain an estimate of that treatment effect and an associated confidence interval. 

The fixed effects model considers the studies that have been combined as the totality of all the studies conducted. An alternative approach considers the collection of studies included in the meta-analysis as a random selection of the studies that have been conducted or a random selection of those that could have been conducted. This results in a slightly changed methodology, termed the random effects model The mathematics for the two models is a little different and the reader is referred to Fleiss (1993), for example, for further details. The net effect, however, of using a random effects model is to produce a slightly more conservative analysis with wider confidence intervals. 

An important question in meta-analysis is the consistency of the results (i.e., its confidence interval). Thus, we not only want to know how much more effective a drug is but whether all the clinical trials agree on the size of the therapeutic effect. 

A meta-analysis for continuous data cannot be calculated unless the pertinent standard deviations are known. Unfortunately, clinical reports often give the sample size and mean ratings for the various groups but do not report the standard deviations (or standard error of the mean), which are necessary for effect size calculations. Thus, investigators should always report the indices of variability (e.g., confidence intervals, SDs) for the critical variables related to their primary hypothesis. 

The efficacy of chronic therapy with oral GPIIb/llla inhibitors has been assessed in five major randomized placebo-controlled trials (EXCITE, OPUS, SYMPHONY SYMPHONY II, and BRAVO) (63,64). These agents were associated with a statistically significant increase in mortality in three out of the five trials. A meta-analysis of these trials (n = 45,523) demonstrated a significant increase in mortality (2.8% vs. 2.1% for placebo, odds ratio 1.35, 95% confidence interval 1.15-1.61), mostly... 

Although the majority of randomized studies revealed only insignificant trends toward benefit in the general population, a meta-analysis of nine such studies performed from 1965 to 1987 (two were double-blinded and seven were open) revealed a significant mortality benefit with an odds ratio (OR) of 0.72 [95% confidence interval (Cl) = 0.57-0.90] (47). In the four most recent trials in the general population to date (48-50), only one presented a significant mortality benefit in the GIK infusion group (51). 

With the data included in the overview of Garg et al. (316), it is possible to calculate that 18 patients need to be treated for 90 days to avoid one death or one hospitalization for congestive heart failure (95% confidence interval [Cl] 16-23). This meta-analysis includes 32 trials with the ACE inhibitors captopril, enalapril, lisinopril, quinapril, ramipril, and perindopril. It is likely that high doses (for instance, lisinopril 35 mg daily) are more effective than low doses (lisinopril 5 mg daily) (302). Treating 30 patients for 4 years with a high dose of lisinopril (95% Cl 16-509) will avoid one hospitalization for cardiovascular reasons or one death in comparison with a low dose, without increasing the number of adverse effects requiring withdrawal from treatment. 

Fig. 15.1. Stroke risks at two and seven days measured in a systematic review of 18 independent cohorts, stratified according to study method and setting (Giles and Rothwell 2007). Cl, confidence interval p (het), p value for heterogeneity between studies p (sig), p value for overall significance of the meta-analysis of comparisons between studies.

Data from the previous three randomized controlled trials on postoperative nausea were appropriate for meta-analysis. The pooled absolute risk reduction for the incidence of postoperative nausea proved the difference between the groups treated with ginger and placebo to lack significance. These values indicate a point of the number-needed-to-treat of 19 and a 95% confidence interval that also includes the possibility of no benefit (16). 

Since the two meta-analyses in 1995, five prospective, randomized, controlled trials of low-dose corticosteroids in vasopressor-dependent septic shock patients (n = 505) have been published. " These smdies used moderate physiologic doses (200 to 300 mg/day) of hydrocortisone. A meta-analysis of these studies showed that steroid therapy was associated with an overall improvement in survival rate (odds ratio [OR] 1.52, 95% confidence interval [Cl] 1.03-2.27 p =. 036) and shock reversal (OR 4.79, 95% Cl 2.07-11.11 p =. 001). These effects were beneficial in both responders and nonresponders to corticotrophin stimulation testing (p =. 63 and p =. 75, respectively). These smdies also showed that low-dose corticosteroid administration improves hemodynamics and reduces the duration of vasopressor support. " All these studies differ from earlier smdies in that steroids were admimstered later in septic shock (23 hours versus less than 2 hours p =. 02). In these studies, steroids were administered longer (6 days versus 1 day p =. 004), doses were tapered, lower doses were used (hydrocortisone eqmvalents 1209 mg versus 23,975 mg p =. 01), aU patients received high doses of catecholamine vasopressors, and control groups had higher mortality rates (mean 57% versus 34% p =. 03). Since only one of the five studies showed a mortality benefit of low-dose steroids in septic shock, further research is required to confirm this finding. ... 

An efficient meta-analysis is supposed to summarize and use all the information from a series of trials. If this claim is true, then once the meta-analysis is available the results from the individual trials are no longer relevant. Suppose now that we have two meta-analyses each based on two trials and that the P-values in each case are highly significant and that the point estimates and confidence intervals are identical. Does it make any difference to know that in the one case (case A) both contributing trials were just significant and that in the second case (case B) one trial was more highly significant but the other not quite. If not, then the two-trials rule is superfluous. 

Meta-analysis may make small studies meaningful by providing a means to combine the results with those of other similar studies to enable estimates of an intervention s efficacy. Small trials may not be able to test a hypothesis, but they may provide valuable information of treatment effects using confidence intervals (Edwards et ai, 1997). Similarly, others argue that a sample size that results in a p value of 0.1 can be informative and decisions have to be made even where there is no trial evidence, a little unbiased evidence is better than none. A study might have only limited ability to detect an effect, but participants should be allowed to make an autonomous decision. 

There are important statistical considerations in meta-analyses for the evaluation of safety. In particular, statistical methods must be valid in the presence of sparse data. As discussed previously, safety outcomes may be infrequent. Some trials may not have any relevant events. We refer to these trials as zero-event trials. The statistical methods should provide estimates with good bias properties and with valid standard errors and confidence intervals in the presence of low event coimts and zero-event trials. In any meta-analysis, the overall estimator and associated standard errors and confidence intervals should be stratified by the trials. Simple pooling of data across the trials can result in misleading results because of Simspon s paradox. With stratification, the randomize comparisons within trials are maintained. 

A practical challenge of Bayesian meta-analysis for rare AE data is that noninformative priors may lead to convergence failure due to very sparse data. Weakly informative priors may be used to solve this issue. In the example of the previous Bayesian meta-analysis with piecewise exponential survival models, the following priors for log hazard ratio (HR) (see Table 14.1) were considered. Prior 1 assumes a nonzero treatment effect with a mean log(HR) of 0.7 and a standard deviation of 2. This roughly translates to that the 95% confidence interval (Cl) of HR is between 0.04 and 110, with an estimate of HR to be 2.0. Prior 2 assumes a 0 treatment effect, with a mean log(HR) of 0 and a standard deviation of 2. This roughly translates to the assumption that we are 95% sure that the HR for treatment effect is between 0.02 and 55, with an estimate of the mean hazard of 1.0. Prior 3 assumes a nonzero treatment effect that is more informative than that of Prior 1, with a mean log(HR) of 0.7 and a standard deviation of 0.7. This roughly translates to the assumption that we are 95% sure that the HR... 

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