Interim analyses in clinical trials: Classical vs. bayesian approaches

This paper concerns interim analysis in clinical trials involving two treatments from the points of view of both classical and Bayesian inference. I criticize classical hypothesis testing in this setting and describe and recommend a Bayesian approach in which sampling stops when the probability that one treatment is the better exceeds a specified value. I consider application to normal sampling analysed in stages and evaluate the gain in average sample number as a function of the number of interim analyses.     

Robust bayesian methods for monitoring clinical trials

Bayesian methods for the analysis of clinical trials data have received increasing attention recently as they offer an approach for dealing with difficult problems that arise in practice. A major criticism of the Bayesian approach, however, has focused on the need to specify a single, often subjective, prior distribution for the parameters of interest. In an attempt to address this critism, we describe methods for assessing the robustness of the posterior distribution to the specification of the prior. The robust Bayesian approach to data analysis replaces the prior distribution with a class of prior distributions and investigations and investigates how the inferences might change as the prior varies over this class. The purpose of this paper is to illustrate the application of robust Bayesian methods to the analysis of clinical trials data. Using two examples of clinical trials taken from the literature, we illustrate how to use these methods to help a data monitoring committee decide whether or not to stop a trial early.     

Interim analyses with delayed observations in clinical trials.

The interim analyses based on group sequential procedures are not convenient if the response time relative to the patient accrual rate is long. Since in most trials patients are accrued and randomized continuously, the response data from those already randomized will continue to accumulate when a trial terminates at an interim test. One should analyse all observations received after the trial terminates along with the data that led to the decision to terminate the trial. Although the most likely case is that the combined results are significant, it could happen that the combined results are not significant. We examined the likelihood of such an event. Our study indicated that the O'Brien-Fleming type of group sequential tests with conservative boundaries in the early stages protects from such an unsettling event.     

Reporting clinical trials from the viewpoint of a patient's choice of treatment

Those who report a clinical trial should acknowledge the right of the 'consumer' to make decisions based on his own valuation of the beneficial and adverse effects which rival treatments may have. Suppose a new patient is inclined to trade one unit of benefit for c units of complication. Then he should (should not) be given the treatment if his estimated utility gain, x1-cx2, is positive (negative) and statistically significant according to the data of the trial; here x1 (x2) denotes the observed average benefit (complication level). If the estimated gain is not statistically significant, the data do not allow any firm recommendation. This c-dependent recommendation in general cannot be determined from inspection of a joint confidence region for the two means concerned. Therefore investigators should present the outcome of the significance test as a function of c (inverted inference). Typically there are several types of adverse effect or benefit, in which case the quantity c must be generalized into a vector of personal relative utility weights.     

Predicting survival in cost-effectiveness analyses based on clinical trials

This study deals with the question of how to model health effects after the cessation of a randomized controlled trial (RCT). By using clinical trial data on severe congestive heart failure patients, we illustrate how survival beyond the cessation of an RCT can be predicted based on parametric survival models. In the analysis, we compare predicted survival and the resulting incremental cost-effectiveness ratio (ICER) of different survival models with actual survival/ICER. Our main finding is that the results are sensitive to the choice of survival model and that an extensive sensitivity analysis in the CE analysis is required.     

On choosing the number of interim analyses in clinical trials

Small but important therapeutic effects of new treatments can be most efficiently detected through the study of large randomized prospective series of patients. Such large scale clinical trials are nowadays commonplace. The alternative is years of polemic and debate surrounding several trials each too small to detect plausible differences with any certainty. Such trials produce equivocal and contradictory results, which could be predicted from power calculations based upon sensible pre-trial estimates of treatment differences. Unfortunately such calculations often lead to sample sizes of several thousands. It is not surprising that investigators tend to be over-optimistic in their estimation of treatment effects (which are necessarily uncertain) especially when the sample size requirements are so stark. In this paper a method is outlined for incorporating into the sample size calculations the uncertainty of the estimate made at the design stage of a clinical trial. In particular a formal scheme is described for deciding how many interim analyses should be performed to satisfy ethical and pragmatic requirements of large clinical trial design. Although the argument will be ‘Bayesian’, the criteria for assessment and comparison will be strictly of a Neyman-Pearson (i.e. significance testing) kind.     

Reporting in randomized clinical trials improved after adoption of the CONSORT statement

OBJECTIVE: To examine the extent to which the Consolidated Standards of Reporting Trials (CONSORT) reporting guidelines improved clinical trials reporting and subject attrition, which may undermine the credibility of published randomized clinical trials (RCTs). STUDY DESIGN AND SETTING: Published RCTs reported in two major medical journals before and after the CONSORT guidelines were systematically reviewed; one used the CONSORT statement (JAMA) and one did not (NEJM). RESULTS: The quality of RCT reporting improved for both journals, but JAMA showed more significant and consistent improvements in all aspects of RCT reporting. Subject attrition was better accounted for after the publication of CONSORT, although the attrition rates for various reasons actually increased. Attrition due to unknown reasons, as a percentage of total attrition, declined dramatically, from 68.7% pre-CONSORT to 13.0% post-CONSORT. CONCLUSIONS: Attrition of study subjects remains a serious problem in RCTs. Bias from selective attrition can undermine the presumptive scientific advantage of RCTs. The CONSORT guidelines improved RCT reporting when they were implemented but did not substantially improve reported attrition rates.     

Interpretation of results from subset analyses within overviews of randomized clinical trials

Evaluating treatment effects within different subsets of patients is a common practice in the analysis of individual randomized clinical trials. Such analyses are limited, however, by the number of patients available. Overviews, by providing evidence based on large numbers of patients, can be useful for overcoming the difficulties of detecting therapeutic effects within subsets of patients. However, inconsistent subset definitions, misclassification of patients, and incomplete availability of patient subsets from the trials included in the overview bias the estimates of effect size. Separate analyses of subsets of studies are also possible within an overview. Studies being pooled generally differ with respect to treatments applied, control groups, patient eligibility, quality control, study conduct, and follow-up maturity. Separate comparisons within subsets defined by these features will be misinterpreted unless confounding factors are recognized. Indirect comparisons between overviews have the same informative value as nonrandomized trials with historical controls.     

Group sequential clinical trials for longitudinal data with analyses using summary statistics

Longitudinal endpoints are used in clinical trials, and the analysis of the results is often conducted using within-individual summary statistics. When these trials are monitored, interim analyses that include subjects with incomplete follow-up can give incorrect decisions due to bias by non-linearity in the true time trajectory of the treatment effect. Linear mixed-effects models can be used to remove this bias, but there is a lack of software to support both the design and implementation of monitoring plans in this setting. This paper considers a clinical trial in which the measurement time schedule is fixed (at least for pre-trial design), and the scientific question is parameterized by a contrast across these measurement times. This setting assures generalizable inference in the presence of non-linear time trajectories. The distribution of the treatment effect estimate at the interim analyses using the longitudinal outcome measurements is given, and software to calculate the amount of information at each interim analysis is provided. The interim information specifies the analysis timing thereby allowing standard group sequential design software packages to be used for trials with longitudinal outcomes. The practical issues with implementation of these designs are described; in particular, methods are presented for consistent estimation of treatment effects at the interim analyses when outcomes are not measured according to the pre-trial schedule. Splus/R functions implementing this inference using appropriate linear mixed-effects models are provided. These designs are illustrated using a clinical trial of statin treatment for the symptoms of peripheral arterial disease.     

ω-3脂肪乳干预临床研究中的把握度(Power)分析

临床营养研究中把握度(Power)(样本量计算)分析对于临床研究方案的设计至关重要,充足的把握度有助于保证临床研究结果的可信性和可靠性.本研究以ω-3脂肪乳干预的临床研究为例,对研究设计过程中的把握度分析进行描述.依据高质量文献报道数据以及Meta分析结果获得估计参数、按照不同参数对样本量进行设计、以及最终结合临床实际确定样本量规模.在此基础上,进一步采用模拟方法,对临床研究过程中可能出现的结果组合进行假设,给出了在所计算的样本量下,真实临床研究获得阳性或阴性结果所对应的各种情形.临床研究的样本量设计应兼顾临床和统计两方面的考虑.     

Reporting of noninferiority trials was incomplete in trial registries

Objective

To examine the registration of noninferiority trials, with a focus on the reporting of study design and noninferiority margins.

Study Design and Setting

Cross-sectional study of registry records of noninferiority trials published from 2005 to 2009 and records of noninferiority trials in the International Standard Randomized Controlled Trial Number (ISRCTN) or ClinicalTrials.gov trial registries. The main outcome was the proportion of records that reported the noninferiority design and margin.

Results

We analyzed 87 registry records of published noninferiority trials and 149 registry records describing noninferiority trials. Thirty-five (40%) of 87 records from published trials described the trial as a noninferiority trial; only two (2%) reported the noninferiority margin. Reporting of the noninferiority design was more frequent in the ISRCTN registry (13 of 18 records, 72%) compared with ClinicalTrials.gov (22 of 69 records, 32%; P = 0.002). Among the 149 records identified in the registries, 13 (9%) reported the noninferiority margin. Only one of the industry-sponsored trial compared with 11 of the publicly funded trials reported the margin (P = 0.001).

Conclusion

Most registry records of noninferiority trials do not mention the noninferiority design and do not include the noninferiority margin. The registration of noninferiority trials is unsatisfactory and must be improved.     

Causal mediation analyses for randomized trials

In the context of randomized intervention trials, we describe causal methods for analyzing how post-randomization factors constitute the process through which randomized baseline interventions act on outcomes. Traditionally, such mediation analyses have been undertaken with great caution, because they assume that the mediating factor is also randomly assigned to individuals in addition to the randomized baseline intervention (i.e., sequential ignorability). Because the mediating factors are typically not randomized, such analyses are unprotected from unmeasured confounders that may lead to biased inference. We review several causal approaches that attempt to reduce such bias without assuming that the mediating factor is randomized. However, these causal approaches require certain interaction assumptions that may be assessed if there is enough treatment heterogeneity with respect to the mediator. We describe available estimation procedures in the context of several examples from the literature and provide resources for software code.     

Incorporating intermediate binary responses into interim analyses of clinical trials: a comparison of four methods

In clinical trials with a long period of time between randomization and the primary assessment of the patient, the same assessments are often undertaken at intermediate times. When an interim analysis is conducted, in addition to the patients who have completed the primary assessment, there will be those who have till then undergone only intermediate assessments. The efficiency of the interim analysis can be increased by the inclusion of data from these additional patients. This paper compares four methods of increasing information based on model-free estimates of transition probabilities to incorporate intermediate assessments from patients who have not completed the trial. It is assumed that the observations are binary and that there is one intermediate assessment. The methods are the score and Wald approaches, each with the log-odds ratio and probability difference parameterizations. Simulations show that all four approaches have good properties in moderate to large sample sizes.     

Oncology clinical trials

In 1971, President Nixon declared a "war on cancer" and initiated substantial funding for the National Cancer Program, which has been sustained through the years with a significant return on investment. Recently released 1998 statistics from the National Cancer Institute (NCI), the Centers for Disease Control and Prevention, and the American Cancer Society show the first real decline in cancer since the 1930s. Still, more than 1.2 million Americans will be diagnosed with cancer this year. New developments in biomedicine and advances in science and technology likely will lead to greater declines in cancer incidence and mortality.     

Bias in frequently reported analyses of subfertility trials

Randomized controlled trials in subfertility are often designed so that participants in each trial arm are offered the randomized treatment for up to k cycles, until success occurs. In clinical journals, success probabilities are often reported 'per cycle' and inferential procedures carried out as if all cycles were independent. However, this assumption does not hold. In this paper we consider the implications of such an assumption when we have a heterogeneous (Beta) patient population. We conducted a simulation study to assess the bias of estimates of the risk difference, risk ratio and odds ratio calculated using the total number of randomized women or the total number of treatment cycles as the unit of analysis, as well as the coverage of their confidence intervals (CIs). We found that the commonly reported 'per cycle' analyses are more biased and have poorer coverage of the CIs than the analyses based on the total number of women, in heterogeneous populations. Such information will help researchers who wish to interpret publications when the number of randomized participants is not extractable.     

Reporting implementation in randomized trials: proposed additions to the consolidated standards of reporting trials statement

Randomized controlled trials of public health interventions are often complex: practitioners may not deliver interventions as researchers intended, participants may not initiate interventions and may not behave as expected, and interventions and their effects may vary with environmental and social context. Reports of randomized controlled trials can be misleading when they omit information about the implementation of interventions, yet such data are frequently absent in trial reports, even in journals that endorse current reporting guidelines. Particularly for complex interventions, the Consolidated Standards of Reporting Trials (CONSORT) statement does not include all types of information needed to understand the results of randomized controlled trials. CONSORT should be expanded to include more information about the implementation of interventions in all trial arms.     

Self-designing clinical trials

I present a method of sequential analysis for randomized clinical trials that allows use of all prior data in a trial to determine the use and weighting of subsequent observations. One continues to assign subjects until one has ‘used up’ all the variance of the test statistic. There are many strategies to determine the weights including Bayesian methods (though the proposal is a frequentist design). I explore further the self-designing aspect of the randomized trial to note that in some cases it makes good sense (i) to change the weighting on components of a multivariate endpoint, (ii) to add or drop treatment arms (especially in a parallel group dose ranging/efficacy/safety trial), (iii) to select sites to use as the trial goes on, (iv) to change the test statistic and (v) even to rethink the whole drug development paradigm to shorten drug development time while keeping current standards for the level of evidence necessary for approval. © 1998 John Wiley & Sons, Ltd.