Early decision in clinical trials when the treatment differences are small. Experience of a controlled trial in head trauma

Seamless phase 2/3 design for trials with multiple co-primary endpoints using Bayesian predictive power

Seamless phase 2/3 design has become increasingly popular in clinical trials with a single endpoint. Trials that define success based on the achievement of all co-primary endpoints (CPEs) encounter the challenge of inflated type 2 error rates, often leading to an overly large sample size. To tackle this challenge, we introduced a seamless phase 2/3 design strategy that employs Bayesian predictive power (BPP) for futility monitoring and sample size re-estimation at interim analysis. The correlations among multiple CPEs are incorporated using a Dirichlet-multinomial distribution. An alternative approach based on conditional power (CP) was also discussed for comparison. A seamless phase 2/3 vaccine trial employing four binary endpoints under the non-inferior hypothesis serves as an example. Our results spotlight that, in scenarios with relatively small phase 2 sample sizes (e.g., 50 or 100 subjects), the BPP approach either outperforms or matches the CP approach in terms of overall power. Particularly, with n1 = 50 and ρ = 0, BPP showcases an overall power advantage over CP by as much as 8.54%. Furthermore, when the phase 2 stage enrolled more subjects (e.g., 150 or 200), especially with a phase 2 sample size of 200 and ρ = 0, the BPP approach evidences a peak difference of 5.76% in early stop probability over the CP approach, emphasizing its better efficiency in terminating futile trials. It's noteworthy that both BPP and CP methodologies maintained type 1 error rates under 2.5%. In conclusion, the integration of the Dirichlet-Multinominal model with the BPP approach offers improvement in certain scenarios over the CP approach for seamless phase 2/3 trials with multiple CPEs.

Statistical Power Analysis in Reliability Demonstration Testing: The Probability of Test Success

Statistical power analyses are used in the design of experiments to determine the required number of specimens, and thus the expenditure, of a test. Commonly, when analyzing and planning life tests of technical products, only the confidence level is taken into account for assessing uncertainty. However, due to the sampling error, the confidence interval estimation varies from test to test; therefore, the number of specimens needed to yield a successful reliability demonstration cannot be derived by this. In this paper, a procedure is presented that facilitates the integration of statistical power analysis into reliability demonstration test planning. The Probability of Test Success is introduced as a metric in order to place the statistical power in the context of life test planning of technical products. It contains the information concerning the probability that a life test is capable of demonstrating a required lifetime, reliability, and confidence. In turn, it enables the assessment and comparison of various life test types, such as success run, non-censored, and censored life tests. The main results are four calculation methods for the Probability of Test Success for various test scenarios: a general method which is capable of dealing with all possible scenarios, a calculation method mimicking the actual test procedure, and two analytic approaches for failure-free and failure-based tests which make use of the central limit theorem and asymptotic properties of several statistics, and therefore simplify the effort involved in planning life tests. The calculation methods are compared and their respective advantages and disadvantages worked out; furthermore, the scenarios in which each method is to be preferred are illustrated. The applicability of the developed procedure for planning reliability demonstration tests using the Probability of Test Success is additionally illustrated by a case study.

Interim Monitoring for Futility in Clinical Trials with Two Co-primary Endpoints Using Prediction

We discuss using prediction as a flexible and practical approach for monitoring futility in clinical trials with two co-primary endpoints. This approach is appealing in that it provides quantitative evaluation of potential effect sizes and associated precision, and can be combined with flexible error-spending strategies. We extend prediction of effect size estimates and the construction of predicted intervals to the two co-primary endpoints case, and illustrate interim futility monitoring of treatment effects using prediction with an example. We also discuss alternative approaches based on the conditional and predictive powers, compare these methods and provide some guidance on the use of prediction for better decision in clinical trials with co-primary endpoints.

Optimal and lead-in adaptive allocation for binary outcomes: a comparison of Bayesian methodologies

We compare posterior and predictive estimators and probabilities in response-adaptive randomization designs for two- and three-group clinical trials with binary outcomes. Adaptation based upon posterior estimates are discussed, as are two predictive probability algorithms: one using the traditional definition, the other using a skeptical distribution. Optimal and natural lead-in designs are covered. Simulation studies show: efficacy comparisons lead to more adaptation than center comparisons, though at some power loss; skeptically predictive efficacy comparisons and natural lead-in approaches lead to less adaptation but offer reduced allocation variability. Though nuanced, these results help clarify the power-adaptation trade-off in adaptive randomization.

CP function: an alpha spending function based on conditional power

Alpha spending function and stochastic curtailment are two frequently used methods in group sequential design. In the stochastic curtailment approach, the actual type I error probability cannot be well controlled within the specified significance level. But conditional power (CP) in stochastic curtailment is easier to be accepted and understood by clinicians. In this paper, we develop a spending function based on the concept of conditional power, named CP function, which combines desirable features of alpha spending and stochastic curtailment. Like other two-parameter functions, CP function is flexible to fit the needs of the trial. A simulation study is conducted to explore the choice of CP boundary in CP function that maximizes the trial power. It is equivalent to, even better than, classical Pocock, O'Brien-Fleming, and quadratic spending function as long as a proper ρ0 is given, which is pre-specified CP threshold for efficacy. It also well controls the overall type I error type I error rate and overcomes the disadvantage of stochastic curtailment.

The utility of Bayesian predictive probabilities for interim monitoring of clinical trials

BACKGROUND

Bayesian predictive probabilities can be used for interim monitoring of clinical trials to estimate the probability of observing a statistically significant treatment effect if the trial were to continue to its predefined maximum sample size.

PURPOSE

We explore settings in which Bayesian predictive probabilities are advantageous for interim monitoring compared to Bayesian posterior probabilities, p-values, conditional power, or group sequential methods.

RESULTS

For interim analyses that address prediction hypotheses, such as futility monitoring and efficacy monitoring with lagged outcomes, only predictive probabilities properly account for the amount of data remaining to be observed in a clinical trial and have the flexibility to incorporate additional information via auxiliary variables.

LIMITATIONS

Computational burdens limit the feasibility of predictive probabilities in many clinical trial settings. The specification of prior distributions brings additional challenges for regulatory approval.

CONCLUSIONS

The use of Bayesian predictive probabilities enables the choice of logical interim stopping rules that closely align with the clinical decision-making process.

A sequential conditional probability ratio test procedure for comparing diagnostic tests

In this paper, we derive sequential conditional probability ratio tests to compare diagnostic tests without distributional assumptions on test results. The test statistics in our method are nonparametric weighted areas under the receiver-operating characteristic curves. By using the new method, the decision of stopping the diagnostic trial early is unlikely to be reversed should the trials continue to the planned end. The conservatism reflected in this approach to have more conservative stopping boundaries during the course of the trial is especially appealing for diagnostic trials since the end point is not death. In addition, the maximum sample size of our method is not greater than a fixed sample test with similar power functions. Simulation studies are performed to evaluate the properties of the proposed sequential procedure. We illustrate the method using data from a thoracic aorta imaging study.

Predicted Interval Plots (PIPS): A Graphical Tool for Data Monitoring of Clinical Trials

Group sequential designs are often used in clinical trials to evaluate efficacy and/or futility. Many methods have been developed for different types of endpoints and scenarios. However, few of these methods convey information regarding effect sizes (e.g., treatment differences) and none uses prediction to convey information regarding potential effect size estimates and associated precision, with trial continuation. To address these limitations, Evans et al. (2007) proposed to use prediction and predicted intervals as a flexible and practical tool for quantitative monitoring of clinical trials. In this article, we reaffirm the importance and usefulness of this innovative approach and introduce a graphical summary, predicted interval plots (PIPS), to display the information obtained in the prediction process in a straightforward yet comprehensive manner. We outline the construction of PIPS and apply this method in two examples. The results and the interpretations of the PIPS are discussed.

A predictive probability design for phase II cancer clinical trials

BACKGROUND

Two- or three-stage designs are commonly used in phase II cancer clinical trials. These designs possess good frequentist properties and allow early termination of the trial when the interim data indicate that the experimental regimen is inefficacious. The rigid study design, however, can be difficult to follow exactly because the response has to be evaluated at prespecified fixed number of patients.

PURPOSE

Our goal is to develop an efficient and flexible design that possesses desirable statistical properties.

METHODS

A flexible design based on Bayesian predictive probability and the minimax criterion is constructed. A three-dimensional search algorithm is implemented to determine the design parameters.

RESULTS

The new design controls type I and type II error rates, and allows continuous monitoring of the trial outcome. Consequently, under the null hypothesis when the experimental treatment is not efficacious, the design is more efficient in stopping the trial earlier, which results in a smaller expected sample size. Exact computation and simulation studies demonstrate that the predictive probability design possesses good operating characteristics.

LIMITATIONS

The predictive probability design is more computationally intensive than two- or three-stage designs. Similar to all designs with early stopping due to futility, the resulting estimate of treatment efficacy may be biased.

CONCLUSIONS

The predictive probability design is efficient and remains robust in controlling type I and type II error rates when the trial conduct deviates from the original design. It is more adaptable than traditional multi-stage designs in evaluating the study outcome, hence, it is easier to implement. S-PLUS/R programs are provided to assist the study design.

Sample size reestimation by Bayesian prediction

We review a Bayesian predictive approach for interim data monitoring and propose its application to interim sample size reestimation for clinical trials. Based on interim data, this approach predicts how the sample size of a clinical trial needs to be adjusted so as to claim a success at the conclusion of the trial with an expected probability. The method is compared with predictive power and conditional power approaches using clinical trial data. Advantages of this approach over the others are discussed.

Predictive probability of success and the assessment of futility in large outcomes trials

We consider a class of futility rules based on a Bayesian approach for computing the predictive probability of success for large clinical trials, given a certain amount of observed data. This paper focuses on outcomes trials in particular, thus we are concerned with binary response variables. The proposed method determines the likelihood of observing a statistically significant treatment effect at the end of a study, conditional on the data observed at an interim time point and assuming that event rates governing future observations follow beta distributions. In particular, the prior distributions for the event rates of interest are updated based on the observed data at an interim time point, such that means and variances are intuitive functions of the data. Computational aspects will be discussed for the case in which event counts are functions of sample size and event rates only, and for situations in which they are functions of sample size, event rates, and exposure duration. We will discuss appropriate thresholds for declaring futility based on this approach, and the potential impact of overdispersion, a common phenomenon particularly in global outcomes trials.

Stochastically curtailed phase II clinical trials

Phase II trials often test the null hypothesis H(0): p <or= p(0) versus H(1): p >or=p(1), where p is the true unknown proportion responding to the new treatment, p(0) is the greatest response proportion which is deemed clinically ineffective, and p(1) is the smallest response proportion which is deemed clinically effective. In order to expose the fewest number of patients to an ineffective therapy, phase II clinical trials should terminate early when the trial fails to produce sufficient evidence of therapeutic activity (i.e. if p <or=p(0)). Simultaneously, if a treatment is highly effective (i.e. if p>or=p(1)), the trial should declare the drug effective in the fewest patients possible to allow for advancement to a phase III comparative trial. Several statistical designs, including Simon's minimax and optimal designs, have been developed that meet these requirements. In this paper, we propose three alternative designs that rely upon stochastic curtailment based on conditional power. We compare and contrast the properties of the three approaches: (1) stochastically curtailed (SC) binomial tests, (2) stochastically curtailed (SC) Simon's optimal design, and (3) SC Simon's minimax design to those of Simon's minimax and Simon's optimal designs. For each of these designs we compare and contrast the number of opportunities for study termination, the expected sample size of the trial under the null hypothesis (p <or=p(0)), and the effective type I and type II errors. We also present graphical tools for monitoring phase II clinical trials with stochastic curtailment using conditional power.

Bayesian predictive approach to interim monitoring in clinical trials

This paper reviews Bayesian strategies for monitoring clinical trial data. It focuses on a Bayesian stochastic curtailment method based on the predictive probability of observing a clinically significant outcome at the scheduled end of the study given the observed data. The proposed method is applied to derive efficacy and futility stopping rules in clinical trials with continuous, normally distributed and binary endpoints. The sensitivity of the resulting stopping rules to the choice of prior distributions is examined and guidelines for choosing a prior distribution of the treatment effect are discussed. The Bayesian predictive approach is compared to the frequentist (conditional power) and mixed Bayesian-frequentist (predictive power) approaches. The interim monitoring strategies discussed in the paper are illustrated using examples from a small proof-of-concept study and a large mortality trial.

Hypothermia on admission in patients with severe brain injury

Data from the "National Acute Brain Injury Study: Hypothermia" were examined to identify the impact of hypothermia on admission. In all patients, temperature was measured at randomization using bladder catheters with thermistors. Patients assigned to hypothermia were cooled using fluid-circulating pads. Outcome was assessed at 6 months using the dichotomized Glasgow Outcome Scale (good outcome = good recovery/moderate disability; poor outcome = severe disability/vegetative/dead). One-hundred and two patients (hypothermia, 62; normothermia, 40) were hypothermic on admission (< or =35.0 degrees C). Hypothermia-on-admission patients assigned to normothermia (n = 40) had a 78% poor outcome, and normothermia-on-admission patients assigned to normothermia had a 52% poor outcome (p < 0.004). Hypothermia-on-admission patients assigned to hypothermia had a lower percentage of poor outcomes than those assigned to normothermia (hypothermia, 61%; normothermia, 78%; p = 0.09). Patients over 45 years of age had an adverse effect of hypothermia regardless of admission temperature due to medical complications. Patients who were hypothermic on admission, age < or = 45 years (n = 81), and assigned to hypothermia had a significantly lower percentage of poor outcomes than those assigned to normothermia (hypothermia, 52%; normothermia, 76%; p = 0.02). Factors associated with hypothermia on admission were increased age, prehospital hypotension, smaller size, positive blood alcohol, larger volume of pre-hospital fluids, slightly higher injury severity, and winter enrollment The treatment effect was found in all of the four centers, which randomized the majority (80%) of the patients. It is unclear whether the improved outcome when hypothermia is maintained is a beneficial effect of very early hypothermia induction or an adverse effect of permitting the patients to rewarm passively.

Intercenter variance in clinical trials of head trauma--experience of the National Acute Brain Injury Study: Hypothermia

OBJECT

In a recently conducted trial of hypothermia in patients with severe brain injury, differences were found in the effects of hypothermia treatment among various centers. This analysis explores the reasons for such differences.

METHODS

The authors reviewed data obtained in 392 patients treated for severe brain injury. Prerandomization variables, critical physiological variables, treatment variables, and accrual methodologies were investigated among various centers. Hypothermia was found to be detrimental in patients older than the age of 45 years, beneficial in patients younger than 45 years of age in whom hypothermia was present on admission, and without effect in those in whom normothermia was documented on admission. Marginally significant differences (p < 0.054) in the intercenter outcomes of hypothermia-treated patients were likely the result of wide differences in the percentage of patients older than 45 years of age and in the percentage of patients in whom hypothermia was present on admission among centers. The trial sensitivity was likely diminished by significant differences in the incidence of mean arterial blood pressure (MABP) less than 70 mm Hg (p < 0.001) and cerebral perfusion pressure (CPP) less than 50 mm Hg (p < 0.05) but not intracranial pressure (ICP) greater than 25 mm Hg (not significant) among patients in the various centers. Hours of vasopressor usage (p < 0.03) and morphine dose (p < 0.001) and the percentage of dehydrated patients varied significantly among centers (p < 0.001). The participation of small centers increased intercenter variance and diminished the quality of data.

CONCLUSIONS

For Phase III clinical trials we recommend: 1) a detailed protocol specifying fluid and MABP, ICP, and CPP management: 2) continuous monitoring of protocol compliance; 3) a run-in period for new centers to test accrual and protocol adherence; and 4) inclusion of only centers in which patients are regularly randomized.

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.

Effects of the bradykinin antagonist Bradycor (deltibant, CP-1027) in severe traumatic brain injury: results of a multi-center, randomized, placebo-controlled trial. American Brain Injury Consortium Study Group

A phase II prospective, randomized, double blind clinical trial of Bradycor, a bradykinin antagonist, was conducted at 31 centers within North America in severely brain injured patients. Patients of Glasgow Coma Score (GCS) 3-8 (n = 139) with at least one reactive pupil were randomized to receive either Bradycor, 3 microg/kg/min or placebo as a continuous intravenous infusion for 5 days, with the infusion beginning within 12 h of the injury. The primary objective was to assess the efficacy of a continuous infusion of Bradycor (3.0 mc/kg/min) in preventing elevation of intracranial pressure (ICP). Other efficacy measures included the effect of Bradycor on the Therapy Intensity Level (TIL), mortality, and functional outcome. A secondary objective was to evaluate the safety of Bradycor in patients with severe brain injury. Randomization was carried out according to a computer generated randomization list. Patients were followed for the first 14 days of hospitalization with long-term outcome assessed at 3 and 6 months after injury. During the infusion and while the ICP monitor was in place, ICP measurements were recorded hourly along with blood pressure and heart rate. A modified version of the TIL was used to record therapeutic interventions hourly, while the ICP was being monitored. Outcome was assessed at 3 and 6 months after injury using the Glasgow Outcome Score (GOS). Bradycor was well tolerated in this patient population, and no adverse events were attributable to the compound. Although positive trends were seen for both ICP and TIL in the Bradycor group, these differences analyzed on a daily basis were not significant. However, a mixed model of variance which included treatment, day, treatment by day interaction, age and GCS revealed that the percentage time ICP of >15 mm Hg on days 4 and 5 was significantly lower in the Bradycor group compared to placebo (p = 0.035). There were fewer deaths in the Bradycor group, which had a 28-day all cause mortality of 20% versus 27% on placebo. Patients treated with Bradycor showed a 10.3% improvement in favorable outcome at 3 months and a 12% improvement in dichotomized GOS at 6 months (p = 0.26). The consistent positive trends seen in ICP, TIL, neuropsychological tests, and, most importantly, 3- and 6-month GOS provide supportive evidence that a bradykinin antagonist may play a neuroprotective role in severe brain injury.

Use of predictive probabilities in phase II and phase III clinical trials

Predictive probability is particularly useful in aiding a decision-making process related to drug development. This is especially true for decisions occurring as the result of interim analyses of clinical trials. Examples of clinical trial applications of Bayesian predictive probability and the use of the beta-binomial distribution are described.

Interim analyses and early termination of clinical trials

The group sequential tests (GST) are appropriate for performing interim analyses in clinical trials. Various GST are reviewed and compared in this paper in terms of the expected sample size, the maximum sample size, and other practical aspects. Also discussed are the p-values of the significant differences for GST. Common problems and difficulties of using GST in practice are examined. One problem is difficulties associated with the delayed data accumulated after a trial is terminated at an interim test. The GST with O'Brien-Fleming type of boundaries are found to be safe in dealing with delayed observations. Possible approaches for performing futility analyses are illustrated with examples. It is recommended that futility analysis with GST be built into the design of large clinical trials.

Ethical considerations in neuroclinical trials

Ethical decision making in clinical trials has become increasingly emphasized at many levels of the review process. Ethical concepts applicable to Neuroclinical Trials (NCT) are reviewed. The discussion is directed towards ethical concerns that investigators must consider and justify prior to Institutional Review Board (IRB) submission. Risk-benefit analysis, methodology (randomization: placebo; design) and consent (informed; deferred; waived) are reviewed and Office for Protection from Research Risk (OPRR) guidelines are described. Our conclusions: Investigators proposing NCT face increasing ethical scrutiny by IRBs. Attention to ethical issues early in trial planning process is recommended.

Bayesian approach to two-stage phase II trial

Consider the situation in which there are several different therapeutic agents. It is desired to select the best agent and to examine its efficacy relative to the control. Too often clinical trials terminate with negative outcomes in part due to inadequate phase II studies. A two-stage phase II based on a Bayesian approach is considered in order to reduce such likelihood. The first stage consists of selecting the best agent and the second stage consists of examining the relative efficacy of the selected agent compared to the control. A formal phase III clinical trial can be initiated when the particular agent is shown to be promising on the basis of the proposed phase II study. The Bayesian approach employed uses an ad hoc likelihood due to the fact that the exact likelihood is complex and intractable. In this sense the proposed approach is thus an approximation. A simulation study is conducted to investigate the performance of the proposed Bayesian approach and compared to two fixed-sample-size approaches. Due to the fact that the procedure is approximate, the simulation study is essential to assess the usefulness of the procedure. The study suggests that the Bayesian approach is an attractive alternative to fixed-sample-size approaches.

Data monitoring committees and problems of lower-than-expected accrual or events rates

Data monitoring committees for randomized clinical trials must frequently decide what action, if any, is required for trials whose accrual has been slower than expected, or whose event rates have been less than expected. We discuss in this article some of the practical issues concerning modifying or closing such trials, including what data and analyses could be helpful to the data monitoring committee in their deliberations.

Ethical considerations in clinical neuroscience. Current concepts in neuroclinical trials

BACKGROUND

Ethical decision making in clinical trials has become increasingly emphasized at many levels of the review process.

SUMMARY OF REVIEW

Ethical concepts applicable to neuroclinical trials are reviewed. The discussion is directed toward ethical concerns that investigators must consider and justify prior to institutional review board submission. Risk-benefit analysis, methodology (randomization, placebo, design), and consent (informed, deferred, waived) are reviewed and guidelines of the Office for Protection From Research Risk are described.

CONCLUSIONS

Investigators proposing neuroclinical trials face increasing ethical scrutiny by institutional review boards. Attention to ethical issues early in the trial planning process is recommended.

A randomized trial of tirilazad mesylate in patients with acute stroke (RANTTAS). The RANTTAS Investigators

BACKGROUND AND PURPOSE

Tirilazad mesylate, a nonglucocorticoid 21-aminosteroid lipid peroxidation inhibitor, has shown promise as a neuroprotectant in experimental models of focal cerebral ischemia.

METHODS

To test whether early treatment with tirilazad, 6 mg/kg per day for 3 days, would improve functional outcome after acute human stroke, 27 North American centers conducted a prospective, randomized, double-blinded, vehicle-controlled trial in patients with acute stroke treated within 6 hours of onset. The primary outcome measures were disability as measured by the Glasgow Outcome Scale and activities of daily living by the Barthel Index determined 3 months after stroke.

RESULTS

From May 1993 through December 1994, 660 patients were randomized. The trial was prematurely terminated on the advice of an independent monitoring committee after review of outcome data at a preplanned interim analysis. In 556 fully eligible patients (276 tirilazad, 280 vehicle), the odds ratio of a favorable outcome in favor of tirilazad was 0.87 (95% confidence interval [CI], 0.60 to 1.25) for the Glasgow Outcome Scale and 0.87 (95% CI, 0.60 to 1.25) for the Barthel Index, after adjustment for imbalances between the groups in preexisting disability, prior stroke, and diabetes.

CONCLUSIONS

These observations suggest that tirilazad, 6 mg/kg per day for 3 days administered beginning at a median of 4.3 hours after stroke, does not improve overall functional outcome.

A simple stopping rule for declaring treatment ineffectiveness in clinical trials

We consider the problem of stopping a clinical trial before its scheduled termination due to the apparent ineffectiveness of the experimental therapy, as compared with a control. We propose a simple-to-implement, intuitive decision rule based on the unadjusted attained significance levels from any appropriate statistical test. The proposed procedure may be used at any time during the study as an aid to help determine whether the study of an experimental treatment should be terminated early with the conclusion of treatment ineffectiveness. Much of the power of the usual fixed-sample test is retained while maintaining the nominal test size.

Termination of a clinical trial with no treatment group difference: the Lupus Nephritis Collaborative Study

The Lupus Nephritis Collaborative Study (LNCS) was a multicenter randomized clinical trial designed to assess the effects of standard drug therapy alone versus drug therapy plus plasmapheresis (plasma exchange) on the incidence of fatal or nonfatal renal failure associated with lupus nephritis. After 86 patients had been entered, with a mean of 97 weeks of follow-up, the trial was terminated partly due to lack of a beneficial effect of plasmapheresis. Although there are numerous methods for the statistical analysis of emerging results in a clinical trial, there have been relatively few descriptions of the application of these methods to the termination of a clinical trial when no favorable difference exists between groups. This report presents a review of the statistical methods employed for the pivotal interim analyses of the LNCS that were performed in order to help reach the decision to terminate the trial. These included the assessment of unconditional power post-hoc and the assessment of conditional power using an exact method appropriate for small sample sizes. Conditional power was used to assess the likelihood of detecting a significant treatment effect in the future given the data thus far observed and given reasonable hypotheses regarding the nature of the possible differences between the treatment groups. In addition, weighted-likelihood ratios (Bayes odds ratios) were computed to assess the likelihood of various alternative hypotheses given the present data. We show how such analyses can be useful in reaching a decision to terminate a trial that fails to show a treatment effect.

A decade of progress in statistical methodology for clinical trials

Clinical trials played a dominant and expanding role in the evaluation of new treatments during the decade of the 1980s. There were major improvements in the quality of clinical trials in many medical fields. There were also important developments in the methodology of designing, monitoring, conducting, analysing, reporting and interpreting clinical trials. This paper attempts to review some of these developments. A comprehensive review is beyond the abilities of any one individual. Consequently, this paper attempts to offer a broad stroke description of this area and to highlight specific topics of importance based on my particular experience. An extensive, but non-comprehensive bibliography is included to provide entry points to the literature of methodologic developments for clinical trials in the 1980s.

Monitoring versus interim analysis of clinical trials: a perspective from the pharmaceutical industry

The definitions of "interim analysis" and "monitoring" of clinical trials are often ambiguous in the current literature. The resulting confusion can lead to erroneous conclusions and misguided decisions, especially when activities that are operational or observational are evaluated in a probabilistic sense as inferential. The authors seek to define "interim analysis" and "monitoring" in a mutually exclusive fashion. These definitions will then provide the opportunity to review and categorize existing clinical trial practices and procedures. This will clarify such issues as "when to look" and "when to pay a price" (e.g., test size and power) and characterize such issues in the context of pharmaceutical industry drug development.

Early termination of a phase II clinical trial

This is a report of an ad hoc application of "predictive probability" to support the decision to terminate a traditional fixed sample phase II clinical trial of endocrine therapy in breast cancer after accrual of only 75% of the planned sample (18 of 25). The analysis was motivated by concerns over low accrual rates and a lower than expected response rate. Statistical analyses included the computation of several sets of probability estimates. The accumulated data were sufficient to reject H0: pi = 0.6 (the desired response rate) in favor of H1: pi less than 0.6 (p less than or equal to 0.02), and at study completion the 95% confidence interval for pi was expected to fail to include 0.6 with probability 0.92. Under no circumstances could the final observed response rate exceed 0.52. These and other computations provided assurance that early termination of the trial was unlikely to miss a treatment as good or better than the standard.

Antibiotic administration to treat possible occult bacteremia in febrile children

We performed a prospective, randomized, placebo-controlled, double-blind clinical trial of antibiotic administration to treat possible occult bacteremia in febrile children. A total of 955 children aged 3 to 36 months with temperatures greater than or equal to 39.0 degrees C and no focal bacterial infection were enrolled at the emergency departments of two children's hospitals from January 1982 until July 1984. Blood samples for culture were obtained, and the children were randomly assigned to receive either oral amoxicillin or placebo and were restudied approximately 48 hours after enrollment. Data were also collected on 228 children who could not be randomly assigned. Twenty-seven of the randomly assigned children (2.8 percent) had bacteremic infections with pathogenic organisms (Streptococcus pneumoniae, Haemophilus influenzae, and salmonella). There were no differences in the incidence of major infectious morbidity associated with bacteremia between the antibiotic and placebo groups--2 of 19 patients (10.5 percent) in the antibiotic group and 1 of 8 (12.5 percent) in the placebo group--although the power for this comparison was low. Antibiotics reduced fever (P less than 0.005) and improved the clinical appearance (P = 0.07) in the children with bacteremia but not in those without bacteremia. Although there were no statistically significant differences in the incidence of side effects, diarrhea tended to occur more often in the patients treated with amoxicillin (15 vs. 11 percent, P less than 0.10). We conclude that our data do not support the routine use of standard oral doses of amoxicillin in febrile children who do not have evidence of focal bacterial disease.

Monitoring distributional assumptions and early stopping for a prospective clinical trial using Monte Carlo simulation

We have applied the technique of Monte Carlo simulation to the determination of sample size for a partially completed clinical trial of chemotherapy for breast cancer. Simulations based on results observed after the entry of 243 patients in 2 years indicated a power greater than that predicted by the calculations made before the protocol was activated, and allowed a recommendation for an eventual trial closure earlier than would have been permitted by traditional methods. Both estimative and predictive approaches to the simulation of expected survival times for censored patients are presented. The use of simulation is recommended as an aid in reassessing the exact nature of the underlying survival distributions (as these affect the sample size calculations) and in optimizing stopping rules relating to patient accrual to a clinical trial in progress.

Projection from previous studies: a Bayesian and frequentist compromise

We present methods that use the results of a previous study to predict the outcome of a specified comparative trial in which each subject's outcome is categorized dichotomously (e.g., response or no response). The methods can be generalized to other two-sample cases for which power can be calculated (e.g., exponential survival), and to one-sample cases such as demonstrating a minimal response rate or demonstrating superiority to a historic control. Bayesian methods are used on the results of the preliminary study to obtain a posterior distribution representing the state of knowledge of the parameters of interest. This distribution provides the probability that the experimental regimen is superior to the standard by any particular amount. The probability that a future study will demonstrate the superiority of the experimental treatment is obtained by using the posterior distribution to average the power of the test over the parameter space.