Clinical and statistical issues in therapeutic equivalence trials

Total versus subtotal tonsillectomy for recurrent tonsillitis - a prospective randomized noninferiority clinical trial

Background: For many years experts have called for randomized controlled trials to resolve the question whether tonsillectomy, which is associated with significant comorbidity, can be replaced by partial tonsillectomy in patients with recurrent tonsillitis.Objective: To find out whether subtotal tonsillectomy is a suitable therapeutic alternative to total tonsillectomy in adult patients with recurrent episodes of acute tonsillitis.Material and methods: Study design - Single-blind prospective non-inferiority randomized clinical trial with intraindividual design. Setting - 80 patients were recruited at a tertiary referral center. Subjects - Adult patients with recurrent tonsillitis received total tonsillectomy on one side and subtotal tonsillectomy on the other side after randomization. Main outcome measure was frequency of postoperative tonsillitis on the side of subtotal tonsillectomy and postoperative pharyngitis in the former tonsil area on the side of total tonsillectomy. The study was registered in the German Clinical Trials Register (DRKS-ID: DRKS00015628).Results: Within 12 months none of the subjects suffered from recurrent tonsillitis after subtotal tonsillectomy. Subtotal tonsillectomy caused less pain than total tonsillectomy.Conclusion: Subtotal tonsillectomy might be an alternative treatment option associated with lower morbidity than total tonsillectomy in adults with recurrent tonsillitis.

Development of a clinical trial to determine whether watchful waiting is an acceptable alternative to surgical repair for patients with oligosymptomatic incisional hernia: study protocol for a randomized controlled trial

BACKGROUND

Incisional hernia is a frequent complication in abdominal surgery. This article describes the development of a prospective randomized clinical trial designed to determine whether watchful waiting is an acceptable alternative to surgical repair for patients with oligosymptomatic incisional hernia.

METHODS/DESIGN

This clinical multicenter trial has been designed to compare watchful waiting and surgical repair for patients with oligosymptomatic incisional hernia. Participants are randomized to watchful waiting or surgery and followed up for two years. The primary efficacy endpoint is pain/discomfort during normal activities as a result of the hernia or hernia repair two years after enrolment, as measured by the hernia-specific Surgical Pain Scales (SPS). The target sample size of six hundred thirty-six patients was calculated to detect non-inferiority of the experimental intervention (watchful waiting) in the primary endpoint. Sixteen surgical centers will take part in the study and have submitted their declaration of commitment giving the estimated number of participating patients per year. A three-person data safety monitoring board will meet annually to monitor and supervise the trial.

DISCUSSION

To date, we could find no published data on the natural course of incisional hernias. To our knowledge, watchful waiting has never been compared to standard surgical repair as a treatment option for incisional hernias. A trial to compare the outcome of the two approaches in patients with oligosymptomatic incisional hernias is urgently needed to provide data that can facilitate the choice between treatment options. If watchful waiting was equal to surgical repair, the high costs of surgical repair could be saved. The design for such a trial is described here. This multicenter trial will be funded by the German Research Foundation (DFG). The ethics committee of the Charité has approved the study protocol. Approval has been obtained from ten study sites at time of this submission. The electronic Case Report Forms have been created. The first patient was to be randomized November 14th, 2011. An initiation meeting took place in Berlin January 9th, 2012.

TRIAL REGISTRATION

ClinicalTrials.gov: NCT01349400.

The role of intention to treat in analysis of noninferiority studies

In analysing clinical trials designed to show superiority of one treatment compared to another, it is standard to use an intention to treat analytic approach. In active-controlled noninferiority studies, this is not standard, due to concerns that such an analysis will inflate the chance of falsely rejecting the null hypothesis, accepting therapeutic noninferiority when it is not justified. The reasons for using intention to treat (ITT) approaches in superiority studies include a desire to capture all information on study subjects, a need to prevent bias, and assurance that comparative groups are, on average, equivalent in prognostic factors. In this commentary, we argue that these same justifications carry over to noninferiority studies, and that for those and other reasons it should be the preferred analytic approach. We review regulatory guidelines, and propose a number of approaches to minimizing the potential disadvantages of the ITT approach in the noninferiority setting.

Randomized trial on the therapeutic equivalence between Eprex and GerEPO in patients on haemodialysis

AIM

Treatment of renal anaemia with epoetin is well established. However, epoetin is expensive. Biogeneric epoetin with proven efficacy would reduce cost and improve access to therapy. We conducted this first ever comparative study of a biogeneric and the original product.

METHODS

Stable haemodialysis patients with haemoglobin (Hb) of at least 9 g/dL and receiving the human recombinant erythropoietin Eprex were randomized to continue Eprex or convert to GerEPO, a biogeneric epoetin, for 12 weeks. The primary efficacy variable was a change in Hb from baseline.

RESULTS

Ninety-three subjects were randomized to each arm. Ninety-two and 87 subjects on the Eprex and GerEPO arms, respectively, completed the trial. Mean Hb in both groups declined over time. The mean decline in Hb was -0.47 g/dL in the Eprex group and -0.45 g/dL in the GerEPO group. The mean difference in the change in Hb from baseline to week 12 between the two groups was 0.02. The 95% confidence interval was -0.42 to 0.46, which lies within the margin of equivalence (+/-0.5 g/dL). The results of intention-to-treat analysis were similar. There were no significant differences in the epoetin dose, iron therapy or iron stores between the groups. Patients receiving GerEPO reported more adverse events.

CONCLUSION

GerEPO was therapeutically equivalent to Eprex with respect to Hb response for patients with Hb in the subtherapeutic target range as is common in this study population. The trial duration was insufficient for safety evaluation, which must await further investigation. More biogeneric products should be subjected to rigorous evaluation.

Role of Combined L-Arginine and Prostaglandin E1 in Renal Ischemia-Reperfusion Injury

BACKGROUND

L-Arginine (L-arg) and Prostaglandin E(1) (PGE(1)) have been used effectively as single agents to ameliorate renal ischemia-reperfusion injury. We hypothesized that combined treatment with L-arg and PGE(1 )would be more effective.

MATERIALS AND METHODS

The left renal artery of male Sprague-Dawley rats was clamped for 45 min and the right kidney was removed. Fifty six rats were randomly allocated into 5 groups each consisted of 12 rats except sham group (n = 8). (1) sham, underwent right nephrectomy only; (2) control, untreated ischemic rats; (3) L-arg group, L-arg-treated ischemic rats; (4) PGE(1) group, PGE(1)-treated ischemic rats; (5) L-arg+PGE(1) group, ischemic rats treated with both L-arg and PGE(1). Renal function and histology were assessed on days 2 and 7 postoperatively.

RESULTS

All rats, except control ones, showed a significant improvement of renal function towards normal on postoperative day 7. Serum creatinine and creatinine clearance were significantly better in L-arg+PGE(1) group compared to all other groups on day 7. With the exception of sham-operated and L-arg+PGE(1)-treated animals, all other groups showed significant increases in fractional excretion of sodium (FE(Na)) in response to renal ischemia-reperfusion. The severest tubular damage was determined in the kidneys of control rats. Rats treated with L-arg+PGE(1) had the least severe tubular damage.

CONCLUSION

The administration of either L-arg or PGE(1) attenuates both functional and structural consequences of renal warm ischemia. A near total protection might be achieved when both agents are administered concomitantly.

A Multicentre, Randomised, Double-Blind Study Comparing the??Efficacy and Tolerability of Intramuscular Dexketoprofen versus Diclofenac in the Symptomatic Treatment of Acute Low Back Pain

BACKGROUND

Low back pain is an important medical problem in Western industrialised countries. NSAIDs are one of the main options for symptomatic pain relief in the early management of this painful condition. Dexketoprofen is an NSAID belonging to the arylpropionic acid group that has demonstrated good analgesic efficacy and a good safety profile in different acute and chronic painful conditions.

METHODS

A randomised, double-blind, parallel, active controlled, multicentre study that included 370 outpatients with acute low back pain was conducted to compare the analgesic efficacy of dexketoprofen 50mg twice daily versus diclofenac 75mg twice daily administered intramuscularly for 2 days. Efficacy outcomes were assessment of pain intensity (PI) measured on a visual analogue scale, total PI scores from baseline to 6 hours after the first-dose administration (primary efficacy endpoint; SAPID(0-6)), score on a physical disability scale using the Roland Disability Questionnaire (RDQ), and use of rescue medication. Tolerability and safety were also assessed as secondary variables.

RESULTS

The adjusted mean (SAPID(0-6)) scores were very similar, 117.3 mm/h with dexketoprofen and 114.7 mm/h with diclofenac. The adjusted ratio of means was 1.023 and the lower 95% confidence limit was 0.81, demonstrating non-inferiority of dexketoprofen (defined by a lower limit of the 95% CI >0.80) in comparison with diclofenac (per-protocol analysis). The median change in the RDQ was -6 points for both groups (p = 0.69), showing an overall improvement on the disability scale. No significant differences between groups were observed regarding the percentage of patients needing rescue medication or in the mean values of pain after repeated doses (SAPID(0-last)). Dexketoprofen was well tolerated, with a reported incidence of adverse events similar to that of diclofenac. No serious adverse events were reported in either treatment group.

CONCLUSION

From the results of this study it can be concluded that dexketoprofen 50mg administered twice daily intramuscularly provides a clinically relevant analgesic effect with good tolerability after single and repeated doses in patients with acute severe low back pain.

The effects of non-compliance on intent-to-treat analysis of equivalence trials

The standard approach for analysing a randomized clinical trial is based on intent-to-treat (ITT) where subjects are analysed according to their assigned treatment group regardless of actual adherence to the treatment protocol. For therapeutic equivalence trials, it is a common concern that an ITT analysis increases the chance of erroneously concluding equivalence. In this paper, we formally investigate the impact of non-compliance on an ITT analysis of equivalence trials with a binary outcome. We assume 'all-or-none' compliance and independence between compliance and the outcome. Our results indicate that non-compliance does not always make it easier to demonstrate equivalence. The direction and magnitude of changes in the type I error rate and power of the study depend on the patterns of non-compliance, event probabilities, the margin of equivalence and other factors.

Adding sirolimus to tacrolimus-based immunosuppression in pediatric renal transplant recipients reduces tacrolimus exposure

In adult renal recipients, coadministration of tacrolimus (TAC) and sirolimus (SIR) results in reduced exposure to TAC at SIR doses of 2 mg/day. Eight pediatric renal recipients (median age at transplant 2.0 years, range: 1.2-12.9 years) were converted to TAC- and SIR-based immunosuppression as a rescue therapy. All patients had biopsy-proven chronic allograft nephropathy. TAC levels were measured using a commercially available EMIT assay and SIR levels with a newly developed assay based on the LC-MS MS technology. SIR was started at 0.13+/-0.05 mg/kg/day (3.51+/-1.26 mg/m2/day) in two divided doses. TAC was given at 0.14+/-0.09 mg/kg/day, resulting in a trough level of 6.3+/-2.5 ng/mL. After the addition of SIR, the median dose required to keep TAC blood trough concentrations within the target range increased by 71.2% (range: 21.9-245.4%), dose-normalized TAC exposure (AUC) decreased to 67.1% and the dose-normalized C(max), a surrogate for absorption rate, to 53.8% (both geometric means) while terminal half-life (t1/2), a pharmacokinetic parameter characterizing systemic elimination, remained unchanged (p<0.93). Adding SIR to TAC-based immunosuppression in young pediatric renal transplant recipients results in a significant decrease of TAC exposure. TAC trough levels should be monitored frequently.

Comparison of the efficacy of a synthetic dog-appeasing pheromone with clomipramine for the treatment of separation-related disorders in dogs

Sixty-seven dogs that showed signs of distress when separated from their owners (destructiveness, excessive vocalisation and house soiling) and hyperattachment were used in a randomised, blind trial to assess the potential value of a dog-appeasing pheromone in reducing the unacceptable behaviours. For ethical reasons, there was no placebo group and the effects of the pheromone were compared with the effects of clomipramine which is regularly used to treat this type of problem. The undesirable behaviours decreased in both groups, but the overall assessment by the owners indicated that there was no significant difference between the two treatments, although there were fewer undesirable events in the dogs treated with the pheromone, and the administration of the pheromone appeared to be more convenient.

Likelihood ratio and a Bayesian approach were superior to standard noninferiority analysis when the noninferiority margin varied with the control event rate

OBJECTIVE

To present and compare three statistical approaches for analyzing a noninferiority trial when the noninferiority margin depends on the control event rate.

STUDY DESIGN AND SETTING

In noninferiority trials with a binary outcome, the noninferiority margin is often defined as a fixed delta, the largest clinically acceptable difference in event rates between treatment groups. An alternative and more flexible approach is to allow delta to vary according to the true event rate in the control group. The appropriate statistical method for evaluating noninferiority with a variable noninferiority margin is not apparent. Three statistical approaches are proposed and compared: an observed event rate (OER) approach based on equating the true control rate to the observed rate, a Bayesian approach, and a likelihood ratio test.

RESULTS AND CONCLUSIONS

Simulations studies indicate that the proportion of trials in which noninferiority was erroneously demonstrated was higher for the OER approach than with the Bayesian and likelihood ratio approaches. In some cases, the Type I error rate exceeded 10% for the OER approach. The OER approach is not recommended for the analysis of noninferiority trials with a variable margin of equivalence. The Bayesian and likelihood ratio methods yielded better operating characteristics.

Report of the American Society of Transplantation conference on immunosuppressive drugs and the use of generic immunosuppressants

Considerable economic and health-related costs are associated with the life-long maintenance immunosuppressive therapy required to prevent transplant rejection. Generic medications have the potential of providing equivalent therapeutic efficacy at a lower economic cost. In 2001, the American Society of Transplantation invited experts to review the data and issues associated with the approval and use of generic immunosuppressants. A summary of that meeting is reported here. The generic medication approval process has been in effect for more than 30 years. All marketed generic cyclosporin formulations have met FDA criteria demonstrating bioequivalence in healthy subjects, and some were also tested in transplant recipients. Most participants agreed that generic narrow therapeutic index immunosuppressive agents provide adequate de novo immunosuppression in low-risk transplant recipients. However, some participants expressed concern regarding the currently unquantified risk that may be associated with switching immunosuppressive agents under uncontrolled circumstances. There was broad agreement among the participants that generic medications should be clearly labeled and distinguishable from innovator drugs, and that patients should be educated to inform their physicians of any switch to or among generic alternatives. There was also strong support in favor of requiring studies to demonstrate bioequivalence in potentially at-risk patient populations, specifically African-Americans and pediatric patients.

The pros and cons of noninferiority trials

Noninferiority trials comparing new treatment with an active standard control are becoming increasingly common. This article discusses relevant issues regarding their need, design, analysis and interpretation: the appropriate choice of control group, types of noninferiority trial, ethical considerations, sample size determination and potential pitfalls to consider.

Practical issues and observations on the use of foreign clinical data in drug development

The International Conference on Harmonization (ICH) has recently developed the ICH guidelines, which are the common guidelines for regulatory requirements in the ICH regions, i.e., European Union, Japan, and the United States of America. The guidelines have been successively implemented in the ICH regions, and the people involved in drug evaluation in the pharmaceutical industry, such as statisticians and pharmaceutical scientists, have referred to the guidelines during their daily work. Probably one of the most influential ICH guidelines on the drug development process in the ICH regions, especially in Japan, is the ICH-E5 guideline, which is encouraging the pharmaceutical industry to use the mountain of foreign clinical data for the registration of a new drug. In this article, we review the issues concerning the ICH-E5 guideline discussed so far, and discuss some practical issues in applying the guideline, especially the design of the study conducted in a new region. This is called a "bridging study." In addition, we introduce some statistical approaches for evaluating the acceptability of foreign clinical data.

Choosing an equivalence limit for noninferiority or equivalence studies

Studies that compare treatments with the purpose of demonstrating that the treatments are similar require an a priori definition of an equivalence limit, how different the treatments can be before the difference is of concern. Defining such an equivalence limit is one of the most difficult aspects of planning the study. Three principles are proposed for setting such limits, depending on the objective of the study: a putative placebo calculation, an approach based on clinically important differences, and methods based on statistical properties. All methods will be useful for many studies, but the study objective should determine the final choice of an equivalence limit. The statistician must play an integral role in determining the final equivalence limit. Advice is offered for helping the statistician participate in the decision on the equivalence limits.

The effects of outcome misclassification and measurement error on the design and analysis of therapeutic equivalence trials

In any clinical trial, the use of imperfect diagnostic procedures or laboratory techniques may lead to misclassification and measurement error in the primary outcome. Although the effects of non-differential outcome misclassification and measurement error on conventional superiority trials have been extensively investigated, less is known about the impact of these errors on the results and interpretation of therapeutic equivalence trials. In this paper we formally investigate the effects of outcome misclassification and measurement error on the estimates of treatment effects, type I error rate, and power of equivalence trials. Our results indicate that, contrary to what one may expect based on the well known attenuating effects of non-differential error in conventional studies, these errors do not always favour the goal of demonstrating equivalence. The magnitude and direction of the influence depend on a number of factors including the nature of the outcome variable, specific formulation of equivalence, size of the error rates, and assumptions regarding the true treatment effect.

Double-blind comparison of olanzapine versus clozapine in schizophrenic patients clinically eligible for treatment with clozapine

BACKGROUND

The treatment of schizophrenic patients who fail to respond to adequate trials of neuroleptic drugs is a major challenge. Clozapine has been one treatment option; however, it is not universally effective and is limited in its use by safety concerns. With the introduction of newer agents, their performance relative to clozapine is of great clinical interest.

METHODS

The primary objective of this study was to evaluate the efficacy and safety of olanzapine versus clozapine among treatment resistant DSM-IV schizophrenic patients. The study was primarily designed to demonstrate the "noninferiority" of olanzapine compared to clozapine after 18 weeks of double-blind treatment. Conclusions were based on the one-sided lower 95% confidence limit about the treatment effect observed from the primary efficacy variable (Positive and Negative Syndrome Scale [PANSS] Total).

RESULTS

Mean changes from baseline to end point in PANSS Total score, using a last observation carried forward technique, showed that both agents were comparably effective in neuroleptic resistant patients, i.e., demonstrated the "noninferiority" of olanzapine when compared to clozapine. Overall, significantly fewer olanzapine-treated patients (4%) discontinued for an adverse event than their clozapine-treated (14%) counterparts (p =.022). Among spontaneously reported adverse events, increased salivation, constipation, dizziness, and nausea were reported significantly more often among clozapine-treated patients, whereas only dry mouth was reported more often among olanzapine-treated patients.

CONCLUSIONS

Olanzapine was demonstrated to be noninferior to clozapine and better tolerated among resistant schizophrenic patients clinically eligible for treatment with clozapine.

Recommendations for bioequivalence testing of cyclosporine generics revisited

The immunosuppressant cyclosporine is generally considered a critical-dose drug. The validity of standard criteria to establish bioequivalence between cyclosporine formulations has recently been challenged. Recommendations included establishment of individual bioequivalence rather than average bioequivalence, establishment of bioequivalence in transplant patients and in subgroups known to be poor absorbers, as well as long-term efficacy and safety studies in transplant patients. However, at the moment individual bioequivalence is a theoretical concept, the practical benefits of which have not statistically been proven. The proposed patient pharmacodynamic studies can be expected to require an unrealistically high number of subjects to achieve sufficient statistical power. It is well established that the common practice of blood-concentration-guided dosing of cyclosporine efficiently compensates for interindividual and intraindividual variability and allows for safely switching cyclosporine formulations as bioinequivalent as Sandimmune and Neoral. Recent studies comparing the generic cyclosporine formulation SangCya with Neoral, including individual bioequivalence, bioequivalence in transplant patients, and long-term safety after switching from Sandimmune to SangCya, confirmed that it was valid to conclude bioequivalence of both cyclosporine formulations based on standard average bioequivalence criteria. Present FDA guidelines for approving bioequivalence can be considered adequate and sufficient for generic cyclosporine formulations.

Design and analysis of three treatment equivalence trials

We consider design and analysis of clinical trials aimed at demonstrating equivalence of three treatments. We discuss analysis methods that require demonstrating that each pair of treatments has an unimportant difference. The critical values that we provide are smaller than the standard normal critical values, pointing out that the adjustment is counter to the usual multiplicity adjustments. Special issues in demonstrating equivalence of three rather than two treatments are discussed. We propose some conservative criteria for estimating sample size. Procedures for choosing pairs of treatments that are equivalent to each other, even when all three treatments are not shown equivalent, are also discussed along with implications for control of type I errors. We also demonstrate the methods with data from the literature.

Noninferiority trials

Noninferiority trials are intended to show that the effect of a new treatment is not worse than that of an active control by more than a specified margin. These trials have a number of inherent weaknesses that superiority trials do not: no internal demonstration of assay sensitivity, no single conservative analysis approach, lack of protection from bias by blinding, and difficulty in specifying the noninferiority margin. Noninferiority trials may sometimes be necessary when a placebo group can not be ethically included, but it should be recognized that the results of such trials are not as credible as those from a superiority trial.

Equivalence concepts in clinical trials

According to the recent ICH E9 Guidance Statistical Principles for Clinical Trials, efficacy is most convincingly established by demonstrating superiority to placebo, by showing superiority to an active control treatment or by demonstrating a dose-response relationship (so-called 'superiority' trials). For serious illnesses, a placebo-controlled trial may be considered unethical if a therapeutic treatment exists which has proven efficacious in relevant superiority trial(s). In that case, the scientifically sound use of an active treatment as a control should be considered. Active control trials designed to show that the efficacy of an investigational product is not relevantly worse than that of the active comparator are called 'non-inferiority' trials (1). After having confirmed non-inferiority, superiority of the alternative test treatment over the reference treatment can additionally be tested without the need to adjust the significance level (2). In contrast to cross-over bioequivalence trials based on pharmacokinetic endpoints such as AUC and Cmax, therapeutic equivalence and non-inferiority trials are based on clinical end-points. Therefore, they are often conducted as parallel group comparisons. It is important to note that the conclusion of equivalence or non-inferiority is based on the inclusion of the appropriate confidence interval in the equivalence acceptance range, and that it cannot be derived from a non-significant test result of the inappropriate null hypothesis of no treatment difference.

Equivalence trials in SLE research: issues to consider

In contrast to the objective of most clinical trials, which is to demonstrate superiority of an experimental treatment over a standard or placebo, the aim of an equivalence trial is to show that two treatments are equivalent in outcome or only marginally different. This would be of interest when an experimental treatment offers advantages such as reduced toxicity, ease of administration, or cost relative to the standard. Demonstrating equivalence may also be a goal when evaluating the safety of certain drugs because similarity in the risks of an adverse event in subjects exposed and unexposed to the drug is an indication of its safety. The classical formulation of the null hypothesis of treatment equality that is used in superiority trials is not applicable to equivalence trials because absolute equivalence between treatment groups cannot be proven. The strategy in equivalence trials is to define a maximum difference between treatment groups that is clinically acceptable and then assess whether there is sufficient evidence from the trial to conclude that the true treatment difference is within this acceptable range. In this paper, we discuss issues surrounding the planning, conduct, and analysis of equivalence trials in the context of SLE, with examples from the SELENA study.

Approximate sample sizes for testing hypotheses about the ratio and difference of two means

This article deals with a unifying approach to approximate sample size determination for different types of hypotheses formulated in terms of two means of normally distributed data. A simple approximation is given to the sample size required for testing hypotheses about the ratio of the means. The formula includes the situations of testing noninferiority, superiority, or equivalence. We present a more general formula that also covers hypotheses formulated in terms of the difference of means. We show that over a wide range of parameter values the approximation provides reliable sample sizes.

Clinical equivalence

When the classical approach of testing the null hypothesis of equality is used and the results are not statistically significant, formal conclusions regarding the "closeness" of the treatments cannot be drawn. When the purpose of the investigation is to exhibit "closeness," misinterpretations may result in inappropriate, or even incorrect, conclusions. Here methodology for use when the goal is to exhibit the equivalence (noninferiority) of the treatments is discussed. The techniques allow direct conclusions to be drawn regarding the equivalence of the treatments. A review is presented.

Simple bioequivalence criteria: are they relevant to critical dose drugs? Experience gained from cyclosporine

A critique of the current bioequivalence regulations is presented with reference to critical dose drugs. Using the development of a new cyclosporine formulation as an example, the deficiencies in current bioequivalence testing guidelines are examined and discussed. Based on the experience gained with cyclosporine, recommendations are made on how therapeutic equivalence, rather than just bioequivalence, should be established.

Comparison of tests and sample size formulae for proving therapeutic equivalence based on the difference of binomial probabilities

To prove the hypothesis that a new treatment is as effective as a standard one, a possibility is to test the one-sided null hypothesis of a clear inferiority of the new treatment against the alternative hypothesis that, if at all, it is only negligibly inferior. Such a problem is of clinical relevance if, for instance, a new treatment with an effectiveness which is comparable to that of the standard one would be preferred if it is less toxic. If the difference between the two treatments is measured by the difference of failure rates, approximate statistical tests and sample size formulae have to be used. This paper reports the results of an extensive empirical investigation comparing the well known calculations proposed by Blackwelder, Rodary, ComNougue and Tournade, which propose a sample size formula for the test of Dunnett and Gent, and Farrington and Manning. The investigation was conducted in order to allow more comprehensive conclusions than those which may be drawn from the limited examples given by the last authors. For the usual settings in clinical trials, the formulae of Farrington and Manning are recommended. However, there are combinations of statistical parameters for which they are not preferred.