Proving non-inferiority or equivalence of two treatments with dichotomous endpoints using exact methods

Are the tests overpowered or underpowered? A unified solution to correctly specify type I errors in design of clinical trials for two sample proportions

As one of the most commonly used data types, methods in testing or designing a trial for binary endpoints from two independent populations are still being developed until recently. However, the power and the minimum required sample size comparisons between different tests may not be valid if their type I errors are not controlled at the same level. In this article, we unify all related testing procedures into a decision framework, including both frequentist and Bayesian methods. Sufficient conditions of the type I error attained at the boundary of hypotheses are derived, which help reduce the magnitude of the exact calculations and lay out a foundation for developing computational algorithms to correctly specify the actual type I error. The efficient algorithms are thus proposed to calculate the cutoff value in a deterministic decision rule and the probability value in a randomized decision rule, such that the actual type I error is under but closest to, or equal to, the intended level, respectively. The algorithm may also be used to calculate the sample size to achieve the prespecified type I error and power. The usefulness of the proposed methodology is further demonstrated in the power calculation for designing superiority and noninferiority trials.

Analysis of two binomial proportions in noninferiority confirmatory trials

In this article, we propose considering an approximate exact score (AES) test for noninferiority comparisons and we derive its test-based confidence interval for the difference between two independent binomial proportions. This test was published in the literature, but not its associated confidence interval. The p-value for this test is obtained by using exact binomial probabilities with the nuisance parameter being replaced by its restricted maximum likelihood estimate. Calculated type I errors revealed that the AES method has important advantages for noninferiority comparisons over popular asymptotic methods for adequately powered confirmatory clinical trials, at 80% or 90% statistical power. For unbalanced sample sizes of the compared groups, type I errors for the asymptotic score method were shown to be higher than the nominal level in a systematic pattern over a range of true proportions, but the AES method did not suffer from such a problem. On average, the true type I error of the AES method was closer to the nominal level than all considered methods in the empirical comparisons. In rare cases, type I errors of the AES test exceeded the nominal level, but only by a small amount. Presented examples showed that the AES method can be more attractive in practice than practical exact methods. In addition, p-value and confidence interval of the AES method can be obtained in <30 s of computer time for most confirmatory trials. Theoretical arguments, combined with empirical evidence and fast computation time should make the AES method attractive in statistical practice.

Early vs Interval Postpartum Intrauterine Device Placement: A Randomized Clinical Trial

Importance

The early postpartum period, 2 to 4 weeks after birth, may be a convenient time for intrauterine device (IUD) placement; the placement could then coincide with early postpartum or well-baby visits.

Objective

To determine expulsion rates for IUDs placed early postpartum compared with those placed at the standard interval 6-week visit.

Design, Setting, and Participants

In this randomized noninferiority trial, people who had a vaginal or cesarean birth were randomly assigned to undergo early (14-28 days) or interval (42-56 days) postpartum IUD placement. Clinicians blinded to participant study group used transvaginal ultrasonography to confirm IUD presence and position at the 6-month postpartum follow-up. The study assessed 642 postpartum people from 4 US medical centers, enrolled a consecutive sample of 404 participants from March 2018 to July 2021, and followed up each participant for 6 months postpartum.

Interventions

Early postpartum IUD placement, at 2 to 4 weeks postpartum, vs standard interval placement 6 to 8 weeks postpartum.

Main Outcomes and Measures

The primary outcome was complete IUD expulsion by 6 months postpartum; the prespecified noninferiority margin was 6%. Secondary outcomes were partial IUD expulsion, IUD removal, pelvic infection, patient satisfaction, uterine perforation, pregnancy, and IUD use at 6 months postpartum. IUD malposition was an exploratory outcome.

Results

Among 404 enrolled participants, 203 participants were randomly assigned to undergo early IUD placement and 201 to undergo interval IUD placement (mean [SD] age, 29.9 [5.4] years; 46 [11.4%] were Black, 228 [56.4%] were White, and 175 [43.3%] were Hispanic). By 6 months postpartum, 53 participants (13%) never had an IUD placed and 57 (14%) were lost to follow-up. Among the 294 participants (73%) who received an IUD and completed 6-month follow-up, complete expulsion rates were 3 of 149 (2.0% [95% CI, 0.4%-5.8%]) in the early placement group and 0 of 145 (0% [95% CI, 0.0%-2.5%]) in the interval placement group (between-group difference, 2.0 [95% CI, -0.5 to 5.7] percentage points). Partial expulsion occurred in 14 (9.4% [95% CI, 5.2%-15.3%]) participants in the early placement group and 11 (7.6% [95% CI, 3.9%-13.2%]) participants in the interval placement group (between-group difference, 1.8 [95% CI, -4.8 to 8.6] percentage points). IUD use at 6 months was similar between the groups: 141 (69.5% [95% CI, 62.6%-75.7%]) participants in the early group vs 139 (67.2% [95% CI, 60.2%-73.6%]) in the interval group.

Conclusions and Relevance

Early IUD placement at 2 to 4 weeks postpartum compared with 6 to 8 weeks postpartum was noninferior for complete expulsion, but not partial expulsion. Understanding the risk of expulsion at these time points may help patients and clinicians make informed choices about the timing of IUD placement.

Trial Registration

ClinicalTrials.gov Identifier: NCT03462758.

Estimating the Risk of Maternal Death at Admission: A Predictive Model from a 5-Year Case Reference Study in Northern Uganda

Background. Uganda is one of the countries in the Sub-Saharan Africa with a very high maternal mortality ratio estimated at 336 deaths per 100,000 live births. We aimed at exploring the main factors affecting maternal death and designing a predictive model for estimation of the risk of dying at admission at a major referral hospital in northern Uganda. Methods. This was a retrospective matched case-control study, carried out at Lacor Hospital in northern Uganda, including 130 cases and 336 controls, from January 2015 to December 2019. Multivariate logistic regression was used to estimate the net effect of the associated factors. A cumulative risk score for each woman based on the unstandardised canonical coefficients was obtained by the discriminant equation. Results. The average maternal mortality ratio was 328 per 100,000 live births. Direct obstetric causes contributed to 73.8% of maternal deaths; the most common were haemorrhage (42.7%), sepsis (24.0%), hypertensive disorders (18.7%) and complications of abortion (2.1%), whereas malaria (23.5%) and HIV/AIDS (20.6%) were the leading indirect causes. The odds of dying were higher among women who were aged 30 years or more (OR 1.12; 95% CI, 1.04–1.19), did not attend antenatal care (OR 3.11; 95% CI, 1.36–7.09), were HIV positive (OR 3.13; 95% CI, 1.41–6.95), had a caesarean delivery (OR 2.22; 95% CI 1.13–4.37), and were referred from other facilities (OR 5.57; 95% CI 2.83–10.99). Conclusion. Mortality is high among mothers referred late from other facilities who are HIV positive, aged more than 30 years, lack antenatal care attendance, and are delivered by caesarean section. This calls for prompt and better assessment of referred mothers and specific attention to antibiotic therapy before and after caesarean section, especially among HIV-positive women.

Short-Term Growth During Treatment with Inhaled Fluticasone Propionate/Formoterol, Fluticasone and Beclomethasone Treatment

BACKGROUND

Fluticasone propionate/formoterol (FP/FORM) is a pressurized metered-dose inhaler (pMDI; Flutiform^®) approved for use in adolescents and adults and under development for pediatric use.

OBJECTIVE

To compare short-term growth in asthmatic children treated with FP/FORM, FP pMDI with valved holding chamber, and beclomethasone dipropionate (BDP) in a breath-actuated device.

METHODS

Children with persistent asthma (n = 48; 5 to <12 years) participated in an assessor-blinded, randomized, three-way crossover trial with run in, wash out, and active treatment periods, each of 2 weeks duration. Interventions were FP/FORM 100/10 μg b.i.d. with an AeroChamber Plus^® Flow-Vu^® Spacer, FP pMDI (Flixotide^®) 100 μg b.i.d. with a Volumatic^® spacer, and extra-fine BDP breath-actuated inhaler (Aerobec^®/QVAR^® Autohaler^®) 100 μg b.i.d. Lower leg growth rate (LLGR) was measured by knemometry.

RESULTS

The least square (LS) mean difference in LLGR between FP/FORM and FP (per protocol population) was -0.006 mm/week (95% CI: -0.095 to 0.084; p < 0.001 for noninferiority [noninferiority margin -0.200 mm/week]). Both treatments elicited no change from baseline off-treatment growth rate. The LS mean treatment difference of FP/FORM versus BDP was 0.116 mm/week (95% CI: -0.004 to 0.235; p = 0.057) and of FP versus BDP 0.163 mm/week (95% CI: 0.078-0.249; p < 0.001). Results in the full analysis population were: FP/FORM versus FP -0.012 mm/week (95% CI: -0.080-0.056; p < 0.001); FP/FORM versus BDP 0.143 mm/week (95% CI: 0.064-0.222; p < 0.001); FP versus BDP 0.163 mm/week (95% CI: 0.093-0.233; p < 0.001).

CONCLUSIONS

FP/FORM pMDI with AeroChamber and FP pMDI with Volumatic spacer did not affect lower leg growth, measured by knemometry, in asthmatic children. Conversely, extra-fine BDP from a breath-actuated inhaler resulted in short-term growth suppression.

Monitoring rare serious adverse events from a new treatment and testing for a difference from historical controls

Background We detail the design of a study to monitor the safety of including albendazole to an existing treatment regimen to eliminate lymphatic filariasis. We wish to show that this new regimen does not increase the rate of a rare serious adverse event (SAE) compared to the old regimen. Controlled but small clinical trials have not detected any increase in the SAE using albendazole, and it is known to have added benefits; therefore, it is unethical to randomize patients to the old regimen.

Purpose A sample size for the new regimen is needed to test that the new rate of SAE is noninferior to the historic rate. If the new regimen does have an inferior rate of SAE then we wish to stop the study early. This setup is different from traditional early stopping for efficacy and futility. In that traditional case, the two stopping decisions are relative to the same null hypothesis of equality, while in our setup, we have two different null hypotheses: the noninferiority null and the equality null. When testing the former, we need not stop early if the new regimen appears better because no subjects are receiving the old regimen anymore anyway. When testing the equality of SAE rates, however, we want to stop early if the new regimen has a significantly higher rate of SAE.

Methods We create a design that uses an exact difference in proportions test for testing noninferiority, but calculates maximal sample size based on conditional power which treats the historical rates as true rates. The design allows for early stopping if the new treatment appears inferior with respect to SAE rate but makes no corrections for multiple testing. We explore the properties of this naive design without assuming the historical rates are known.

Results For our example, we show that our naive design strategy bounds the type I error of the noninferiority hypothesis in all cases and bounds it for the equality hypothesis at 0.05, as long as the true SAE rate is <0.00015. The same design has unconditional power for the noninferiority hypothesis greater than the nominal 80% as long as the true SAE rate for both regimens are <0.00025.

Limitations The type I and power results above hold only for our historical sample size of 17 877. We expect similar type I and power properties to hold with studies with SAE rates similar or less (i.e., < 0.00015) and historical sample sizes similar or smaller.

Conclusions Our design for comparing very rare historical SAE rates to SAE rates of a new treatment has large power to conclude noninferiority of the new treatment SAE rate when both rates are equal, but allows early stopping if the new SAE rates are worse. Clinical Trials 2007; 4: 598—610. http://ctj.sagepub.com

Analysis of feature intervisibility and cumulative visibility using GIS, Bayesian and spatial statistics: a study from the Mandara Mountains, northern Cameroon

The locations of diy-geδ-bay (DGB) sites in the Mandara Mountains, northern Cameroon are hypothesized to occur as a function of their ability to see and be seen from points on the surrounding landscape. A series of geostatistical, two-way and Bayesian logistic regression analyses were performed to test two hypotheses related to the intervisibility of the sites to one another and their visual prominence on the landscape. We determine that the intervisibility of the sites to one another is highly statistically significant when compared to 10 stratified-random permutations of DGB sites. Bayesian logistic regression additionally demonstrates that the visibility of the sites to points on the surrounding landscape is statistically significant. The location of sites appears to have also been selected on the basis of lower slope than random permutations of sites. Using statistical measures, many of which are not commonly employed in archaeological research, to evaluate aspects of visibility on the landscape, we conclude that the placement of DGB sites improved their conspicuousness for enhanced ritual, social cooperation and/or competition purposes.

A Comparison of Short-Term Growth During Treatment with Two Dry Powder Combinations of Inhaled Corticosteroids and Long-Acting β₂-Agonists

BACKGROUND

A combination of the inhaled corticosteroid budesonide and the long-acting β2-agonist formoterol has been formulated in a novel dry powder inhaler, Spiromax(®). The objective was to compare lower leg growth in children with asthma treated with inhaled budesonide+formoterol (BF) delivered from the Spiromax inhaler with BF from the Symbicort Turbohaler(®).

METHODS

Prepubescent children with persistent asthma (n=75, aged 6-11 years) were included in a randomized, double-blind, double-dummy, placebo-controlled, three-way crossover study with active treatment and placebo periods of 2 weeks duration. Lower leg length was measured every second week. As a secondary outcome parameter, 24-hr urine was collected for assessment of free cortisol. Interventions were dry powder BF 160+9 μg twice daily (b.i.d.; delivered dose) from the Spiromax inhaler and dry powder BF 200+12 μg b.i.d. (metered dose) from the Symbicort Turbohaler.

RESULTS

The least squares mean difference in lower leg growth rates (LLGR) between BF Spiromax and Symbicort Turbohaler was -0.086 mm/week [95% confidence interval (CI) -0.203, 0.032]. The pre-specified non-inferiority margin was -0.200 mm/week, so the lower limit of the 95% CI was just outside this margin. The difference between BF Spiromax and placebo was -0.20 mm/week (95% CI: -0.322, 0.086); p<0.001), between Symbicort Turbohaler and placebo -0.118 mm/week (95% CI: -0.236, -0.001; p=0.048). No statistically significant differences were seen in urine free cortisol assessments.

CONCLUSIONS

As the lower limit of the CI of LLGR was marginally outside of the pre-specified non-inferiority margin between BF Spiromax 160+9 μg b.i.d. and Symbicort Turbohaler 200+12 μg b.i.d., non-inferiority could not be demonstrated. Further studies may be needed for comparison of systemic activity of BF Spiromax and Symbicort Turbohaler in children before firm conclusions about their comparability may be drawn.

A new noninferiority test for independent dichotomous variables based on a shrinkage proportion estimator

A new noninferiority test for the difference between two independent proportions is presented. The test is based on a Wald-type statistic in which maximum likelihood estimators and a type of shrinkage estimator are used to estimate proportions. This new test was compared with another Wald-type test that has been shown to behave well in terms of test size and power. For the comparison, the behavior of the new test, in terms of its size and power, was analyzed over several configurations. While the two tests exhibited similar behavior, the new test is easier to implement and thus constitutes a practical alternative.

Sample size considerations in active-control non-inferiority trials with binary data based on the odds ratio

This paper presents an approximate closed form sample size formula for determining non-inferiority in active-control trials with binary data. We use the odds-ratio as the measure of the relative treatment effect, derive the sample size formula based on the score test and compare it with a second, well-known formula based on the Wald test. Both closed form formulae are compared with simulations based on the likelihood ratio test. Within the range of parameter values investigated, the score test closed form formula is reasonably accurate when non-inferiority margins are based on odds-ratios of about 0.5 or above and when the magnitude of the odds ratio under the alternative hypothesis lies between about 1 and 2.5. The accuracy generally decreases as the odds ratio under the alternative hypothesis moves upwards from 1. As the non-inferiority margin odds ratio decreases from 0.5, the score test closed form formula increasingly overestimates the sample size irrespective of the magnitude of the odds ratio under the alternative hypothesis. The Wald test closed form formula is also reasonably accurate in the cases where the score test closed form formula works well. Outside these scenarios, the Wald test closed form formula can either underestimate or overestimate the sample size, depending on the magnitude of the non-inferiority margin odds ratio and the odds ratio under the alternative hypothesis. Although neither approximation is accurate for all cases, both approaches lead to satisfactory sample size calculation for non-inferiority trials with binary data where the odds ratio is the parameter of interest.

Would tirofiban have been shown non-inferior to abciximab had the TENACITY trial not been terminated for financial reasons?

OBJECTIVES

To investigate whether tirofiban would have been non-inferior to abciximab had the trial completed enrollment and place the termination of this trial in a broader research ethics context.

BACKGROUND

TENACITY was terminated by the sponsor for financial reasons. At the time, event rates for the 2 treatment arms were unknown.

METHODS

TENACITY was designed to compare tirofiban with abciximab in approximately 8,000 patients; however, enrollment was terminated after 383 (4.8%) patients. The primary end-point was a composite of 30-day death, myocardial infarction, and urgent target vessel revascularization. Non-inferiority was defined as the likelihood that tirofiban would preserve at least 50% of the ability of abciximab to reduce the primary end-point at 30 days, based on abciximab's demonstrated ability to reduce such events by 43% (relative risk, 0.573; 95% confidence interval [CI], 0.507-0.648; P < 0.001). To determine the probability of non-inferiority given the patients already enrolled, a Bayesian approach was used.

RESULTS

The primary composite end-point occurred in 8.8% of patients randomized to abciximab versus 6.9% receiving high-bolus-dose tirofiban (odds ratio, 0.77; 95% CI, 0.37-1.64). The estimated conditional power for the test that tirofiban would be non-inferior to abciximab if all patients been enrolled is 93.7%. Using the estimated predictive power method, the likelihood was 84.8%.

CONCLUSIONS

TENACITY was well powered to identify non-inferiority with tirofiban versus abciximab, and the patients enrolled strengthened the probability that this would have been the outcome had the trial been completed. When a clinical trial is terminated solely for financial reasons, it is incumbent upon the sponsor to provide proper patient follow-up and publication of the findings.

Safety of aspiration abortion performed by nurse practitioners, certified nurse midwives, and physician assistants under a California legal waiver

OBJECTIVES

We examined the impact on patient safety if nurse practitioners (NPs), certified nurse midwives (CNMs), and physician assistants (PAs) were permitted to provide aspiration abortions in California.

METHODS

In a prospective, observational study, we evaluated the outcomes of 11 487 early aspiration abortions completed by physicians (n = 5812) and newly trained NPs, CNMs, and PAs (n = 5675) from 4 Planned Parenthood affiliates and Kaiser Permanente of Northern California, by using a noninferiority design with a predetermined acceptable risk difference of 2%. All complications up to 4 weeks after the abortion were included.

RESULTS

Of the 11 487 aspiration abortions analyzed, 1.3% (n = 152) resulted in a complication: 1.8% for NP-, CNM-, and PA-performed aspirations and 0.9% for physician-performed aspirations. The unadjusted risk difference for total complications between NP-CNM-PA and physician groups was 0.87 (95% confidence interval [CI] = 0.45, 1.29) and 0.83 (95% CI = 0.33, 1.33) in a propensity score-matched sample.

CONCLUSIONS

Abortion complications were clinically equivalent between newly trained NPs, CNMs, and PAs and physicians, supporting the adoption of policies to allow these providers to perform early aspirations to expand access to abortion care.

Systemic activity of inhaled beclomethasone dipropionate: a double-blind comparison of volume spacers

BACKGROUND

To which extent volume spacers may influence systemic activity of inhaled beclomethasone dipropionate (BDP) has not been evaluated.

AIM

To assess whether the AeroChamber Plus™ spacer is equivalent to the Volumatic™ spacer for administration of inhaled hydroflouroalkane 134a propelled BDP in terms of lower leg growth rate (LLGR).

PATIENTS AND METHODS

Prepubertal children with mild asthma (n = 26, aged 6-14 years) were included in a 3-time periods of 2 weeks duration randomized double-blind cross-over study with a single-blind placebo run-in and two washout periods. LLGR was measured with the knemometer. Interventions were inhaled BDP hydroflouroalkane 134a pressurized metered dose inhaler 100 μg and 200 μg b.i.d. with the AeroChamber Plus and 200 μg b.i.d. with the Volumatic spacer.

RESULTS

Beclomethasone dipropionate 200 μg b.i.d. from the AeroChamber Plus was non-inferior to BDP 200 b.i.d. from the Volumatic spacer as the lower margin of confidence interval of the difference between treatments (-0.18 to 0.13 mm/week) was greater than the prespecified lower limit for non-inferiority (-0.20 mm/week). UFC/creatinine data showed no statistically significant variations.

CONCLUSION

The systemic activity of BDP, via the Volumatic™, and AeroChamber Plus™ spacers is similar. The AeroChamber Plus spacer may be used in children without risk of increasing systemic activity of BDP.

Short-term lower leg growth in 5- to 11-year-old asthmatic children using beclomethasone dipropionate inhalers with chlorofluorocarbon or hydrofluoroalkane propellants: a 9-week, open-label, randomized, crossover, noninferiority study

BACKGROUND

Beclomethasone dipropionate-hydrofluoroalkane (BDP-HFA) is a non-chlorofluorocarbon (CFC)-propelled metered dose inhaler. Data is needed to support the registration of BDP-HFA in pediatric populations for countries in the European Union.

OBJECTIVE

The aim of the study was to assess short-term lower leg growth in children with asthma during treatment with BDP-HFA 100 μg BID compared with BDP-CFC 200 μg BID.

METHODS

Children with asthma were included in this open-label, randomized, crossover study with 2-week run-in, active treatment, and washout periods. Lower leg length was measured every second week. As a secondary outcome parameter, 24-hour urine was collected for assessment of free cortisol. Interventions were inhaled BDP-HFA 100 μg BID with AeroChamber Plus spacer and BDP-CFC 200 μg BID with Volumatic spacer.

RESULTS

In 63 patients with asthma aged 5 to 11 years, BDP-HFA 100 μg BID was noninferior to BDP-CFC 200 μg BID, as the lower margin of CI (-0.03 to 0.10 mm/wk) of the estimated difference (0.03 mm/wk) was greater than the prespecified lower limit for noninferiority of -0.12 mm/wk. Mean (SD) lower leg growth rate during run-in, BDP-HFA 100 μg BID, and BDP-CFC 200 μg BID was 0.36 (0.17), 0.27 (0.21), and 0.23 (0.18) mm/wk, respectively (BDP-HFA estimate of difference, -0.09 [95% CI, -0.16 to -0.03 mm/wk; P < 0.01]; BDP-CFC estimate of difference, -0.13 [95% CI, -0.19 to -0.06 mm/wk; P < 0.001]). No statistically significant differences were seen in urinary free cortisol assessments. Eight and 6 mild to moderate adverse events in 10 children were reported during treatment with BDP-HFA and BDP-CFC, respectively. One event in each group was judged to be probably related to the study medication; no others were judged to be related.

CONCLUSIONS

No statistically significant differences were found in lower leg growth between BDP-HFA 100 μg BID with AeroChamber Plus spacer and BDP-CFC 200 μg BID with Volumatic spacer during 2-week treatment. Evidence of differences in systemic activity between the treatments was not found. EudraCT registration: 2007-007455-14.

Outpatient versus inpatient treatment for patients with acute pulmonary embolism: an international, open-label, randomised, non-inferiority trial

BACKGROUND

Although practice guidelines recommend outpatient care for selected, haemodynamically stable patients with pulmonary embolism, most treatment is presently inpatient based. We aimed to assess non-inferiority of outpatient care compared with inpatient care.

METHODS

We undertook an open-label, randomised non-inferiority trial at 19 emergency departments in Switzerland, France, Belgium, and the USA. We randomly assigned patients with acute, symptomatic pulmonary embolism and a low risk of death (pulmonary embolism severity index risk classes I or II) with a computer-generated randomisation sequence (blocks of 2-4) in a 1:1 ratio to initial outpatient (ie, discharged from hospital ≤24 h after randomisation) or inpatient treatment with subcutaneous enoxaparin (≥5 days) followed by oral anticoagulation (≥90 days). The primary outcome was symptomatic, recurrent venous thromboembolism within 90 days; safety outcomes included major bleeding within 14 or 90 days and mortality within 90 days. We used a non-inferiority margin of 4% for a difference between inpatient and outpatient groups. We included all enrolled patients in the primary analysis, excluding those lost to follow-up. This trial is registered with ClinicalTrials.gov, number NCT00425542.

FINDINGS

Between February, 2007, and June, 2010, we enrolled 344 eligible patients. In the primary analysis, one (0·6%) of 171 outpatients developed recurrent venous thromboembolism within 90 days compared with none of 168 inpatients (95% upper confidence limit [UCL] 2·7%; p=0·011). Only one (0·6%) patient in each treatment group died within 90 days (95% UCL 2·1%; p=0·005), and two (1·2%) of 171 outpatients and no inpatients had major bleeding within 14 days (95% UCL 3·6%; p=0·031). By 90 days, three (1·8%) outpatients but no inpatients had developed major bleeding (95% UCL 4·5%; p=0·086). Mean length of stay was 0·5 days (SD 1·0) for outpatients and 3·9 days (SD 3·1) for inpatients.

INTERPRETATION

In selected low-risk patients with pulmonary embolism, outpatient care can safely and effectively be used in place of inpatient care.

FUNDING

Swiss National Science Foundation, Programme Hospitalier de Recherche Clinique, and the US National Heart, Lung, and Blood Institute. Sanofi-Aventis provided free drug supply in the participating European centres.

A comparison of methods for sample size estimation for non-inferiority studies with binary outcomes

Non-inferiority trials are motivated in the context of clinical research where a proven active treatment exists and placebo-controlled trials are no longer acceptable for ethical reasons. Instead, active-controlled trials are conducted where a treatment is compared to an established treatment with the objective of demonstrating that it is non-inferior to this treatment. We review and compare the methodologies for calculating sample sizes and suggest appropriate methods to use. We demonstrate how the simplest method of using the anticipated response is predominantly consistent with simulations. In the context of trials with binary outcomes with expected high proportions of positive responses, we show how the sample size is quite sensitive to assumptions about the control response. We recommend when designing such a study that sensitivity analyses be performed with respect to the underlying assumptions and that the Bayesian methods described in this article be adopted to assess sample size.

Methodology and implications of knemometry in growth assessment of inhaled glucocorticoids

When validated recommendations for standardization and measurement procedures are used short-term assessment of lower leg growth by knemometry is a highly accurate and reproducible method for assessment of systemic activity of inhaled glucocorticoids. Crossover and parallel designs applying consistent measurement intervals can be used. Crossover designs with a single-blind run in and washout and double-blind active periods are as sensitive as designs using randomized placebo periods. In populations of children, short-term knemometry appears to be capable of defining specific glucocorticoids, application devices and doses that do not suppress long-term height growth. Although no specific cut-off level can be identified in individuals from the available randomized, double-blind short-term knemometry and intermediate-term height growth rate studies, good evidence have been provided that if the short-term lower leg growth suppression in populations of children is higher than approximately 25%, the risk of intermediate-term growth suppression becomes significant with a mean height growth rate retardation in the range of approximately 0.5-1.5 cm during the first year of treatment. Short-term knemometry should be performed as an integral part of the safety assessments of new inhaled glucocorticoids and inhalation devices in children with asthma, before intermediate-term height growth evaluations are initiated.

A mixed approach for proving non-inferiority in clinical trials with binary endpoints

When a new treatment is compared to an established one in a randomized clinical trial, it is standard practice to statistically test for non-inferiority rather than for superiority. When the endpoint is binary, one usually compares two treatments using either an odds-ratio or a difference of proportions. In this paper, we propose a mixed approach which uses both concepts. One first defines the non-inferiority margin using an odds-ratio and one ultimately proves non-inferiority statistically using a difference of proportions. The mixed approach is shown to be more powerful than the conventional odds-ratio approach when the efficacy of the established treatment is known (with good precision) and high (e.g. with more than 56% of success). The gain of power achieved may lead in turn to a substantial reduction in the sample size needed to prove non-inferiority. The mixed approach can be generalized to ordinal endpoints.

Blinded sample size reestimation in non-inferiority trials with binary endpoints

Sample size calculations in the planning of clinical trials depend on good estimates of the model parameters involved. When the estimates of these parameters have a high degree of uncertainty attached to them, it is advantageous to reestimate the sample size after an internal pilot study. For non-inferiority trials with binary outcome we compare the performance of Type I error rate and power between fixed-size designs and designs with sample size reestimation. The latter design shows itself to be effective in correcting sample size and power of the tests when misspecification of nuisance parameters occurs with the former design.

Active-control trials with binary data: a comparison of methods for testing superiority or non-inferiority using the odds ratio

This paper considers methods for testing for superiority or non-inferiority in active-control trials with binary data, when the relative treatment effect is expressed as an odds ratio. Three asymptotic tests for the log-odds ratio based on the unconditional binary likelihood are presented, namely the likelihood ratio, Wald and score tests. All three tests can be implemented straightforwardly in standard statistical software packages, as can the corresponding confidence intervals. Simulations indicate that the three alternatives are similar in terms of the Type I error, with values close to the nominal level. However, when the non-inferiority margin becomes large, the score test slightly exceeds the nominal level. In general, the highest power is obtained from the score test, although all three tests are similar and the observed differences in power are not of practical importance.

Rethinking statistical approaches to evaluating drug safety

PURPOSE

The current methods used to evaluate the efficacy of drug products are inadequate. We propose a non-inferiority approach to prove the safety of drugs.

MATERIALS AND METHODS

Traditional hypotheses for the evaluation of the safety of drugs are based on proof of hazard, which have proven to be inadequate. Therefore, based on the concept of proof of safety, the non-inferiority hypothesis is employed to prove that the risk of new drugs does not exceed a pre-specified allowable safety margin, hence proving that a drug has no excessive risk. The results from papers published on Vioxx and Avandia are used to illustrate the difference between the traditional approach for proof of hazard and the non-inferiority approach for proof of safety.

RESULTS

The p-values from traditional hypotheses were greater than 0.05, and failed to demonstrate that Vioxx and Avandia are of cardiovascular hazard. However, these results cannot prove that both Vioxx and Avandia are of no cardiovascular risk. On the other hand, the non-inferiority approach can prove that they are of excessive cardiovascular risk.

CONCLUSION

The non-inferiority approach is appropriate to prove the safety of drugs.

Short-term growth and adrenal function in children with asthma treated with inhaled beclomethasone dipropionate hydrofluoroalkane-134a

Inhaled beclomethasone dipropionate (BDP) with the propellant hydrofluoroalkane-134a (HFA) has been designed to be equivalent in terms of safety to chlorofluorocarbon (CFC)-formulated metered dose inhalers (MDI). The aim was to assess whether BDP HFA MDI 100 microg twice daily was equivalent to BDP CFC MDI 100 microg twice daily in terms of effects on short-term lower leg growth rate (LLGR) and measures of hypothalamic-pituitary-adrenal (HPA) function. The study consisted of a randomized double-blind cross-over trial with three active, a run-in and two wash-out periods each consisting of 2 wk. The place of study was a secondary referral outpatient clinic. The subjects involved were 14 boys and 10 girls with asthma, aged 7-12 yr. They were all administered BDP HFA 100 microg, BDP CFC 100 microg and 200 microg twice daily. The outcome measures included LLGR and 24-h urine-free cortisol (UFC) and total cortisol metabolites (TCM). Mean (SD) LLGR during run-in and BDP HFA 100 microg, BDP CFC 100 microg and 200 microg twice daily periods were 0.43 (0.23), 0.09 (0.29), 0.10 (0.45) and 0.08 (0.27) mm/wk. The one-sided 97.5% confidence interval for the difference in LLGR between BDP HFA 100 microg and BDP CFC 100 microg was 0.24, thus, below the predefined criterion of 0.20 mm/week. Inter-period comparisons of active treatments showed no differences between means of LLGR, UFC or TCM. Though non-inferiority between BDP HFA and CFC 100 microg twice daily in terms of effects on LLGR was not found, equivalence was suggested by comparisons of LLGR during run-in and active treatments and by HPA function measures.

Statistical considerations for noninferiority/equivalence trials in vaccine development

Noninferioritylequivalence designs are often used in vaccine clinical trials. The goal of these designs is to demonstrate that a new vaccine, or new formulation or regimen of an existing vaccine, is similar in terms of effectiveness to the existing vaccine, while offering such advantages as easier manufacturing, easier administration, lower cost, or improved safety profile. These noninferioritylequivalence designs are particularly useful in four common types of immunogenicity trials: vaccine bridging trials, combination vaccine trials, vaccine concomitant use trials, and vaccine consistency lot trials. In this paper, we give an overview of the key statistical issues and recent developments for noninferioritylequivalence vaccine trials. Specifically, we cover the following topics: (i) selection of study endpoints; (ii) formulation of the null and alternative hypotheses; (iii) determination of the noninferioritylequivalence margin; (iv) selection of efficient statistical methods for the statistical analysis of noninferioritylequivalence vaccine trials, with particular emphasis on adjustment for stratification factors and missing pre-or post-vaccination data; and (v) the calculation of sample size and power.

Problems with Existing Procedures to Calculate Exact Unconditional P-Values for Non-Inferiority/Superiority and Confidence Intervals for Two Binomials and How to Resolve Them

Recently several papers have been published that deal with the construction of exact unconditional tests for non-inferiority and confidence intervals based on the approximative unconditional restricted maximum likelihood test for two binomial random variables. Soon after the papers have been published the commercially available software for exact tests StatXact has incorporated the new methods. There are however gaps in the proofs which since have not been resolved adequately. Further it turned out that the methods for testing non-inferiority are not coherent and test for non-inferiority can easily come to different conclusions compared to the confidence interval inclusion rule. In this paper, a proposal is made how to resolve the open problems. Berger and Boos (1994) developed the confidence interval method for testing equality of two proportions. StatXact (Version 5) has extended this method for shifted hypotheses. It is shown that at least for unbalanced designs (i.e. largely different sample sizes) the Berger and Boos method can lead to controversial results.

Statistical Methods for the Analysis of Two-Arm Non-inferiority Trials with Binary Outcomes

The aim of this contribution is to give an overview of approaches to testing for non-inferiority of one out of two binomial distributions as compared to the other in settings involving independent samples (the paired samples case is not considered here but the major conclusions and recommendations can be shown to hold for both sampling schemes). In principle, there is an infinite number of different ways of defining (one-sided) equivalence in any multiparameter setting. In the binomial two-sample problem, the following three choices of a measure of dissimilarity between the underlying distributions are of major importance for real applications: the odds ratio (OR), the relative risk (RR), and the difference (DEL) of both binomial parameters. It is shown that for all three possibilities of formulating the hypotheses of a non-inferiority problem concerning two binomial proportions, reasonable testing procedures providing exact control over the type-I error risk are available. As a particularly useful and versatile way of handling mathematically nonnatural parametrizations like RR and DELTA, the approach through Bayesian posterior probabilities of hypotheses with respect to some non-informative reference prior has much to recommend it. In order to ensure that the corresponding testing procedure be valid in the classical, i.e. frequentist sense, it suffices to use straightforward computational techniques yielding suitably corrected nominal significance levels. In view of the availability of testing procedures with satisfactory properties for all parametrizations of main practical interest, the discussion of the pros and cons of these methods has to focus on the question of which of the underlying measures of dissimilarity should be preferred on grounds of logic and intuition. It is argued that the OR clearly merits to be given preference also with regard to this latter kind of criteria since the non-inferiority hypotheses defined in terms of the other parametric functions are bounded by lines which cross the boundaries of the parameter space. From this fact, we conclude that the exact Fisher type test for one-sided equivalence provides the most reasonable approach to the confirmatory analysis of non-inferiority trials involving two independent samples of binary data. The marked conservatism of the nonrandomized version of this test can largely be removed by using a suitably increased nominal significance level (depending, in addition to the target level, on the sample sizes and the equivalence margin), or by replacing it with a Bayesian test for non-inferiority with respect to the odds ratio.

Reduction of postoperative chemotherapy in children with stage I intermediate-risk and anaplastic Wilms' tumour (SIOP 93-01 trial): a randomised controlled trial

BACKGROUND

Present treatment for Wilms' tumour is very successful. Now, efforts are aimed at reducing toxicity and burden of treatment by shortening schedules without loss of effectiveness. The objective of this randomised trial was to assess whether postoperative chemotherapy for patients with stage I intermediate-risk and anaplastic Wilms' tumour could be shortened to only 4 weeks from the standard 18 weeks, while maintaining equivalent event-free survival.

METHODS

Between June, 1993, and June, 2000, 410 patients were randomly assigned after four doses of vincristine plus one course of dactinomycin postoperatively either to stop further adjuvant chemotherapy (no further chemotherapy group, n=200), or to receive a further two courses of the same chemotherapy (standard group, n=210). Previous treatment consisted of chemotherapy before nephrectomy of four doses of vincristine and two courses of dactinomycin followed by surgical resection of the tumour. Eligible patients were at least 6 months old and had stage I tumours with either intermediate-risk histology or anaplasia. The primary endpoint of this equivalence trial was 2-year event-free survival. Both per-protocol and intention-to-treat analyses were done.

FINDINGS

By 2 years, 18 recurrences were reported in the standard group, and 22 in the no further chemotherapy group. Event-free survival was 91.4% (95% CI 87.5-95.2) for the no further chemotherapy group and 88.8% (84.3-93.2) for the standard group (difference=2.6%, upper 97.5% confidence limit 8.4%). The null hypothesis, that experimental treatment is less effective than standard treatment, could be rejected (p=0.008).

CONCLUSIONS

Shortening duration of chemotherapy could reduce acute and late side-effects and inconvenience for patient and parents while maintaining effectiveness, and could be beneficial in terms of health costs.

Colon cancer controls versus population controls in case-control studies of occupational risk factors

Background

Since updated population registers do not exist in many countries it is often difficult to sample valid population controls from the study base to a case-control study. Use of patient controls is an alternative option if the exposure experience under study for these patients are interchangeable with the experience for population controls. Patient controls may even be preferable from population controls under certain conditions. In this study we examine if colon cancer patients can serve as surrogates for proper population controls in case-control studies of occupational risk factors.

Methods

The study was conducted from 1995 to 1997. Incident colon cancer controls (N = 428) aged 35–69 years with a histological verified diagnosis and population controls (N = 583) were selected. Altogether 254 (59%) of the colon cancer controls and 320 (55%) of the population controls were interviewed about occupational, medical and life style conditions.

Results

No statistical significant difference for educational level, medical history or smoking status was seen between the two control groups. There was evidence of a higher alcohol intake, less frequent work as a farmer and less exposure to pesticides among colon cancer controls.

Conclusions

Use of colon cancer controls may provide valid exposure estimates in studies of many occupational risk factors for cancer, but not for studies on exposure related to farming.