Design and analysis of three-arm trials with negative binomially distributed endpoints

Partially supervised exercise programmes for fall prevention improve physical performance of older people at risk of falling: a three-armed multi-centre randomised controlled trial

BACKGROUND

Falls have a major impact on individual patients, their relatives, the healthcare system and related costs. Physical exercise programmes that include multiple categories of exercise effectively reduce the rate of falls and risk of falling among older adults.

METHODS

This 12-month, assessor-blinded, three-armed multicentre randomised clinical trial was conducted in adults aged ≥ 65 years identified as at risk of falling. Four hundred and five participants were randomly allocated into 3 groups: experimental group (n = 166) with the Test&Exercise partially supervised programme based on empowerment delivered with a tablet, illustrated manual and cards, reference group (n = 158) with the Otago partially supervised programme prescribed by a physiotherapist delivered with an illustrated manual and control group (n = 81) with the Helsana self-administrated programme delivered with cards. Experimental and reference groups received partially supervised programmes with 8 home sessions over 6 months. Control group received a self-administered program with a unique home session. The 3 groups were requested to train independently 3 times a week for 12 months. Primary outcome was the incidence rate ratio of self-reported falls over 12 months. Secondary outcomes were fear of falling, basic functional mobility and balance, quality of life, and exercise adherence.

RESULTS

A total of 141 falls occurred in the experimental group, 199 in the reference group, and 42 in the control group. Incidence rate ratios were 0.74 (95% CI 0.49 to 1.12) for the experimental group and 0.43 (95% CI 0.25 to 0.75) for the control group compared with the reference group. The Short Physical Performance Battery scores improved significantly in the experimental group (95% CI 0.05 to 0.86; P = 0.027) and in the reference group (95% CI 0.06 to 0.86; P = 0.024) compared with the control group.

CONCLUSION

The self-administered home-based exercise programme showed the lowest fall incidence rate, but also the highest dropout rate of participants at high risk of falling. Both partially supervised programmes resulted in statistically significant improvements in physical performance compared with the self-administered programme.

TRIAL REGISTRATION

NCT02926105.

CLINICALTRIALS

gov. Date of registration: 06/10/2016.

A more powerful test for three-arm non-inferiority via risk difference: Frequentist and Bayesian approaches

Necessity for finding improved intervention in many legacy therapeutic areas are of high priority. This has the potential to decrease the expense of medical care and poor outcomes for many patients. Typically, clinical efficacy is the primary evaluating criteria to measure any beneficial effect of a treatment. Albeit, there could be situations when several other factors (e.g. side-effects, cost-burden, less debilitating, less intensive, etc.) which can permit some slightly less efficacious treatment options favorable to a subgroup of patients. This often leads to non-inferiority (NI) testing. NI trials may or may not include a placebo arm due to ethical reasons. However, when included, the resulting three-arm trial is more prudent since it requires less stringent assumptions compared to a two-arm placebo-free trial. In this article, we consider both Frequentist and Bayesian procedures for testing NI in the three-arm trial with binary outcomes when the functional of interest is risk difference. An improved Frequentist approach is proposed first, which is then followed by a Bayesian counterpart. Bayesian methods have a natural advantage in many active-control trials, including NI trial, as it can seamlessly integrate substantial prior information. In addition, we discuss sample size calculation and draw an interesting connection between the two paradigms.

Bayesian sample size determination in a three-arm non-inferiority trial with binary endpoints

A three-arm non-inferiority trial including a test treatment, a reference treatment, and a placebo is recommended to assess the assay sensitivity and internal validity of a trial when applicable. Existing methods for designing and analyzing three-arm trials with binary endpoints are mainly developed from a frequentist viewpoint. However, these methods largely depend on large sample theories. To alleviate this problem, we propose two fully Bayesian approaches, the posterior variance approach and Bayes factor approach, to determine sample size required in a three-arm non-inferiority trial with binary endpoints. Simulation studies are conducted to investigate the performance of the proposed Bayesian methods. An example is illustrated by the proposed methodologies. Bayes factor method always leads to smaller sample sizes than the posterior variance method, utilizing the historical data can reduce the required sample size, simultaneous test requires more sample size to achieve the desired power than the non-inferiority test, the selection of the hyperparameters has a relatively large effect on the required sample size. When only controlling the posterior variance, the posterior variance criterion is a simple and effective option for obtaining a rough outcome. When conducting a previous clinical trial, it is recommended to use the Bayes factor criterion in practical applications.

New approaches for testing non-inferiority for three-arm trials with Poisson distributed outcomes

With the availability of limited resources, innovation for improved statistical method for the design and analysis of randomized controlled trials (RCTs) is of paramount importance for newer and better treatment discovery for any therapeutic area. Although clinical efficacy is almost always the primary evaluating criteria to measure any beneficial effect of a treatment, there are several important other factors (e.g., side effects, cost burden, less debilitating, less intensive, etc.), which can permit some less efficacious treatment options favorable to a subgroup of patients. This leads to non-inferiority (NI) testing. The objective of NI trial is to show that an experimental treatment is not worse than an active reference treatment by more than a pre-specified margin. Traditional NI trials do not include a placebo arm for ethical reason; however, this necessitates stringent and often unverifiable assumptions. On the other hand, three-arm NI trials consisting of placebo, reference, and experimental treatment, can simultaneously test the superiority of the reference over placebo and NI of experimental treatment over the reference. In this article, we proposed both novel Frequentist and Bayesian procedures for testing NI in the three-arm trial with Poisson distributed count outcome. RCTs with count data as the primary outcome are quite common in various disease areas such as lesion count in cancer trials, relapses in multiple sclerosis, dermatology, neurology, cardiovascular research, adverse event count, etc. We first propose an improved Frequentist approach, which is then followed by it's Bayesian version. Bayesian methods have natural advantage in any active-control trials, including NI trial when substantial historical information is available for placebo and established reference treatment. In addition, we discuss sample size calculation and draw an interesting connection between the two paradigms.

Simultaneous confidence interval for assessing non-inferiority with assay sensitivity in a three-arm trial with binary endpoints

A three-arm trial including an experimental treatment, an active reference treatment and a placebo is often used to assess the non-inferiority (NI) with assay sensitivity of an experimental treatment. Various hypothesis-test-based approaches via a fraction or pre-specified margin have been proposed to assess the NI with assay sensitivity in a three-arm trial. There is little work done on confidence interval in a three-arm trial. This paper develops a hybrid approach to construct simultaneous confidence interval for assessing NI and assay sensitivity in a three-arm trial. For comparison, we present normal-approximation-based and bootstrap-resampling-based simultaneous confidence intervals. Simulation studies evidence that the hybrid approach with the Wilson score statistic performs better than other approaches in terms of empirical coverage probability and mesial-non-coverage probability. An example is used to illustrate the proposed approaches.

Sequential parallel comparison design for "gold standard" noninferiority trials with a prespecified margin

Three-arm noninferiority trials (involving an experimental treatment, a reference treatment, and a placebo)-called the "gold standard" noninferiority trials-are conducted in patients with mental disorders whenever feasible, but often fail to show superiority of the experimental treatment and/or the reference treatment over the placebo. One possible reason is that some of the patients receiving the placebo show apparent improvement in the clinical condition. An approach to addressing this problem is the use of the sequential parallel comparison design (SPCD). Nonetheless, the SPCD has not yet been discussed in relation to gold standard noninferiority trials. In this article, our aim was to develop a hypothesis-testing method and its corresponding sample size calculation method for gold standard noninferiority trials with the SPCD. In a simulation, we show that the proposed hypothesis-testing method achieves the nominal type I error rate and power and that the proposed sample size calculation method has adequate power accuracy.

Effects of three home-based exercise programmes regarding falls, quality of life and exercise-adherence in older adults at risk of falling: protocol for a randomized controlled trial

Background

Fall prevention interventions with home-based exercise programmes are effective to reduce the number and the rate of falls, by reducing risk factors. They improve balance, strength, function, physical activity, but it is known that older adults’ exercise adherence declines over time. However, it is unclear which delivery-modalities of the home-based exercise programmes show the best adherence and the largest effect.

We created a new home-based exercise programme, the Test-and-Exercise (T&E) programme, based on the concepts of self-efficacy and empowerment. Patients learn to build their own exercise programme with a mobile application, a brochure and cards, as well as with eight coaching sessions by physiotherapists.

The main objective of this study is to compare the T&E programme with the Otago Exercise Programme and the recommendation-booklet and exercise-cards of Helsana regarding incidence of falls. Other outcomes are severity of falls, functional capacities, quality of life and exercise-adherence.

Methods

The design of this study is a Swiss multicentre assessor blind randomized controlled trial. A block-randomization, stratified in groups for age and risk of fall categories, will be used to allocate the participants to three groups. The targeted study sample consists of 405 older adults, ≥ 65 years of age, living in the community and evaluated as at “risk of falling”. Experimental group will receive the T&E programme (N = 162). Second group will receive the Otago programme (N = 162) and the third group will receive the Helsana programme (N = 81). All interventions last six months. Blinded assessors will assess participants three times: at baseline before the start of the intervention, after six months of intervention and a final assessment after twelve months (six months of follow up).

Discussion

Although home-based exercises programmes show positive effects in fall prevention in elderly persons, existing programmes do often not include patients in the decision-making process about exercise selection. In our programme the physiotherapist and the older adult work together to select the exercises; this collaboration helps to increase health literacy, pleasure of exercising, and empowers patients to be more autonomy.

Trial registration

ClinicalTrials.gov: NCT02926105, First Posted: October 6, 2016, Last Update: November 11, 2016: Enrolment of the first participant.

Non-inferiority Testing for Risk Ratio, Odds Ratio and Number Needed to Treat in Three-arm Trial

Three-arm non-inferiority (NI) trial including the experimental treatment, an active reference treatment, and a placebo where the outcome of interest is binary are considered. While the risk difference (RD) is the most common and well explored functional form for testing efficacy (or effectiveness), however, recent FDA guideline suggested measures such as relative risk (RR), odds ratio (OR), number needed to treat (NNT) among others, on the basis of which NI can be claimed for binary outcome. Albeit, developing test based on these different functions of binary outcome are challenging. This is because the construction and interpretation of NI margin for such functions are non-trivial extensions of RD based approach. A Frequentist test based on traditional fraction margin approach for RR, OR and NNT are proposed first. Furthermore a conditional testing approach is developed by incorporating assay sensitivity (AS) condition directly into NI testing. A detailed discussion of sample size/power calculation are also put forward which could be readily used while designing such trials in practice. A clinical trial data is reanalyzed to demonstrate the presented approach.

Design and analysis of a 3-arm noninferiority trial with a prespecified margin for the hazard ratio

A 3-arm trial design that includes an experimental treatment, an active reference treatment, and a placebo is useful for assessing the noninferiority of an experimental treatment. The inclusion of a placebo arm enables the assessment of assay sensitivity and internal validation, in addition to the testing of the noninferiority of the experimental treatment compared with the reference treatment. In 3-arm noninferiority trials, various statistical test procedures have been considered to evaluate the following 3 hypotheses: (i) superiority of the experimental treatment over the placebo, (ii) superiority of the reference treatment over the placebo, and (iii) noninferiority of the experimental treatment compared with the reference treatment. However, hypothesis (ii) can be insufficient and may not accurately assess the assay sensitivity for the noninferiority of the experimental treatment compared with the reference treatment. Thus, demonstrating that the superiority of the reference treatment over the placebo is greater than the noninferiority margin (the nonsuperiority of the reference treatment compared with the placebo) can be necessary. Here, we propose log-rank statistical procedures for evaluating data obtained from 3-arm noninferiority trials to assess assay sensitivity with a prespecified margin Δ. In addition, we derive the approximate sample size and optimal allocation required to minimize the total sample size and that of the placebo treatment sample size, hierarchically.

Group sequential designs for negative binomial outcomes

Count data and recurrent events in clinical trials, such as the number of lesions in magnetic resonance imaging in multiple sclerosis, the number of relapses in multiple sclerosis, the number of hospitalizations in heart failure, and the number of exacerbations in asthma or in chronic obstructive pulmonary disease (COPD) are often modeled by negative binomial distributions. In this manuscript, we study planning and analyzing clinical trials with group sequential designs for negative binomial outcomes. We propose a group sequential testing procedure for negative binomial outcomes based on Wald statistics using maximum likelihood estimators. The asymptotic distribution of the proposed group sequential test statistics is derived. The finite sample size properties of the proposed group sequential test for negative binomial outcomes and the methods for planning the respective clinical trials are assessed in a simulation study. The simulation scenarios are motivated by clinical trials in chronic heart failure and relapsing multiple sclerosis, which cover a wide range of practically relevant settings. Our research assures that the asymptotic normal theory of group sequential designs can be applied to negative binomial outcomes when the hypotheses are tested using Wald statistics and maximum likelihood estimators. We also propose two methods, one based on Student's t-distribution and one based on resampling, to improve type I error rate control in small samples. The statistical methods studied in this manuscript are implemented in the R package gscounts, which is available for download on the Comprehensive R Archive Network (CRAN).

Blinded sample size re-estimation in three-arm trials with 'gold standard' design

In this article, we study blinded sample size re-estimation in the 'gold standard' design with internal pilot study for normally distributed outcomes. The 'gold standard' design is a three-arm clinical trial design that includes an active and a placebo control in addition to an experimental treatment. We focus on the absolute margin approach to hypothesis testing in three-arm trials at which the non-inferiority of the experimental treatment and the assay sensitivity are assessed by pairwise comparisons. We compare several blinded sample size re-estimation procedures in a simulation study assessing operating characteristics including power and type I error. We find that sample size re-estimation based on the popular one-sample variance estimator results in overpowered trials. Moreover, sample size re-estimation based on unbiased variance estimators such as the Xing-Ganju variance estimator results in underpowered trials, as it is expected because an overestimation of the variance and thus the sample size is in general required for the re-estimation procedure to eventually meet the target power. To overcome this problem, we propose an inflation factor for the sample size re-estimation with the Xing-Ganju variance estimator and show that this approach results in adequately powered trials. Because of favorable features of the Xing-Ganju variance estimator such as unbiasedness and a distribution independent of the group means, the inflation factor does not depend on the nuisance parameter and, therefore, can be calculated prior to a trial. Moreover, we prove that the sample size re-estimation based on the Xing-Ganju variance estimator does not bias the effect estimate. Copyright © 2017 John Wiley & Sons, Ltd.