Sample size
The trial concerns an important but rare subgroup of severe asthma patients, and recruitment is anticipated to be highly challenging. Consequently, the trial has been designed around a maximum feasible sample size, meaning a sample size we can recruit using an extended network of centres over a timely period. The trial uses a Bayesian framework to incorporate existing information, and we have undertaken simulations to explore what could be demonstrated with this fixed and limited sample size. This is presented in terms of the probability of NI for three scenarios, that is, if mepolizumab is inferior, the same as, or superior to omalizumab. These results were presented to the trial funder (National Institute for Health Research, Efficacy and Mechanism Evaluation Panel who agreed that there was value in undertaking a trial of this size.
CYP with PSA are expected to have a minimum of four asthma attacks in the previous year, or at least one PICU admission.17 A NI margin of 0.5 attacks per year was selected after discussion with clinicians and parents. A reduction of one attack per year was reasoned to be the minimum benefit required given 12 months of injections with either treatment, and the primary NI margin was taken to be half the minimum benefit required. We demonstrate the value of the trial based on a primary NI margin.
To calculate the maximum feasible sample size, we undertook a survey of 11 specialist paediatric severe asthma centres in the UK originally identified to take part in this trial. These centres combined have 170 new annual PSA referrals, and each centre had an existing cohort of approximately 50 eligible children. Over a 3-year period, we estimated there will be 1060 children with PSA to be eligible for invitation to the run-in study. Assuming a 50% acceptance rate, based on previous experience in this population and parent representative group feedback, we estimate n≈500 will be recruited to the run-in study. Pilot data show approximately 30% of PSA will have STRA, and 15% have RDA giving 225 eligible CYP.18 Assuming a recruitment rate of 66% of these CYP (reasoned on their commitment to the run-in study and the severity of their condition), we anticipate the feasible maximum will be 150 children in the randomised trial. The estimated withdrawal rate is unlikely to be higher than 15% (seen in a 48-week trial where children had to cross-over treatments).19 We therefore estimate that we will obtain 130 CYP who have full (52 weeks) follow-up data.
12 scenarios were explored to examine the strength of evidence this trial may provide under three potential outcomes (mepolizumab is better, no different or worse than omalizumab) using a sample size of 130 (n=65 per arm). Results based on 1000 simulations were repeated to indicate what would be expected for 75% of the sample size and introducing overdispersion in the outcome. The summarised simulation results by calculating the average posterior probability of being non-inferior for a 0.5 NI margin demonstrate that a trial of this size is likely to provide results that would be convincing to change prescribing practice. More information on the simulation results can be seen in online supplemental tables 3 and 4.
Analysis
The trial results will be reported according to Consolidated Standards of Reporting Trials (CONSORT) and the CONSORT extension for NI and equivalence randomised trials.20 21
We will use a Bayesian analysis for the primary outcome only and this will include informative clinician elicited priors on the log treatment effect and log attack rate on the omalizumab arm. More information on the clinician elicitation and the results of this activity can be found in online supplemental material section 8. We will also examine the use of alternative priors on the mean exacerbation rate and the treatment effect. Emerging randomised evidence during the trial will be used to provide an update to the clinician elicited prior as a sensitivity analysis. The first supplementary analysis on the primary outcome (treatment policy approach) will also be undertaken in the Bayesian framework. All other analyses on primary and secondary outcomes will be undertaken in the frequentist framework. In analysis of secondary outcomes, focus will be on estimation of the treatment effect rather than testing NI hypothesis as the NI margins have not been prespecified.
The primary analysis of 52-week asthma attack rate will be done on the modified ‘while on treatment’ population, which will include all randomised CYP who receive at least one dose and up to the time they complete the study, withdraw consent from the study or take another biologic to that which they were allocated (either through switching between arms or new biologic). As a consequence, there will be no multiple imputation for the primary outcome analysis. The analysis population sets for supplementary analysis can be seen in online supplemental table 5.
A Bayesian Poisson regression model will be used to model the primary outcome with treatment arm and minimisation stratification variables (centre, blood eosinophils (<300/≥300 per µL) and IgE (<30, 30–1500, >1500 IU/mL), type (refractory DA/STRA) included as covariates. The recruitment site will be included as a random effect unless there are fewer sites than expected or another reason to model the site as a fixed effect.22
Follow-up time will be included as an offset term to model the rate of exacerbations. Follow-up time will be calculated from the time of randomisation to the CYP’s last study visit (regardless of treatment discontinuation for any reason but in absence of other biologics). A negative binomial regression will replace the Poisson model if there is evidence for over dispersion, which will be checked by fitting a negative binomial and examining the overdispersion parameter. We will report the probability of mepolizumab being non-inferior to omalizumab, as well as the IRR and 95% credible intervals.
Based on the results of the elicitation workshop, a Gamma distribution with parameters (6.36, 4.5) was selected as a final prior for parameter 1; the mean of exacerbation rate in omalizumab arm, exp(α); and a normal distribution (mean=−5.05, SD=12) was confirmed as a prior distribution for parameter 2; the per cent change in exacerbation rate between mepolizumab and omalizumab, expressed as (exp(β1)−1)×100 or incidence rate ratio (IRR−1)×100 (see online supplemental figures 3 and 4). rjags V.4-12 will be used to include the priors in the primary analysis model.
Three supplementary analyses on the primary outcome will be performed: (1) to estimate the treatment effect targeting the treatment policy estimand, (2) to estimate the treatment effect in CYP that adhered to the treatment they were assigned and (3) to estimate the treatment effect if other biologics were not available and CYP did not cross over to the other treatment arm.
All secondary efficacy outcomes are continuous and have been measured repeatedly. As a result, we will fit a mixed effect linear regression model with random subject and centre effects, minimisation stratification variables and time. We will use the same analysis population as the primary analysis.
The baseline randomisation season of CYP will also be included a categorical variable with four levels defined as September–November; December–February; March–May and June–August. NI will not be the focus of these analyses, but we aim to estimate the adjusted mean difference between treatment arms with a 95% CI. A time-by-arm interaction will be included to obtain estimates for mean differences at 4, 16, 32 and 52 weeks. Models will be fitted using restricted maximum likelihood and assumptions will be examined using residual analysis, including the examination of graphical displays such as normal quantile plots as recommended to provide unbiased and robust variance parameter estimates. For CASI, FEV1 and QoL outcomes, we will plot model results over time with 95% CIs by the arm.
We will undertake subgroup analysis based on the type of asthma (STRA and refractory DA) and ethnicity by including an interaction between these variables and treatment arm into the model. Since we are not powered to conduct hypothesis testing in subgroups, the findings will be presented using forest plots and will serve as a basis for generating hypotheses rather than drawing definitive conclusions.
Adverse events will be coded using Medical Dictionary for Regulatory Activities and will be summarised at the Preferred Term and System Organ Class levels. AEs will be tabulated by arm and severity for the number of CYP with at least one adverse event, presented as frequencies and proportions, and number of events occurring among all CYP, presented as counts, mean (SD) number of events per participant and incident rates. Calculation of proportions will use denominators per the safety population definition, and incident rates will use total CYP follow-up time to account for differential follow-up.
For counts that are reasonably large at the system organ class level, we will estimate the IRR and 95% CIs using a negative Binomial model or suitable model, adjusting where possible for minimisation stratification variables. The results from these models will be presented graphically along with the raw counts using visual approaches such as dot plots.23
Mechanistic analysis will be undertaken to explore whether baseline serum IgE and baseline blood/BAL/sputum eosinophils are associated with treatment benefit (measured using both CASI and then asthma exacerbations count) using within arm and between arm modelling and suitable generalised linear models.
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