Timing of analysesInterim analysis

The proposed interim analysis—with the purpose to perform a sample size re-estimation—will be conducted when at least 29 patients have completed the primary endpoint, which is initially expected to happen at month 21. The primary rationale behind the timing of the interim analysis is based on the minimum sample size needed to make precise enough estimates of the variance parameters in each arm of the trial. A range of published literature exists on the topic of minimum sample size for pilot studies, which is akin to the sample size requirements for an interim sample size re-estimation or internal pilot.

Traditionally, a “rule of thumb” approach was used to set the sample size for pilot studies at around 30, though there have also been a number of important papers published giving a more scientific basis for the selection of sample size for pilot studies.

For two-arm studies with a continuous outcome, Julious (2005) recommends a total sample size of 24 [17] and Keiser (1996) recommends a total sample size of 20–40 [18], whilst Sim (2011) recommends a total sample size of at least 50 [19] and Teare (2014) recommends a total sample size of at least 70 [20]. More discussions can be found in the work of Whitehead et al. [21].

Our recommendation for performing the interim sample size re-estimation after at least 29 patients have completed their primary endpoint sits towards the lower end of these figures. This must be carefully balanced with the duration of treatment and follow-up, particularly in the case of trials using a cross-over design, which will naturally delay the point at which the interim analysis occurs. In addition, if there is a large amount of missing data for the primary endpoint, then the interim analysis may be delayed.

Final analysis

The final analysis will be undertaken after data cleaning and following database lock, which may take place once the final participant has completed their 24 weeks of total follow-up.

Trial populationRecruitment and eligibility

The progress of all participants through the trial will be shown within a CONSORT flow diagram. This will include (but is not limited to) the following:

Assessed for eligibility at screening

Eligible at screening

Ineligible at screening*

Eligible and randomised

Eligible but not randomised*

Received the randomised allocation

Did not receive the randomised allocation*

Lost to follow-up*

Discontinued the intervention*

Randomised and included in the primary analysis

Randomised and excluded from the primary analysis*

*Reasons will be provided.

Eligibility criteria are provided in the protocol. The frequency of each exclusion criterion will be reported.

Withdrawal and follow-up

The level of consent withdrawal will be tabulated. Timing of withdrawal and loss to follow-up data will be incorporated into the CONSORT diagram. Reasons for withdrawal and loss to follow-up will be tabulated, where known.

Baseline participant characteristics

Participant characteristics at baseline will be reported for both the analysis population and for all randomised participants. Categorical data will be summarised by numbers and percentages. Continuous data will be summarised by mean, SD, median, IQR, and range. No statistical analysis of baseline data is planned. Characteristics include (but are not limited to) standard demographic information such as age, sex, and BMI, as well as those listed in “Outcomes in detail” above.

Analysis populations

Before database lock, each patient will be included or excluded from each of the analysis populations defined below. This will be carried out prior to unblinding to avoid bias of any analyses.

Both statistics and health economics teams will receive the same data sets for final analyses.

Safety population

The safety population includes all subjects entered into the study, regardless of whether they received any study treatment. The safety population will be used to provide summary statistics on adverse events and serious adverse events.

The interim analysis will include safety data. In this instance, the safety population should include all subjects entered into the study at the time of database lock for the interim analysis, regardless of whether they are formally included in the interim analysis population. We will include anyone who has withdrawn if they consent to their data still being used. Safety data will be split into participants who are still in the trial and those who are not.

Interim analysis population

The interim analysis population will include all patients who have completed the study, with the exception of those who provide very little adherence data (see section “Missing data at interim analysis”).

Intention-to-treat population

The intention-to-treat analysis population includes all subjects who were randomised, regardless of whether they received the treatment randomly allocated to them and also completed the two therapies (CPAP or CPAP-MAD combination). The data will be analysed assuming that the patient received both treatments and in the order that they were randomly allocated.

Per-protocol population

In general, the per-protocol population is the group of participants who are most compliant with the protocol and/or “received the randomised treatment” for some definition that is pre-specified and appropriate for each study. However, it is not possible to accurately assess the extent to which participants receive the CPAP + MAD combination treatment, as days of combined use are not recorded. As such, no per-protocol population is defined, and no per-protocol analysis is planned.

Subgroup-analysis population

The planned subgroup-analysis population is comprised of the participants from the two recruiting centres (Royal Papworth Hospital and Bristol Royal Infirmary).

Missing data

Missing data will be quantified per variable with missing frequencies and proportions (%) by groups. All essential variables for the outcomes are expected to be complete or at least low missing percentages (less than 5%) before starting analysis. Variables with > 25% missing data may not be used in modelling as covariates or outcomes unless they have clinical importance. Such variables will be summarised and reported if listed as intended covariates or outcomes.

For participants who discontinue the allocated treatment CPAP + MAD but continue to use the CPAP machine, we will use their adherence data as if they were still continuing their allocated treatment (i.e. intention to treat). For participants who discontinue the allocated treatment CPAP (and thus no longer provide adherence data), we will impute their adherence as 0 h for each remaining day. This pragmatic approach reflects the primary endpoint, which is the number of hours of CPAP adherence, and the wider research question, which is to examine if CPAP adherence is greater for participants allocated to CPAP + MAD compared to those allocated to CPAP only.

For the primary endpoints and the planned covariates for the primary analysis, if the proportion of missing data is at most 5% or the mechanism is missing completely at random (MCAR), we will ignore the missing data and run a complete-case analysis. If the proportion of missing data is greater than 5% and not MCAR, we may impute the missing data by using multiple imputation by chained equations techniques (MICE) [22]. The imputed data would be analysed as a sensitivity analysis for the primary analysis only. When MICE is used, the imputation model will include endpoints and predictors of baseline variables with missing data. The number of imputed datasets depends on the overall missing proportion in the analysis data [23]. The imputation methods for variables with missing values may depend on the variable type or the fixed formula (such as BMI). Sensitivity analysis will be carried out to evaluate the robustness of the estimated coefficients where missing data has been imputed. Missingness indicators will be created for examining the mechanism by using statistical testing (such as Little’s test [24], t-test, and chi-squared test) or graphical inspection.

Missing data at interim analysis

Participants who provide at least 14 days of CPAP adherence data for both treatment arms will be included in the sample size re-estimation; otherwise, they will be excluded. If > 10% of participants do not reach this threshold, we will attempt to include their data, appropriately weighted in comparison to the more complete data from other participants.