The study was done in accordance with Good Clinical Practiceand the Declaration of Helsinki.The protocol was approved by each study site's institutional review board, and all patients gave informed consent before entering the study.

To be eligible for the study, patients had to be aged 18–65 years, have an Expanded Disability Severity Scale (EDSS)score of 4·0–6·5 and fulfil the revised McDonald criteria for multiple sclerosis,and at randomisation have entered the secondary progressive stage.The definition of secondary progressive stage was in keeping with that used in other secondary progressive multiple sclerosis trials.Steady progression rather than relapse had to be the major cause of increasing disability in the preceding 2 years, confirmed on the basis of either an increase of at least one point on the EDSS or clinically documented increasing disability. Patients were ineligible if they had primary progressive multiple sclerosis; had a relapse or had been treated with corticosteroids within 3 months of screening; or used immunosuppressants (eg, azathioprine, methotrexate, ciclosporin) or disease modifying treatments (avonex, rebif, betaferon, glatiramer acetate) within the previous 6 months. Detailed inclusion and exclusion criteria are available elsewhere.Patients were seen at months 1, 6, 12, and 24 with telephone follow-up at months 3 and 18.

Patients were randomised in a 1:1 ratio to receive simvastatin 80 mg, or matching placebo drug (after a first month at 40 mg a day), for 24 months. Randomisation was done by a centralised web-based service, with block size of eight, and minimisationon the following variables: age (<45, ≥45 years old); sex; EDSS (4–5·5, 6·0–6·5); centre; and assessing physician. Patients, treating physicians, and outcome assessors (including MRI scan analysts) were masked to treatment allocation. To ensure full masking, both a treating and an independent qualified examining neurologist were involved in the trial.

We investigated phenotypic markers with whole blood specimens collected at baseline, 6, 12, and 24 months. Intracellular cytokine expression was examined in CD3+ T cells for IFN-γ, IL-4, and IL-17 as markers of Th/Tc1, Th/Tc2, and Th/Tc17 T-cell populations, respectively. Intracellular cytokine (IL-4, IFN-γ, IL-10, IL-17) expression on unstimulated T cells and cells stimulated with 50 ng per mL of Phorbol 12-myristate 13-acetate and 1 μg per mL ionomycin was done as previously described ( appendix ).Coexpression of CD4+ and intracellular expression of FoxP3 and IL-10 were examined as markers of regulatory T cells.

Clinical outcomes assessed at baseline, 12 months, and 24 months were EDSS,multiple sclerosis functional composite scale (MSFC),multiple sclerosis impact scale-29 (MSIS-29)version 2, and relapse frequency. The MSFC Z score was normalised with the study baseline scores. Cholesterol levels were taken at baseline and 24 months.

The predefined primary endpoint was the rate of whole-brain atrophy per year, measured as relative change in brain volume by K-means normalisation brain boundary shift integral (BSI),based on each pair of volumetric T1 MRI scans between baseline, 12 months, and 25 months. BSI, like structural image evaluation using normalisation of atrophy (SIENA) is a well-validated and established registration-based, semi-automated, direct measure of volume change that has robust performance characteristics.The volumetric scan was acquired twice at baseline, with the best-quality scan chosen for analysis on the basis of expert visual rating of motion and artifact. Scan acquisition sequence parameters were also reviewed to ensure longitudinal consistency. The final scan was 1 month after last medication to minimise any potential effect of changes in artifactual volume, such as pseudoatrophy (a short term reduction in brain volume due to an anti-inflammatory effect);thus, both the baseline and end-of study scans were off-medication. The MRI secondary endpoint, assessed at 12 months and 25 months was the number of new and enlarging T2 brain lesions (for acquisition parameters see appendix ).

Statistical analysis

The sample size was chosen to give the trial 90% statistical power (with a conventional two-sided significance level of 5%) to detect a difference of 0·25% a year in whole-brain atrophy between the groups assuming a mean atrophy rate in the placebo group of 0·6% a year and a standard deviation of 0·4% a year. With these assumptions 54 patients would be needed in each treatment group: in anticipation of dropouts and incomplete follow-up this was increased to 70 patients per group. Analysis of all imaging and clinical outcomes were prespecified in a statistical analysis plan. Primary analyses were by intention to treat. A secondary analysis was undertaken using a per-protocol dataset, which comprised patients who complied with treatment and completed follow-up to 25 months. Participants were considered compliant with treatment if they reported taking, on average, at least 90% of their drug at a dose of 80 mg. Compliance was assessed by examination of the self-reported proportion of capsules taken in the month before the 6, 12, 18, and 24 month assessments. All analyses were done with STATA (version 12.1).

38 Frost C

Kenward MG

Fox NC The analysis of repeated ‘direct’ measures of change illustrated with an application in longitudinal imaging. BSI-derived changes in whole-brain volume were converted into a percentage of the baseline whole-brain volume for each available scan interval giving up to three BSI values per participant (change between 0–12 months, 12–25 months, and 0–25 months). A positive value for percentage change shows a decrease in brain volume. We compared mean rates of atrophy in the two treatment groups with the family of linear mixed models developed for the analysis of repeated measures of direct change.These models allow simultaneous analysis of the changes over the three time intervals, appropriately allowing for the correlation between these points. Therefore all available atrophy measures were included in this analysis, with participants included in the analysis if they have at least one BSI measure of atrophy.

39 Little RJA

Rubin DB An interaction between treatment group and time was included in the model as were other interactions between time and the minimisation variables and MRI site. The treatment effect therefore represents the difference between the treatment and placebo group in mean annual percentage change in whole-brain volume adjusted for minimisation variables and MRI site. Analysis of repeated measures with a properly specified linear mixed model including all follow-up data is more robust to dropouts than a complete case analysis. Specifically, the estimated treatment effect is unbiased under the missing-at-random assumption rather than the more stringent completely-missing-at-random assumption, which is necessary for a complete case analysis to be unbiased.We judged that because whole-brain atrophy is the primary outcome variable in this trial, the additional statistical complexity introduced by using this approach was justified. However, we also report results from a simple comparison of rates of change over 25 months (adjusting for minimisation variables and site).

40 Frison LJ

Pocock SJ Repeated measures in clinical trials: analysis using mean summary statistics and its implications for design. 41 Efron B

Tibshirani RJ 42 Davison AC

Hinkley DV 43 Breslow NE Extra-poisson variation in log-linear models. For EDSS, MSFC and subscales, and MSIS-29 and subscales, mean score at 24 months was compared between treatment groups using an ANCOVAmodel adjusting for baseline score and minimisation variables. Here a complete case approach was taken for missing data, so participants were included in the analysis only when they had both a baseline and 24 month score for the outcome measure being examined. Because these variables showed divergence from a normal distribution, non-parametric, bias corrected and accelerated, bootstrap CIs were calculated from 2000 replications(bootstrapping is a computer intensive technique that can give valid CIs even when normality assumptions do not hold). A consequence of use of the bootstrap is that exact p values are not calculated: however, whether or not p<0·05 (or p<0·01) was inferred from the 95% (or 99%) CI. We compared incidence of new and enlarging T2 hyper-intense brain lesions and the relapse rate between treatment groups with an over-dispersed Poisson model,with adjustment for minimisation variables and adjustment for MRI site where relevant. All available data were used for analysis of relapse rates and new and enlarging lesions, with participants included in the analysis if they had information recorded on at least one follow-up assessment.

44 Frost C

Kenward MG

Fox NC Optimizing the design of clinical trials where the outcome is a rate. Can estimating a baseline rate in a run-in period increase efficiency?. 44 Frost C

Kenward MG

Fox NC Optimizing the design of clinical trials where the outcome is a rate. Can estimating a baseline rate in a run-in period increase efficiency?. Percentage expression of FoxP3 on CD4+ T cells and inducible levels (unstimulated subtracted from the stimulated value) of IFN-γ, IL-4, IL-10 and IL-17 on all CD3+ T cells were calculated after suitable transformation (natural logarithm or square root). Linear mixed models were used to compare the mean value of each marker between the placebo and simvastatin group at 6, 12, and 24 months, with adjustment for minimisation variables. To make this analysis essentially equivalent to an ANCOVA,adjusting for baseline, measures of the marker at baseline were treated as an additional outcome in the model with treatment effects and effects of minimisation variables constrained to be zero at baseline.This approach allows use of all available measures of the marker for each participant to be included in the analysis.

Safety was examined by testing the null hypothesis that there was no increase in the proportion of participants with at least one serious adverse event in the active compared with the placebo group, with a one-sided test.