Overall Statement or Summary: This is a well written manuscript with important findings that needs to be published. There are no major flaws in this study. The limitations such as lack of minimal clinically important difference (in MSIS 29 v2 and MFIS), and the lack of physical activity level estimation between groups are not necessarily major flaws. However, the large rate of attrition needs attention. An equal dropout rates between groups can still result in biased treatment effect estimation. As noted in Table 1, the dropouts were significantly younger in age and had more walking endurance (possibly have increased motivation to participate in regular exercise/walking after study completion). So, I assume that the outcomes (MSIS 29 v2, MFIS, 6MWT) of the dropouts would not have been the same whether they dropped out or not. Such ‘missing not at random’ data require sensitivity analyses (1,2).

References: 1. Bell, Melanie L., et al. "Differential dropout and bias in randomised controlled trials: when it matters and when it may not." Bmj 346 (2013): e8668. 2. Molenberghs, Geert, et al. "Analyzing incomplete longitudinal clinical trial data." (2004). Biostatistics, 5(3). p. 445-464.

Strengths of the Article: The authors have clearly described the aim, methods and results. The study design (stratified, assessor blind, block RCT) is appropriate for a study of this size (n = 243) and aims. The explanation of inclusion criteria and interventions in the methods section was clear and succinct. The authors have used valid and reliable outcome measures for data collection. The authors have made a good choice in performing completer analysis instead of intention to treat analysis. The authors have correctly identified the large variance between groups on 6MWT scores and acknowledged its influence on the results (pg 795, 2nd paragraph, line 6).

Weaknesses of the Article: There is a large rate of attrition in this study and this needs further statistical analyses. Please consider my suggestions in the overall summary.

Also, the standard deviations (SD) for all MSIS 29 v2 values (unstandardized) in the table 2 are more than 50% of their mean values, indicating increased dispersion. For normal distribution, we expect 68% of data to be within 1 SD and 95% of data within 2 SDs. I suggest you to test for possible outliers in your dataset which you have assumed as normal. To test for outliers in your dataset, I recommend you to compute ‘studentized residuals’ (as you may not know population mean /or SD) and compare to the expected frequencies. If you identify many data points more than 3 SDs, then you have dispersed data (for your primary outcome, MSIS 29 v2). If so, you will need to choose non-parametric tests. This suggestion is directed to make an appropriate choice between parametric vs non-parametric tests and also, to explore/identify the reason (? possible outliers) for non-significance with group and group x time effects in the MSIS 29 v2 physical and psychological variables.

Other minor weaknesses/corrections are mentioned under specific comments.

Specific Comments: 1. In page 792, 3rd paragraph, line 7, add (table 1) within parenthesis in this sentence after the first two words ‘Completer analysis’, to direct the reader appropriately. 2. In page 792, 3rd paragraph, lines 9-14, indicate if you used week 12 data for non-completers. 3. In page 792, 4th paragraph, line 3, it is mentioned that all data were found to be reasonably normally distributed. Please cite your previous publication (a) to explain baseline distribution or add a table on baseline characteristics as a supplementary file. This is important as it explains your decision to use parametric tests. 4. Under discussion (2nd paragraph, lines 3-6), you have mentioned that the mean MSIS 29 v2 scores for PT led group remained improved. Please provide evidence for this finding. My suggestion is to mention this finding by adding symbols (asterisk, dagger) on table 2. 5. In Figure 2, please be consistent on italicizing the reasons for lost to follow-up. 6. In table 1, please indicate if you used week 12 data for non-completers. 7. In table 2, you have mentioned the missing data. Please explain how you handled these missing data during analyses. You have mentioned the missing data for 6MWT in the FI led group as n = 22. Please explore and explain if this could be a reason for not having time effects on 6MWT in FT led group. 8. Please keep consistent with the titles of top 2 graphs in figure 2. It appears as if you have used version 2 only for psychological component. 9. Please follow the format used in the table 2 for the first column in table 3, i.e. remove the primary outcome variable (MSIS 29 v2 – physical component) from the top row and move it to the second row as in table 2. 10. Please be consistent in using superscript ‘a’ to highlight the statistical significance in table 3 like the table 2.

Reference: a. Coote, Susan, et al. "Getting the balance right: a randomised controlled trial of physiotherapy and Exercise Interventions for ambulatory people with multiple sclerosis." BMC neurology 9.1 (2009): 34.