Referee 3's review (Eduardo Azziz-Baumgartner):

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N.B. These are the comments made by the referee when reviewing an earlier version of this paper. Prior to publication, the manuscript has been revised in light of these comments and to address other editorial requirements.
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The Wong et al manuscript is very interesting and would make a good addition to the literature with minor revisions. Below are a few suggestions to the authors:

1. The abstract should be clearer and use parallel text to that of the main body of the manuscript. Authors should also attempt to change most sentences to active voice for clarity. There are several run-on sentences, colloquialisms, and dangling modifiers that could use editing to clarify findings.

2. Authors should briefly provide details about the LIMOR study as readers will require this information to contextualize the data. Although the LIMOR study is referenced, I was distracted by the lack of information about the parent study.

3. The authors indicated that questions about physical exercise date to a time period "about ten years before their death." I did not understand if authors meant that informants were asked about decedents exercise habits during the ten years prior to their death (a ten year history) or about decedents exercise habits ten years prior to the death (as a cross-sectional view or snapshot ten years prior). I suspect from the data analysis that authors asked about exercise during the past ten years but they should state explicitly the actual language used during the interviews.

4. I was unclear as to the exact variables that went into the logistic models as this is not the typical Boolean model of dead/alive = α + β1(E) + β2(smoking) + etc. Stating the explicit models used may clarify the analyses.

5. I was distracted by the use of the terms "risk" during the odds ratio discussion and "sensitivity" during in the first paragraph of the section called "Statistical Analysis", subsection "Influenza epidemic." I would suggest that authors use alternate terms for precision.

6. I really liked the authors' attempts to account for a variety of potential interaction terms. Was there any data available on decedent's influenza vaccination status during the year of their death?

7. I am concerned about the authors' suggestion that people older than 65 years may need to exercise less than frequently. While the findings are compelling, there are many potential confounders that have not been examined (e.g. vaccination status, etc.). I would more comfortable if the discussion section acknowledge the limitations of the analyses, the need for further studies, and the complexity of the risk/benefit of exercise as well as the need for increasing vaccination coverage. It would make more sense to me to see the authors recommend moderate exercise coupled with increase vaccination coverage.

8. While it is interesting to see the authors first time use of population based data, I would encouraged them to explicitly state that the decedents are not linked to influenza sampling early in the manuscript. In addition, they should discuss the inherent limitations of mortality data de-linked from individual influenza sample data.

9. I would recommend that authors consider deleting part 'a" of table 1 as this data is also presented as figure 1. I am uncertain of the origin of the p values in section "c" of table 1 as it would seem that Chi squares would originate from bivariate analyses. Some of these comparisons would seem more appropriate for ANOVAs or something akin to them. Disaggregating the findings of E1 and E2 may also help. Clarifying what is being compared may help. It is also difficult to visualize the difference between E1 and E2 in Figure 2. I would also recommend deleting appendix 1 as it seems unnecessary.

10. I do not understand why influenza intensity was presented "as a percentage per 10% increase of influenza." It would seem that these regression models could use influenza intensity as a continuous independent variable.

11. The first sentence of the second paragraph of the discussion section seems awkward.

12. The third paragraph suggests that the interaction between exercise and immune function is clearly understood (i.e. "can be explained..."). I would suggest the use of more cautious language. While many in-roads have been made on this subject, there is much about causality that needs to be learned.

Good work and good luck with the revisions.