Reviewer response for version 1
We thank the authors for this very interesting study. 
We have some comments and suggestions which we think will enhance the manuscript.
1.
The primary outcome measure is the citation counts from publications associated with the successful application. 
Publications were produced from 1 to 8 years after the peer review date (average 4.3 years). 
This does not appear to take account of varying time since the projects were funded (i.e. 7 year gap between projects that were funded from 1999 to 2006). 
Thus, older studies would have had more time for publications to be produced and cited. 
We therefore suggest a more meaningful outcome measure would be either the number of citations per year per study, or the total number of citations in, say, the 5 years following the final project report, or some other standardised project milestone. 
Adding the review year to the model does not seem to adequately control for this factor (though qualified statistical advice is needed to clarify this). 
We think this is the issue that likely affects the interpretation of the results the most in our critique.
2.
The number of citations was standardised by academic field – i.e. molecular biology. 
Was there any variation in study designs within this field that might also change the expected number of citations (e.g. systematic reviews may attract more citations than primary experimental studies in some fields)? 
It would be useful for context if there could be a table with some basic aggregate details of the funded studies, such as types of study design, molecular biological application, study sample characteristics, duration of study etc. 
This would help to put the results into context.
3.
The impact of a piece of research on which referees could not agree might be either lower or higher than those on which they could. 
So, it would be useful to plot the standard deviation of the citations against the standard deviation of the peer review score.
4.
As well as using multiple imputation to correct for missing data, a sensitivity analysis in which cases with missing data are omitted would be useful.
5.
Some measure of the model fit would be useful, eg. 
adjusted R squared
6.
There was a wide variation in the number of reviewers per article from 2 to 18. 
Was this due to differences in the kind of research, amount of funding requested or some other perceived risk on behalf of the funder? 
Could this artificially influence the standard deviation of the score, confounding any association with citations?
7.
Fractional polynomial model results are only presented for the best fitting model with the smallest deviance. 
This is acceptable in principle, but it would be useful for the authors to comment on whether there was any variation in the results according to the other fractional polynomial transformations (if available). 
This will provide confidence in the robustness of the findings.
8.
Reference is made in the first paragraph to a “recent systematic review” by Guthrie et al (2018 1 ) (and also in the third paragraph). 
We note that this publication doesn’t refer to itself as being a systematic review, and indeed, it is an update of a 2009 review which describes itself as a non-systematic review. 
We would suggest using the tern “non-systematic review”, or just “literature review”.
9.
Thank you for citing our own recent systematic review on peer review of grants in health. 
You mention that the review included eight studies and called for further research in this area, which is correct. 
However, the review focused specifically on studies aiming to improve the effectiveness and efficiency of peer review. 
These were drawn from a wider set of 83 studies on peer review which we systematically mapped. 
In the map there were some studies which focused on assessing the impact of funded research, eg. 
In terms of bibliometrics. 
Thus, there is a body of evidence on this topic, though we didn't systematically review it in detail. 
We are happy to provide you with a list of these studies.
10.
The sentence on page 3 beginning “A recent systematic review found “suggestive” evidence that funding peer review can have an anti-innovation bias 2 and that innovation and risk may not often be sufficiently addressed in review feedback 7 ” needs re-wording as not only is the Guthrie et al paper a non-systematic review, but the second reference cited in that sentence by Gallo et al is a survey (i.e. not a review at all). 
The way the sentence is phrased implies that it is a systematic review.
11.
Suggest amending the sentence on page 3 “Many studies using large sample sizes found either no association or only a weak association between the mean score and the VOLUME of citations of subsequent publications”
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