In the current issue of Science, Li and Agha present an analysis of the ability of the NIH peer review system to predict subsequent productivity (in terms of publications, citations, and patents linked to particular grants). These economists obtained access to the major NIH databases in a manner that allowed them to associate publications, citations, and patents with particular R01 grants and their priority scores. They analyzed R01 grants from 1980 to 2008, a total of 137,215 grants. This follows on studies (here and here) that I did while I was at NIH with a much smaller data set from a single year and a single institute as well as a publication from NHLBI staff.

The authors' major conclusions are that peer review scores (percentiles) do predict subsequent productivity metrics in a statistically significant manner at a population level. Because of the large data set, the authors are able to examine other potentially confounding factors including grant history, institutional affiliation, degree type, career stage) and they conclude the statistically significant result persists even when correcting for these factors.

Taking a step back, how did they perform the analysis?

(1) They assembled lists of funded R01 grants (both new (Type 1) and competing renewal (Type 2) grants from 1980 to 2006.

(2) They assembled publications (within 5 years of grant approval) and citations (through 2013) linked to each grant.

(3) They assembled patents linked either directly (cited in patent application) or indirectly (cited in publication listed in application) for each grant.

There are certainly challenges in assembling this data set and some of these are discussed in the supplementary material to the paper. For example, not all publications cite grant support and other methods must be used. Also, some publications are supported by more than one grant and, in this case, the publication was linked to both grants.

The assembled data set (for publications) is shown below:

By eye, this shows a drop in the number of linked publications with increasing percentile score. But this is due primarily to the fact that more grants were funded with lower (better) percentile scores over this period. What does this distribution look like?

I had assembled an NIH-wide funding curve for FY2007 as part of the Enhancing Peer Review study (shown below):

To estimate this curve for the full period, I used success rates and numbers of grants funded to produce the following:

Of course, after constructing this graph, I noticed that Figure 1 in the supplementary material for the paper includes the actual data on this distribution. While the agreement is satisfying, I was reminded of a favorite saying from graduate school: A week in the lab can save you at least an hour in the library. This curve accounts (at least partially) for the overall trend observed in the data. The ability of peer review scores to predict outcomes lies in more subtle aspects of the data.

To extract the information about the role of peer review, the authors used Poisson regression methods. These methods assume that the distribution of values (i.e. publications or citations) at each x-coordinate (i.e. percentile score) can be approximated as a Poisson distribution. The occurrence of such distributions in these data makes sense since they are based on counting numbers of outputs. The Poisson distribution has the characteristic that the expected value is the same as its variance so that only a single variable in necessary to fit the trends in an entire curve that follows such a distribution. The formula for a Poisson distribution at a point k (an integer) is f = (λ^k*e^-λ)/k!. Here, λ corresponds to the expected value on the y axis and k corresponds to the value on the x axis.

Table 1 in the paper presents "the coefficient of regression on scores for a single Poisson regression of grant outcomes on peer review scores." These coefficients have values from -0.0076 to -0.0215. These values are the β coefficients in a fit of the form ln(λ) = α + βk where k is the percentile score from 1 to 100 and λ is the expected value for the grant outcome (e.g. number of publications).

From the paper, a model which includes corrections for five additional factors (subject-year, PI publication history, PI career characteristics, PI grant history, and PI institution/demographics (see below and supplementary material for how these corrections are included)), the coefficient of regression for both publications and citations is β = -0.0158. A plot of the value of λ as a function of percentile score (k) for publications (with α estimated to be 3.7) is shown below:

The shape of this curve is determined primarily by the value of β.

The value of λ at each point determines the Poisson distribution at the point. For example, in this model at k=1, λ=39.81 and the expected Poisson distribution is shown below:

There will be a corresponding Poisson distribution at each percentile score (value of k). These distributions for k=1 and k=50 superimposed on the overall curve of λ as a function of k (from above) are shown below:

This represents the model of the distributions. However, this does not take into account the number of grants funded at each percentile score shown above. Including this distribution results in an overall distribution of the expected number of publications as a function of percentile score corresponding to this model shown as a contour plot below (where the contours represent 75%, 50%, 25%, 10%, and 1% of the maximum density of publications):

This figure can be compared with the first figure above with the data from the paper. The agreement appears reasonable although there appear to be more grants with a smaller number of publications than would be expected from this Poisson regression model. This may reflect differences in publication patterns between fields, the unequal value of different publications, and differences between the productivity of PIs.

With this (longwinded) description of the analysis methods, what conclusions can be drawn from the paper?

First, there does appear to be a statistically significant relationship between peer review percentile scores and subsequent productivity metrics for this population. This relationship was stronger for citations than it was for publication numbers.

Second, the authors studied the effects of correcting force various potential confounding factors. These included:

(i) "Subject-year" determined by correcting for differences in metrics by study section and by year as well as by funding institute. This should at least partially account for differences in fields although some study sections review grants from fields with quite different publication patterns (e.g. chemistry versus biochemistry or mouse models versus human studies).

(ii) "PI publication history" determined by the PIs publication history for the five years prior to the grant application including the number of publications, the number of citations up to the time of grant application, the number of publications in the top 0.1%, 1% and 5% in terms of citations in the year of applications and these same factors limited to first author publications or last author publications.

(iii) "PI career characteristics" determined by Ph.D., M.D., or both, and number of years since the completion of her/his terminal degree.

(iv) "PI grant history" categorized as one previous R01 grant, more than previous R01 grant, 1 other type of NIH grant, or 2 or more other NIH grants.

(v) "PI institution/demographics" determined as whether the PI institution falls within the top 5, top 10, top 20, or top 100 institutions within this data set in terms of the number of awards with demographic parameters (gender, ethnicity (Asian, Hispanic) estimated from PI names.

Including each of the factors sequentially in the regression analysis did not affect the value of β substantially, particularly for citations as an output. This was interpreted to mean that the statistically significant relationship between percentile score and subsequent productivity metrics persists even correcting for these factors. In addition, examining results related to these factors revealed that (from supplementary material):

"In particular, we see that competing renewals receive 49% more citations, which may be reflective of more citations accruing to more mature research agendas (P<0.001). Applicants with M.D. degrees amass more citations to their resulting publications (P<0.001), which may be a function of the types of journals they publish in, citation norms, and number of papers published in those fields. Applicants from research institutions with the most awarded NIH grants garner more citations (P<0.001), as do applicants who have previously received R01 grants (P<0.001). Lastly, researchers early in their career tend to produce more highly cited work than more mature researchers (P<0.001)."

So what is the bottom line? This paper does appear to demonstrate that NIH peer review does predict subsequent productivity metrics (numbers of publications and citations) at a population level even correcting for many potential confounding factors in reasonable ways. In my opinion, this is an important finding given the dependence of the biomedical enterprise on the NIH peer review system. At the same time, one must keep in mind the relatively shallow slope for the overall trend and the large amount of variation at each percentile score. A 1 percentile point change in peer review score resulted in, on average, a 1.8% decrease in the number of citations attributed to the grant. By my estimate (based on the model in this paper), the odds that funding a grant with a 1 percentile point better peer review score over an alternative will result in more citations are 1.07 to 1. The slight slope and the large amount of "scatter" are not at all surprising given that grant peer review is largely about predicting the future, is a challenging process, and the NIH portfolio includes many quite different areas of science.

One disappointing aspect of this paper is the title: "Big names or big ideas: Do peer-review panels select the best science proposals?" This is an interesting and important question, but the analysis is not suited to address it except peripherally. The analysis does demonstrate that PI factors (e.g. publication history, institutional affiliation) do not dominate the effects seen with peer review, but this is does not really speak to "big names" versus "big ideas" in a more general way. Furthermore, while the authors admit that they cannot study unfunded proposals, it is likely that some of the "best science proposals" fall into this category. The authors do note that some of the proposals funded with poor percentile scores (presumably picked up by NIH program staff) were quite productive.

There is a lot more to digest in this paper. I welcome reactions and questions.

UPDATE

Aaron and Drugmonkey commented on the fact that the figure showed an expected value of 40 publications for grants at the 1st percentile. As I noted in the post and in the comments, the analysis depends on a parameter α which does not affect the conclusion about the predictive power of percentile scores but does affect the appearance of the curves. When I first started analyzing this paper, I estimated α to be 3.7 by eye and did not go back and do a reality check on this.

The supplementary material for the paper includes a histogram of the number of publications per grant shown below:

This shows the actual distribution of publications from this data set.

From this distribution, the value of α can be estimated to be 2.2. This leads to revised plots for the expected number of publications at the 1st percentile and an overall expected number of publications per grant shown below:

These data are consistent with results that I obtained in my earlier analysis of one set of NIGMS grants.

I am sorry for the confusion caused by my rushing the analysis.