A substantial proportion of all medical research funding is administered through the MRC.
This is clearly a very competitive field, with the potential for high returns to successful bidders but a low success rate. The risk of failure when bidding is not spread evenly accross the sector.
The data, which are freely available from the MRC, are aggregated to institutional level. Therefore it is not possible to analyse the characteristics of each individual grant application. However some statistical patterns can still be looked at. For each institution data are provided on the number of grants submitted, the total amount of funding requested, the total amount of funds awarded and the number of successful bids. The number of successful bids together with the number of applications can be analysed by assuming they follow a binomial distribution and modelling the results of p successes from n trials. With a continous explanatory variable this can be modelled through logistic regression.
Fitting a logistic regression model with a logit link function shows a highly significant (p<0.001) negative relationship between the probability of success of a bid and the number of bids submitted by the institution. Clearly if institutions submit low numbers of bids it is possible to obtain either no funding at all or to obtain 100% of the requested funding. The statistical model considers these outcomes as being the result of chance variability around an underlying trend line. As institutions increase the overall ammount of their bidding activity their proportion of successful bids will stabilise and will tend to cluster around the expected proportional success rate (figure 1).
In order to summarise the continuous relationship shown in figure one in an easily communicable manner the institutions were grouped into three groups. Group 1 consisted of institutions submitting less than 10 bids. Group 2 consisted of institutions submitting between 10 and 50 bids. Group 3 consisted of institutions submitting over fifty bids.
The 90% confidence interval for the success rate for group 1 (<10) is between 11% and 19% with a best estimate of 15%
The 90% confidence interval for the success rate for group 2 (10 to 50) is between 13% and 39% with a best estimate of 23%
The 90% confidence interval for the success rate for group 1 (over 50) is between 16% and 45% with a best estimate of 28%
The success rate for named institutions with over 20 bids is shown in figure 2. The 90% onfidence intervals are derived from a binomial model. This assumes that success or failure of each individual bid is a stochastic event with a probability determined by the overall institutional success rate. The interval can then be interpreted as a range within which annual bidding activity would be expected to fall with 90% confidence, assuming the overall success rate remains constant. Although there is a range of success rates for the major institutions, only one (Oxford University) has a statistically significantly higher rate than the overall mean.
The absolute size of the awards also varies between groups. As data is not available for individual grants only the mean award size can be calculated as the sum of all successful bid awards divided by the total number of successful bids. The expected value is the mean size of the award divided by the probability of success, which can also be calculated as the sum of the total awards divided by the number of bids submitted.
If failure to win any MRC grant is considered to be likely to lead to closure of a medical science department it may be useful to show the risk of failure to win any bid based on the overall success rate. This can be calculated from \((1-psuccess)^n)\). The risk of falure for institutions submitting less than 10 grants per year with a success probability of 15% is shown in figure 4.
Note that to have at least a 90% probability of at least one successful bid requires 14 bids or more for an instiution with the success probability of group 1.
The total research funding available from the medical reseaarch council is substantial. Successful bids also receive large awards. However the probability of success and the amounts awarded per bid is highly significantly related to the number of bids that an instition as a whole submits. There are a variety of explanations for this pattern, but an inspection of the identities of the most succesful institutions suggests that the key to success involves reputation and track record in the field.
The relationship shown in Figure 4 does not show a clear trend. The slope of a logistic regression model was not significant (p>0.1).
Fellowship applications have a lower overall success rate than MRC grant applications, but the success rate is not linked to the number of bids per institution. This is probably because fellowships are linked to the academic quality of the individual applicant rather than host insitution.