# Manually calculating false negative risk (using Likelihood ratio and Bayesian analysis)

The question is with reference to this paper: https://arxiv.org/pdf/1802.04888.pdf and https://royalsocietypublishing.org/doi/full/10.1098/rsos.171085

It give clearly how to calculate false positive risk or false discovery risk. A real life example is also given on page 17-18

However, how can false NEGATIVE risk be calculated manually? What exact formulae can we use?

Thanks for the link to my paper. I have been thinking of adding the false negative risk to my web calculator (but after 110 days of lockdown I'm having difficulty in concentrating). Presumably it should be defined as (false neg)/(false neg + true neg).

Incidentally, our web calculator at http://fpr-calc.ucl.ac.uk/ is down at the moment (a cock-up at UCL), but there is another copy at http://shiny.ieis.tue.nl/fpr_calc/

There are also later papers on the topic, in which I'm more explicit about the assumptions) at https://www.tandfonline.com/doi/full/10.1080/00031305.2018.1529622 and at https://royalsocietypublishing.org/doi/10.1098/rsos.190819

• Look forward to your method for estimating false negative risk. Many drugs have been found to have non-significant effect against COVID-19. It will be important to know false negative risk for these studies.
– rnso
Commented Jul 1, 2020 at 11:51
• Of course it's always possible that the drugs don't work. The prior probability of a random drug being effective for a viral infection must be very low. Commented Jul 1, 2020 at 16:09
• These are not random agents. They have some prior study indicating their likely efficacy. I would put prior probability as 2/3 or 0.67
– rnso
Commented Jul 1, 2020 at 16:16
• That seems much too high to me. But we are both guessing. That's why I suggest citing, along with the p value and CI, the FPR_50 ie the value for a prior of 0.5. That's the nearest we can get to equipoise. Commented Jul 2, 2020 at 8:38
• I want to focus on how to calculate False NEGATIVE Risk. Same principles as FPR will need to be applied to power?
– rnso
Commented Jul 2, 2020 at 8:42