From the study: It was found that there was a linear relationship (Pnon-linearity = 0.242) between BMI and the risk of critical COVID-19 They seem

From the study: It was found that there was a linear relationship (Pnon-linearity = 0.242) between BMI and the risk of critical COVID-19 They seem to mean that the log odds ratio is a linear function of BMI. This just can't be true. Sufficiently low BMI has to be bad, not good. Figures 7 and 8 in the paper actually show a near-constant risk from BMI of 18 to BMI of about 27. The good results for BMI of 18, which is pretty definitely underweight, actually seem rather dubious, on the basis of past studies (see my blog post at https://radfordneal.wordpress.com/2020/04/06/body-mass-and-risk-from-covid-19-and-influenza https://radfordneal.wordpress.com/2020/04/06/body-mass-and-r...). But in any case, there is clearly no reason to think that risk goes down linearly as BMI gets smaller than about 27, and there's little reason to think it goes up linearly above that either, considering the very small number of data points.