I want to perform a univariate analysis to predict if a higher BMI is associated with an increased incidence of complications after surgery. I divided the BMI of patients in 4 categories (<18.5; 18.5-25; 25-30; >30) and complications in 2 categories (yes; no). I tried to use the chi squared test to perform this univariate analysis, but the assumptions were not fulfilled. The expected counts were not higher than 1 in all cells and they were smaller than 5 in more than 20% of the cells. Which test can I use to perform this univariate analysis in a 2x4 table if the assumptions of the chi squared test are not met?
I would do away with the BMI grouping altogether and, at least as a start, run logistic regression on the BMI values. Then you can test the coefficient on BMI to get your p-value for BMI’s effect on rate of complications.
Grouping BMI puts you in the position of saying that 24.9 and 25.1 are as different as 18.5 and 30, which you probably do not believe.