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we are researching whether the date of a certain medical procedure impacts the complication rate of said procedure. To this end we have identified multiple risk factors we would like to study more closely (e.g. the day of the week, holiday seasons, winter/summer and so on).

Simplified, we have a table of the form

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where the reference group is the subset of patients that have neither risk factor A, B or C. Please note that $A \cap B \neq \emptyset$ etc, i.e. we cannot eliminate dependency between columns.

What is now the appropriate statistical test or model to compare the individual risk groups against the reference group? Our null-hypothesis is that group A/B/C do not have more infections in comparison to the reference group.

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2 Answers 2

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You should look into logistic regression. There are a lot of posts on this site, so search ...

For more specific advice, you will need to give more details.

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You could consider using a linear regression model (if applicable) which allows you to do a ANCOVA test to determine the impact of the risk factors and date on infection rate. $Infections=\beta_0+\beta_1Date+\beta_2Group A+\beta_3GroupB+\beta_4GroupC+\beta_5Reference+\epsilon$

Or you could do a $\chi^2$ test of homogeneity between the different treatment groups.

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