# Comparing rates of a risk factor in 2 groups

Hello statisticians,

So, I understand that comparing the difference of means involves a t-test, and determining the effect of an intervention uses an OR and chi-squared test, but how do I compare the difference of a rate of occurrence of a risk factor in 2 groups?

I have 2 groups: liver resection and pancreatic resection, with a rate of post-operative infection in each. I’m trying to compare the rates of infection and comment on the statistical significance of the difference. Which test do I use?

As always, many thanks for all your help

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It is not entirely clear to me what you want to do here, but do you want to compare the count of events (infections) per some unit (e.g. time)? Could Poisson Regression be considered here?

Thanks for the response.

I’m working on a systematic review and, for this part of it, I have a list of studies that report on infection rate in pancreatic surgery, and a separate list of studies that report the infection rate for liver surgeries. I have calculated an average infection rate for each of these groups (pancreatic and liver) by adding the absolute values of all the studies. Based on this data, I’m wanting to do a test of statistical significance on the difference between the 2 groups.

But neither of these groups can be considered an intervention, so using the chi-squared doesn’t seem correct. Is a difference of means t-test the appropriate test?

My gut feeling is that you should probably be using some form of meta-analysis approach… use the individual study data to estimate the overall rate/proportion and do the test in the same framework… There’s lots of R packages that can do this stuff… metafor is a reasonable choice.

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Blockquote
So, I understand that comparing the difference of means involves a t-test, and determining the effect of an intervention uses an OR and chi-squared test, but how do I compare the difference of a rate of occurrence of a risk factor in 2 groups?

A researcher can use mean differences or odds ratios to assess the effect of an intervention, each with benefits and drawbacks. I think the OR is a more useful measure of effect in most cases, with the actual statistical analysis done on log(OR). This is a heuristic “rule of thumb”, not a mathematically provable recommendation. Without going into too much detail, there exist certain contexts where the mean could be better.

The OR has close relationships with nonparametric tests and the logistic model. A good presentation on the merits of nonparametric methods can be found here:

Biostatistics and Bioinformatics Core Seminar: “Introduction to Nonparametric Statistical Tests” (link)

Some things to keep in mind:

1. You will need to think of predictive factors that might lead one group to have a higher infection rate vs. another – ie. age, disease severity, sex, comorbidities, etc.

2. You will need to consider whether your literature search method is biased or not.

3. You will need to consider whether the publication process itself might lead to a biased presentation. Are there any reasons why one group might have more published reports of higher infections vs. the other?

In terms of the question being asked, am I the only one who thinks it would be very hard for a retrospective meta-analysis to help here? It might be useful only to generate hypotheses.

If a meta-analysis can help, conducting it is towards the higher end of the complexity spectrum. Much thought will need to go into the study plan to make it convincing.

This question seems to be something that would be studied using observational methods. My concern is that I doubt the observational studies provide enough data to make valid statistical adjustments in order to compare apples with apples.

If I understand you correctly:

list the individual study infection rates in separate groups and treat them as a if they were individual participants i.e. do a t-test?