Hypothesis test for summary data involving percentages

Question

500 patients had an operation to remove stomach cancer. There exists a clinical guideline that suggests that a minimum of ten lymph nodes should be removed during the operation. I am therefore interested in the proportion of patients who had at least ten nodes removed. The variable Fewer_or_more_than_ten contains this information. I am using R.

# Example data
set.seed(10)
study_data <- data.frame(
              Gender = sample(c("Male","Female"),500,T),
              Fewer_or_more_than_ten = sample(c("Fewer","More"),500,T))

I can tabulate these data to see how many people got an adequate lymph node dissection (i.e., had more than ten nodes removed).

# Tabulate data
table(study_data$Fewer_or_more_than_ten)

I want to know whether this varies with gender, so I can type:

# Stratify by gender
table(study_data$Gender, study_data$Fewer_or_more_than_ten)

What I want to do is to report the percentage of women and men who got an adequate lymph node dissection. So for that I would report the percentage shown under the "More" column in the below table.

# Calculate frequencies
prop.table(table(study_data$Gender, study_data$Fewer_or_more_than_ten), 1) * 100

My question is:

I would also like to report a p value with these numbers to show whether or not there appears to be a significant difference between the proportion of men versus women who got an adequate dissection. How should I do this?

I wasn't sure whether I should try to calculate confidence intervals for the percentages and then compare them to see if they overlap, or if I should apply a Chi-square test or Fisher's exact test to the tabulated data, etc.

I am also curious, if gender could take on three values rather than two (e.g., Male, Female, and Unknown), and I wanted to extend my hypothesis test to these three groups, how would that change my approach?

Answer 1

You probably want a chi-square test.

chisq.test( table(study_data) )

This is a test of the interaction between sex and whether there were more than 10.

(as an aside, if you just want tables of all of the columns of a data.frame there's no need to pass each column like you are, just pass the whole data.frame to the table command)