How to analyze binary categorical vs ordinal data?

Question

Context: I have a dataset in which I am analyzing whether a patient having 1 disease (binary) influences the number of other diseases the patient has (ordinal; range = 0-7), which is the outcome variable.

Questions:

1. Is the number of other diseases the patient has in fact ordinal?

2. What regression method would I use to analyze this data where the outcome variable is ordinal?

3. My other explanatory variables include age, race, gender, etc. I am using SAS, so could I use PROC LOGISTIC or PROC GLM?

4. Also, what method would I use to test the simple correlation between the two? Is there something similar to the chi-square for a 2 by 8 table?

Answer 1

1. The number of diseases that the patient has would be interval as opposed to ordinal in most usual representations- certainly, if the number represents a count of the individual diseases (among n, where it appears in this case n = 7), this would be more properly characterized as interval data.

2. The general pattern of regressing to levels of response is called ordinal regression- this is not to say that this is the only method that would be applicable to this question. Many multiclass regression methods could be applicable as well, some are discussed in this answer.

3. Proc Logistic is capable of ordinal regression using the oddsratio option, as discussed in this SAS documentation example.

4. As it happens, a Chi-Squared measure is reported in the output of Proc Logistic using the method described in the example in 3.