# Should I treat variables representing level of disease risk as ordinal?

I'm working with a study where we have collected the subjects' genotypes for risk factors for a disease. These can be homozygous non-risk (e.g. AA), homozygous risk (e.g. TT) or heterozygous (e.g. AT) where that may have no risk or partial risk.

Typical analysis:

logistic regression: Does MarkerConcentration predict disease independently of the risk factors, or visa versa?

lm(Case ~ MarkerConcentration + Genotype1 + Genotype2)

linear regression: Can the risk factors affect marker concentration independently of disease state?

lm(MarkerConcentration ~ Case + Genotype1 + Genotype2)

In our analysis, we only include cases which homozygous risk or non-risk. and coding those as 1 and 0 respectively.

Would there be any value to treating these as ordinal variables with risk > non-risk?

Note that we do not have sufficient confidence in any estimate of relative risk to use that information

EDIT: I have rephrased the question to clarify that the genotype risk-factors are predictor variables.

## 1 Answer

I assume that you are willing to run some sort of (generalized) linear model in which you want to use this variable. I understood that your treat your risk as a binary variable. And ask if makes any difference for your binary variable to treat it as categorical versus ordinal.

If you want to use this variable as a predictor, you may even treat it as a quasi-metric variable - you can use it in your model without changing any thing. It only slightly affects the interpretation of the parameters (which a then predicted means for the categories).

If you want to use it as a dependent variable, you need to account for the fact that the outcome is dichotomous, e.g. by running a logistic regression.

Long story short: In both cases, you would not treat the variable differently depending on its ordinal or categorical nature. For most models, differences in the statistical procedure between ordinal and nominal categorical variables only occur when you have more than two categories.

As long as there are only 2 categories, there is no difference between ordinal and nominal variables. It only makes a difference, if you have at least 3 categories - and then we'd need to know more about your data (e.g., frequencies of the categories) to judge if it is worth the hassle.

A similar discussion can be found here.

Edit: Added some comments from the discussion to the answer + a useful reference.

• Thanks @MagunSimurgh, and welcome to Cross Validated! I edited my question to highlight typical analysis cases. – abalter Jul 29 '19 at 18:32
• Clarification question: Do you mean an ordinal variable with no risk < heterozygous risk < homozygous risk? Or do you mean anyGenoType risk > no risk? Or do you mean no risk < homozygous risk for all GenoTypes separately? – StoryTeller0815 Jul 29 '19 at 20:13
• Good question. In the full model, we have homo-risk, homo-non-risk, and hetero. If ordinal, I would put homo-non-risk < homo-risk. We are also looking at the disease subgroup and doing a regression against a single risk factor with homo-non-risk and homo-risk. If ordinal, we would use homo-non-risk < homo-risk. I'm not sure we should be doing a separate analysis against each risk factor excluding all other variables, but that is a different question. – abalter Jul 30 '19 at 0:00
• As long as there are only 2 categories, there is no difference between ordinal and nominal variables. It only makes a difference, if you have at least 3 categories - and then we'd need to know more about your data (e.g., frequencies of the categories) to judge if it is worth the hassle. – StoryTeller0815 Jul 30 '19 at 6:31
• Thanks! Add this to your answer so I can accept it. Also, if you have any supporting details or references, that can be a big help to both me and future readers. – abalter Jul 30 '19 at 19:38