Odd ratio for cumulative effect of risk variants I'm trying to calculate odds ratios to summarize associations between some risk factors and the number of risk variants in a subject. Number of risk variants is ordinal. I did a multinomial logistic regression that summarizes separate odds ratios for observing 1, 2, 3, or 4 risk variants versus 0 with different medication steps. This is my code:
test <- multinom( risk.variant.number2 ~ medication_steps + age, data = merge3)
summary(test)
z <- summary(test)$coefficients/summary(test)$standard.errors
z
# 2-tailed z test
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
## extract the coefficients nad CI from the model and exponentiate
oddratio <- exp(coef(test))
oddratio
ci <- exp(confint(test, level=0.95))
ci

The matter is when I execute this what I'm getting is the Odd ratio for each risk category instead instead of odd ratios for increase of one in the number of risk variants.
This is my output
    Intercept) medication_stepsstep_2 medication_stepsstep_3 medication_stepsstep_4      age
1    11.87786          0.7764290          0.2199499          0.3999115 1.019621
2    57.41383          0.4681173          0.1603767          0.1310747 1.102033
3   133.42880          0.5098369          0.1559243          0.2070830 1.089148
4    14.71933          0.6190965          0.2108455          0.2834067 1.108850

However, I do not know how to summarize these results. Furthermore, I do not know if it is the right model for my question. Can someone provide an example of interpreting this output or suggest a different model to fit in this scenario?
 A: I'll point out a couple things: the risk variants are the outcome here. We do not study their effect (on disease) but rather the effect of medication on the risk variants. As such I hope they are not genotypes; medication doesn't change genes, it may change gene expression. The multinomial model is a very general model which can predict the risk of observing the number of variants for each combination of medication and age. The intercept term is the log odds for observing 1, 2, 3, or 4 variants in a person using no medication having age 0. It is an uninterpretable term unless you standardize age. The coefficients for medication summarize the log ratio of odds for being in one particular variant level compared to 1 controlling for age.
However, this has the undesirable property of ignoring the cumulative structure of genetic variants. If the medication is effective, it will on average suppress one or more genetic variants. Therefore, you would expect to see at least one-lower number of genetic variants in a person using medication compared to an age-matched person not using medication. I would discredit the multinomial model for that reason.
For that reason, two better models to consider are the proportional odds model MASS::polr or simple linear regression. While linear regression can overpredict the number of genetic variants or predict numerical interpolations (such as 3.4 variants), it is an effective tool for summarizing associations and gives output on the desired scale of an expected difference in the number of variants comparing medication levels in an age-standardized population.
