How to deal with the missingness of numerical data that is only relevant to some of the observations when making regression models?

Question

Firstly i'm completely new to data science (first project) and to StackExchange, so sorry if i'm asking a stupid question or not providing adequate information in my question. Please tell if i could do anything to make it easier for you guys to answer.

I'm doing a statistical analysis trying to explore the association between the risk of developing the lung disease COPD in different age groups of alcohol debut (ordered categorical: <14, 15-16, 17-18, 19-20, 21-25, >25) and create both a simpel logistic regression model as well as a multiple logistic model including different variables. One of these variables is age of smoking debut (numeric). My problem is that only some of the participants in the study are either smokers or ex-smokers, while the other part of participants are never-smokers. In these never-smokers the age of smoking debut is obviously not relevant and is displayed as NA. This results in 35% of my dataset containing missing data and is automatically removed in the regression models. For the missing data among the other variables i'm using the mice package in R to impute.

Example df:

| Smoking_status | Age_of_smoking_debut | Age_of_alcohol_debut |
| ---------------| -------------------- | -------------------- |
| Never smoker   | NA                   | 15-16 yrs            |
| Ex-smoker      | 16                   | Never                |
| Current smoker | 20                   | >25 yrs              |
| Never smoker   | NA                   | <14 yrs              |

I've tried doing the logistic regression with the df as is, but results in all never-smokers being excluded.

Any way to deal with this in a clever manner? Would the results be valid if i replaced NA with 0 in the case of smoking status being "never smoker" and then treated the rest of NAs in Age_of_smoking_debut like the NAs among the other variables? Also how would i go by this the easiest?

Answer 1

Although it may seem odd to do this in some analyses, I think the strategy that makes the most sense is to set the values of Age_of_smoking_debut to a single value, e.g., 0 (it doesn't matter which value), for never-smokers. As long as you include Smoking_status as a categorical predictor (or at least include a dummy variable for Never smoker), you can estimate the relationship between Age_of_smoking_debut and your outcome for smokers and just a single intercept for never smokers. This approach is sometimes called the "missingness indicator" approach, but in this case the missingness isn't just because the data were lost somehow; the data are missing because there is no possible value the variable could take.