A case-control study investigated 1) the association between passive smoking and risk of tuberculosis (TB) in non-smokers in China and 2) a potential interaction between passive smoking and a single nucleotide polymorphism in the mannose-binding lectin (MBL) gene on the susceptibility to TB. The MBL gene encodes for a protein that is important in immune function.

The incident cases (n = 207), identified from 2016 to 2018, were non-smoking individuals with tuberculosis confirmed using criteria developed by the Chinese Ministry of Health. They were randomly selected from all new TB patients in that period who were registered within four county-level centers for disease control. The four county-level centers for disease control were randomly selected from 122 counties in Hunan Province.

After all TB cases were identified, controls (n = 218) were selected as healthy, non-smoking individuals with a history of M. tuberculosis contact, but no abnormalities on their chest x-ray. To select controls, one community health center serving Hunan Province was randomly selected and then one of the six communities served by this health center was randomly selected. Controls were selected randomly from the permanent residents of this one community.

Exposure to second-hand smoke was self-reported on a questionnaire that inquired about exposure at multiple places (home, workplace, restaurants) and was categorized as yes or no. The MBL gene was categorized as wildtype (i.e., normal) or mutant alleles. Assume that the prevalence of TB in Hunan Province is 8%.

Original data:

	TB Patients	Healthy Controls
Passive Smoking
Yes	122	104
No	85	114

1. The authors further analyzed the data using a logistic regression model to evaluate the association between passive smoking and TB diagnosis adjusting for sex. Please name the 3 criteria that the variable sex would need to meet in order to be considered a potential confounder.

2. You learn that the OR for the association between passive smoking and TB after adjusting for sex was 1.72. Please evaluate whether sex was a confounder using the 10% change guideline.

3. If we did not adjust for sex, how would our results be impacted? (1 point)

a. The crude (unadjusted) association would overestimate the true (adjusted) association

b. The crude (unadjusted) association would underestimate the true (adjusted) association

c. Since sex does not act as a confounder, leaving sex unadjusted for would have no impact on our results

4. The authors ran additional logistic regression models to examine the association between passive smoking and TB that adjusted for all of the following covariates: sex (male vs. female), age (continuous), marital status (married vs. other), educational background ( primary school (ref), junior high school, high school), body mass index (<18.5 (ref), 18.5 24.9, 25), and alcohol drinking (yes vs. no). Please write out the logistic regression model statement for this fully adjusted model and make sure to write out the label for each variable.

5.If the variable age was modeled as a continuous variable as indicated in Question 4, what assumption would the authors be making about its relationship to the outcome? and How could you go about evaluating whether this assumption is valid?