10 MCQ questions on hypothetical scenarios statistics

1. Consider a case where we do a simple linear regression of the relationship between daily coffee intake (predictor, a quantitative variable expressed in number of 8oz cups per day) and sleep quantity (outcome, a quantitative variable measured in hours slept per night). What kind of measure of effects does a simple regression give us?

a. Unadjusted effect of daily coffee intake on sleep quantity, measured in the amount of change in hours slept per night we expect for every unit increase in cups of coffee consumed per day

b. Adjusted effect of daily coffee intake on sleep quantity, measured in the amount of change in hours slept per night we expect for every unit increase in cups of coffee consumed per day

c. Unadjusted effect of daily coffee intake on sleep quantity, measured in the odds of having a low number of hours slept per night for high coffee intake subjects compared to low coffee intake subjects

d. Adjusted effect of daily coffee intake on sleep quantity, measured in the odds of having low hours slept per night for high coffee intake subjects compared to low coffee intake subjects

2. Take a look at this output, which uses a categorical predictor (gender, RIAGENDR) and a binary logistic outcome (coughed up blood in the last month? labeled SPQ100).

What's the adjusted odds ratio that we will use to determine whether Age is a significant confounder? Remember, we're not asking if age influences disease (the OR for age itself), only asking if age is somehow hiding or exaggerating the effect of gender on coughing up blood. To find that we want the age-adjusted effect of the gender variable on the risk of the coughing up blood outcome.

a. 2.862

b. -6.270

c. -0.007

d. 2.853

3. Imagine we wanted to do a study investigating a bunch of predictors (both categorical and quantitative) that relate to risk of heart disease (coded as Yes or No). What type of regression would we use? And what kind of measure of effects would this regression give us?

a. Logistic regression, with odds ratios

b. Linear regression, with odds ratios

c. Logistic regression, with slopes

d. Linear regression, with slopes

4. Imagine that we hypothesized heart disease risk was higher for women than men. What would be the reference category?

a. Women

b. Men

c. Yes CVD

d. No CVD

5. Imagine that we hypothesized that the way gender influenced heart disease risk was because of biological predisposition (and any learned cultural differences between men and women were extraneous to the hypothesis).

In this scenario:

a. Estrogen might be a mechanism of our hypothesized effect, while an emotional, very feminine refusal to visit the doctor for checkups would be a confounder

b. Emotional refusals to visit the doctor for checkups and other feminine health behavior choices would be the mechanism of the hypothesized effect, while estrogen levels and other innate neuroendocrine characteristics of women would be confounders

6. Imagine that we ran a regression testing for the effects of self-reported gender on self-reported answer to “have you ever had a heart attack?” in a sample of adults recruited from the general American population.

Imagine that the results show women have 5 times higher odds of being in the yes heart attack group than men, and that this difference is significant.

Imagine that we next controlled for age (by putting age into the regression along with gender, so there were 2 predictor variables at once for the heart attack outcome), and now we found an odds ratio telling us women had a 2 times higher risk of heart attack than men.

It seems that age was a confounder that was partly inflating how big the effect of gender on heart attacks really is. At first it seemed like women's gender increased risk five- fold, but later, we saw that risk was more like 2 times higher. This seems like a pretty big deal. But as statisticians, we always want to know if any difference between two numbers is likely to have happened by chance.

One of the models described above tells us that women have 2 times higher risk than men of having a heart attack. Which model is it?

a. The simple-regression model

b. The age-adjusted regression

7. Let's say that in some study, the original slope for the effect of weight on 60 second heart rate is a 1.615 bpm decrease in heart rate per 1 unit increase in weight (kg). This slope of 1.615 is our best estimate of the effect size (can be called the main effect or effect estimate), but as statisticians we know that it might be a little higher or lower. The standard error of this effect was 0.046 bpm/kg , which we can use to calculate a confidence interval around the main effect (a 95% CI ranges from 2 standard errors above the estimate to 2 standard errors below the estimate). After controlling for age, the new estimate of the main effect was 1.31.

a. The difference of 1.615 - 1.31 is equal to 0.305. Double the standard error is 0.046 times 2, which is 0.092. The difference is bigger than double the standard error, so age really is a confounder that meaningfully tricks us about the size of the effect of body weight on heart rate.

b. The difference of 1.615 - 1.31 is equal to 0.305. Double the standard error is 0.046 times 2, which is 0.092.The difference is smaller than double the standard error, so age is NOT really a confounder that meaningfully tricks us about the size of the effect body weight on heart rate.

8. So let's go back to gender and aneurysm example. In the original model, the effect of being a male was 1.33, with a 95% CI from 0.264 to 1.769. The age adjusted model has an odds ratio main estimate of 0.890. Was gender really a statistically significant confounder?

a. Yes, because the adjusted odds ratio is inside the original 95% interval

b. Yes, because the adjusted odds ratio is outside the original 95% interval

c. No, because the adjusted odds ratio is inside the original 95% interval

d. No, because the adjusted odds ratio is outside the original 95% interval

9. Let's practice on another worked example.

First, the simple regression.

Predictor: Ever served in the US armed forces?; recoded as yes = 1, no = 0.

Outcome: Cigarettes smoked in the last 30 minutes?; recoded as yes = 1, no = 0.

Odds ratio without controlling for sex differences: 1.176

95% CI: 0.657-2.106

These results say what?

a. Sex has a significant effect on smoking in the last thirty minutes, and it is also a significant confounder of the relationship between smoking and having served in the US armed forces (it masks how large the effect of smoking really is).

b. Sex has a significant effect on smoking in the last 30 minutes , but it is not a significant confounder of the relationship between smoking and having ever served in the US armed forces (it doesn't change the effect more than you would expect by chance).

c. Sex has no significant effect on smoking in the last 30 minutes, but it is a significant confounder of the relationship between smoking and ever serving in the US armed forces (it masks how large the effect of smoking really is).

10. The last thing to know is the concept of independent effects and dependent effects of different predictors on the same outcome. We've done all this work to say if something is a confounder or not. If something ends up being a confounder, it means the simple effect of the predictor on the outcome are (at least partly) dependent on the confounder, but after controlling for it, the adjusted effects are independent of the confounder.

Therefore, multiple regression models that control for many variables show us the effects of the predictor on the outcome that are _________ of the other variables in the model, while simple regression models show effects that might be _________ on other confounders that aren't in the model.

a. Independent, dependent

b. Dependent, independent