BIOS 1 - Homework 2 • bios1

Source code and data for this assignment

Note: The code used to create this document is here.

In this homework we will again use the NHEFS dataset. Take a look at the codebook linked to from https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/.

This time we will test the hypothesis that quitting smoking between 1971 and 1981 (variable qsmk) reduces the probability of death by 2001 (variable death).

Data import and recoding

Download the dataset, import it into R, and recode variables as instructed in Homework 1.

library(readr)
nhefs <- read_csv("https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/1268/20/nhefs.csv")

Question 1 (2 points): filter any missing data

Remove any observations that are missing any of the following variables:

death
active
age
education
exercise
qsmk
race
sex
smokeintensity
smkyrs
wt82_71

You would ordinarily want to perform a sensitivity analysis and consider the possibility of bias from informative censoring, but you can ignore that possibility for the purposes of this assignment.

Question 2 (4 points): Table 1

Create a table of descriptive statistics like in HW1, but this time stratify it by the exposure variable qsmk

Question 3 (4 points): fit crude and adjusted logistic regression models

Fit simple and adjusted multiple logistic regression models for the probability of death with quitting smoking as the exposure. In the multivariate model, adjust for sex, race, age, education, and exercise as hypothesized confounders. Use a B-spline from the splines package to correct for age, ie:

\[ death \sim qsmk + sex + race + bs(age) + education + exercise \]

For the purpose of this question, assume that conditional exchangeability holds when controlling for these confounders.

Interpret the coefficient of qsmk in the crude model and in the adjusted model. Compare them.

Question 4 (3 points): model diagnostics

Create a binned residual plot using the binnedplot function from the arm library. Interpret the plot.

Question 5 (7 points): Inverse probability weighting

a (2 points)) Create a model to calculate the propensity of exposure given the values of the hypothesized confounders (propensity score). This is your “denominator” model of Lecture 11, Slide 15. ie,

\[ \textbf{denom.fit}:qsmk \sim sex + race + bs(age) + education + exercise \]

Also fit your “numerator model”, \[ \textbf{num.fit}: qsmk \sim 1 \]

b (2 points)) Calculate IPTW weights using this model. Hint - you can use code like this:

pdenom <- predict(denom.fit, type = "response")
pnum <- predict(num.fit, type = "response")
nhefs$iptw <- ifelse(nhefs$qsmk == 0, ((1-pn.qsmk)/(1-pd.qsmk)),
                     (pn.qsmk/pd.qsmk))

c (2 points)) Use the geeglm function from the geepack library to use these weights to estimate the causal effect of quitting smoking on death.

Notes: - the id argument to geepack is arbitrary in this case because there is no grouping or hierarchical structure of participants. You can use the seqn variable or 1:nrow(nhefs). - The corstr argument is also arbitrary for the same reason; if you don’t specify it you will be using the default corstr="independence" - Remember that when using these weights, do not include confounders in the model.

d (1 point)) Compare the coefficient and standard error for quitting smoking to Question 2, and comment. Recall the discussion in lecture about geepack standard errors being too conservative.

BIOS 1 - Homework 2

Levi Waldron