The NHEFS dataset contains a variable called 'death' which is a binary indicator of whether

participants died by $($let$\text{'}$s say, I$\text{'}$m not sure$)2001.$ In this assignment, we'll consider the effect of

quitting smoking between $1971$ and $1981$ on death by $2001.$ We do not need to address loss to

follow up for this analysis, since death seems to have been ascertained even for subjects who

did not participate in the $1981$ survey.

A$.$ Fit the full model predicting treatment that we've been using in labs. Make a calibration plot,

ROC curve, and binned residuals plot for this model. Also, check the weighted covariate balance

for any covariates that were imbalanced $($i$.$e$.$ their means were different in the treated and

untreated$)$ in the data. Describe the interpretation and implications of each diagnostic. Is the

model a good fit?

B$.$ Compute the IPW$-$weighted estimate of the effect of quitting smoking on mortality by $2001.$ Use

bootstrap to compute the standard error.

C$.$ Compute the standardized estimate and bootstrap standard error of the effect of quitting

smoking on mortality by $2001$ using a logistic regression model for death given treatment and

confounders $($using the same outcome regression formula we've used for standardization on

NHEFS data in the past$).$

D$.$ Compute the doubly robust effect estimate and bootstrap standard error of the effect of

quitting smoking on mortality by $2001.$