# R语言代写 | MA 592 Homework 3: Estimating the effect of a treatment

### R语言代写 | MA 592 Homework 3: Estimating the effect of a treatment

1. The effect of statins on MI.

Suppose we would have the following (hypothetical) data regarding the incidence of
Myocardial Infarction (MI) in men who were observed for 1 year (these are the same
data as in Homework 1, you have the dataset):

(a) Estimate the risk of Myocardial Infarction in the entire group of 300,006 men,
had none of them used statins, based on the data above, using Inverse Probability
of Treatment Weighting.

(b) Estimate the risk of Myocardial Infarction in the entire group of 300,006 men,
had they all used statins, based on the data above, using Inverse Probability of
Treatment Weighting.

(c) Estimate the average effect of statins on Myocardial Infarction in the entire
group of 300,006 men, based on the data above, using (a) and (b).

(d) Compare your results with the results you obtained in Questions 1(a), (b), and

(c) of Homework 2. Are your answers the same? Can you explain this?

(e) Compare your results with the results you obtained in Question 9 of Homework 1.

Can you say a few words about bias, and in this case, provide the numeric value
of the bias? For now, just ignore random variation.

(f) Show that for this particular case, if we have No Unmeasured Confounding
when including this cardiovascular risk variable, that your Inverse Probability
of TreatmentWeighting estimator leads to unbiased estimating equations. What
are the benefits of such a result?

2. The effect of antibiotic medications on hospital death. The simulated HW2
2000 data, posted on the course website when Homework 2 was posted, were simulated
based on numbers reported in Duin et al. (2017). I will provide some background
in class this coming week. The meaning of the variables is as follows. patid is a
patient identification number. Treatment=1 for caz-avi, treatment=0 for colistin.
Creatininehigh=1 for patients with high creatinine levels, 0 otherwise (a high crea-
tinine level was known to indicate a worse prognosis than lower creatinine levels).
Infectiontype=1 for bloodstream infections, 2 for urinary tract infections, and 3 for
other types of infection. The Pitt score is a measure of disease severity. For this ques-
tion, please provide your code. The primary outcome was hospital death, variable
hospitaldeath=1 for patients who died in the hospital and hospitaldeath=0 otherwise.

(a) Estimate the probability of hospital death in the entire simulated population,
had everyone been treated with caz-avi, using Inverse Probability of Treatment
Weighting.

(b) Estimate the probability of hospital death in the entire simulated population,
had everyone been treated with colistin, using Inverse Probability of Treatment
Weighting.

(c) What are the assumptions you made in 2(a) and 2(b)? Mention all assumptions,
including potential modeling assumptions.

(d) Estimate the average effect of caz-avi, as compared to colistin, on hospital death,
in the entire simulated population, using 2(a) and (b).

(e) Compare your results from the conditioning arguments in Homework 2 with the
results from Inverse Probability of Treatment Weighting you found here. What
do you see? Can you explain why this is happening?

(f) Now that you have carried out this analysis in two ways, do you think your
results are very sentitive to model specification? Why/why not?