本次美国代写是R Causal Inference的一个assignment

**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):

Using these hypothetical data, please answer the following questions.

(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?