Problem: Special Delivery: In the developed world most people with HIV receive some form of "highly active antiretroviral therapy" or HAART. (HAART regimens are basically cocktails of multiple drugs that are more effective because the virus is less likely to become resistant in their presence.) However in underdeveloped nations HAART is rarer because of its cost. Professor Helpful believes that HAART regimens will help reduce the risk of HIV positive pregnant women passing on the infection to their babies and must therefore be aggressively promoted in poor countries. He has followed n=600 HIV positive pregnant women, 200 of whom are receiving at most a basic non-HAART treatment, 200 of whom are taking HAART regimen A, and 200 of whom are taking HAART regimen B. He records Y, whether or not the baby is HIV positive (1 = yes, 0 = no) and which treatment regimen the mother was on (X1 = 1 if the mother was on HAART A and 0 otherwise, X2 = 1 if mother was on HAART B and 0 otherwise). Professor Helpful recognizes that there are probably many factors besides

treatment regimen that affect whether a mother transmits HIV to her baby, and also collects data on the following factors: X3, the mother’s viral load in copies per milliliter

of blood (higher viral load is worse), X4, the mother’s age in years, X5, the number of years the mother has been HIV positive, X6, the number of weeks during the pregnancy for which the mother was receiving HAART therapy, and X7 the method by which the baby was delivered (1 = C-section, 0 = natural delivery). A logistic regression model is then fit to the data collected to investigate the association between HAART therapy and transmission of HIV infection in the newborn.

Below is the output from the investigation:

1. State the fitted logistic regression model
2. Is there evidence that HAART A reduces risk of HIV transmission to the baby compared to basic non HAART therapy adjusted for all other factors considered? State null and alternative hypothesis, calculate OR, corresponding 95% CI for the OR and conclusion.
3. Is there evidence that HAART B reduces risk of HIV transmission to the baby compared to basic non HAART therapy adjusted for all other factors considered? State null and alternative hypothesis, calculate OR, corresponding 95% CI for the OR and conclusion.
4. Find the estimated odds ratio comparing the risk of HIV transmission for mothers in the HAART A group compared to those in the HAART B group holding all other variables fixed (the same value of all other variables in the model). Show your work.
5. Estimate and provide a a 95% confidence interval for the odds ratio associated with an extra MONTH

(4 weeks) of HAART treatment. Based on this latter interval can you be confident that, all else equal, an extra month of HAART treatment will reduce the odds of mother to child transmission by at least 10%? (hint: an OR of 0.90 indicates a 10% reduction in the odds of transmission).

BONUS: Find the probability that a 30 year old women on HAART A for 20 weeks of her pregnancy with a viral load of 10,000 who has been HIV positive for 10 years will have an HIV negative baby if she delivers by Cesarean Section. Show your work.

This is a prospective study from which we can estimate the probability of disease given exposure. Use the definition of the logit --- and that logit (P) is modeled as a linear function of predictors.

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Solution: The downloadable solution consists of 6 pages, 850 words and 1 charts.
Deliverable: Word Document