ART treatments in HIV-infected patients

A study estimated the effect of 3-drug ART treatments versus 4-drug ART treatments for HIV-infected patients on the risk of virologic failure in the first 144 weeks. Virologic failure is a (binary) outcome of interest in HIV clinical trials, with medications intended to prevent virologic failure. A table with results of some univariate analyses (each result representing one analysis with one predictor) and a table with results from a multivariate analysis (one analysis with the predictors mentioned) is posted here at TopHat, as "tables safety for MA 214".

a. A logistic regression model was fitted with one predictor, injection drug use (1 for ever, 0 for never). Write out the model/the prediction equation for the fitted model. You do not need to fill out the estimated parameter values.

b. A logistic regression model was fitted with one predictor, injection drug use (1 for ever, 0 for never). We found that the odds ratio for virologic failure was 2.21. Please explain this finding to clinicians.*

c. The parameters for logistic regression are typically on the log odds scale. Provide an estimate for the parameter value in b.

d. A logistic regression model was fitted with one predictor, age (per 10 years older). We found that the odds ratio was 0.97, with a p-value of 0.81. Please explain this finding to clinicians.*

e. The same study also fitted a logistic regression model for the probability of virologic failure with more predictors, including age, race, viral load, injection drug us, and an interaction between ART treatment type (4-drug versus 3-drug) and injection drug use. We found that the odds ratio for viral load (measured on the log_10 scale) was 1.29.What is the odds ratio for virologic failure if the viral load increases by 2 (on the log_10 scale), if all other predictors remain the same?

f. The reported confidence intervals for (for example) the Odds Ratio for injection drug use in the multivariate and the univariate models are not symmetric around the point estimate. If you think this is a mistake, please explain. If you think this is not a mistake, please explain.*

Table 1: Univariate analyses. Events in weeks 0 - 144. Estimated Odds Ratios (95%-confidence intervals), and p-values for baseline covariates Baseline covariate Virologic Failure (VF) ART: 4 drugs (vs 3 drugs) 0.76 (0.52,1.08), p=0.12 sex: male (vs female) 1.02 (0.64,1.76), p=0.90 age (per 10 years older) 0.97 (0.79,1.18), p=0.81 age