Question

3. For your dependent (Y) variable, you code it 0 for each person where CD4 is below 200 at the end of study and 1 if CD4 is 200 or above. Then you build a model predicting a function of Y based on age, gender, time since infection, and ARV group in predicting whether or not CD4 count is above or below 200 by the end of the study.

a. What is the name for this type of model?

Many of the patients were very sick, and quite a few died from AIDS-associated opportunistic infections or TB before one year. Since the CD4 count at one year was unavailable for these patients, one of the investigators proposed changing the analysis to compare the time to CD4 count < 200, and censoring the patients who died or reached the end of the study without falling below 200.

b. What important assumption does this idea seem to violate? Explain.

After hearing your explanation, the investigator agrees to change the endpoint to time to event, where an event is any of: CD4<200, AIDS defining illness, or death.

c. What kind of plot could he make to visually compare the time to event in the two treatment groups?

Answer 1

a) The name for this type of model is Logistic regression where the dependent variable CD4 takes two values: 0 and 1.

b) The data of the patients who reached the end of the study without falling below 200 were censored, this means that the survival time (or the time to reach count<200 is taken to be atleast as long as the duration of the study but we are not sure of the exact time). These cases are known as right-censored.

Here, the main assumption was that the CD4 count is the only dependent variable which is the measure of how risky it is to develop serious illness. When CD4<200, it means that you are at high risk. If the model is built to compare the time when CD4<200 and you are censoring the observations for those patients who died without falling below 200, you are missing up on those patients who died early (which is important for the study). Hence, if the study is being done to predict the riskiness of a patient, these observations are important as AIDs associated infections should be considered here. This is the reason why the event should be taken as either CD4<200 or AIDS defining illness or death.

c) To compare the time between two treatment groups, a box plot for the two groups on the same graph would be a great way.