# Question

An important challenge in clinical trials is patients who drop out before the trial is completed. This can cost pharmaceutical companies millions of dollars because patients who have received a tested treatment for months must be combined with those who received it for a much shorter time. Can we predict who will drop out of a study early? We have data for 428 patients from a clinical trial of depression. We have data on their Age, and their Hamilton Rating Depression Scale (HRDS) and whether or not they completed the study (Drop 1 = Yes; 0 = No. Completed the study).

Here is the output from a logistic regression model of Drop on HRDS and Age.

a) Write out the estimated regression equation.

b) What is the predicted log odds (logit) of the probability that a 30-year-old patient with an HDRS score of 30 will drop out of the study?

c) What is the predicted dropout probability of that patient?

d) What is the predicted log odds (logit) of the probability that a 60-year-old patient with an HDRS score of 8 will drop out of the study?

e) What is the associated predicted probability?

Here is the output from a logistic regression model of Drop on HRDS and Age.

a) Write out the estimated regression equation.

b) What is the predicted log odds (logit) of the probability that a 30-year-old patient with an HDRS score of 30 will drop out of the study?

c) What is the predicted dropout probability of that patient?

d) What is the predicted log odds (logit) of the probability that a 60-year-old patient with an HDRS score of 8 will drop out of the study?

e) What is the associated predicted probability?

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