14 Question Three [** marks] In a clinical trial for treatment of lung cancer, patients were randomly assigned to two chemotherapy treatment groups, namely the sequential and the alternating therapy groups. The following table shows the results of the clinical trial. Response to treatment Progressive No Partial Complete Therapy Gender Disease Change Recovery Recovery Sequential Male 30 47 31 28 Female 6 14 7 4 Alternating Male 43 46 22 22 Female 9 5 3 Suppose that you have been asked to assist in analyzing the data. (a) Fit a cumulative logit model with main effects for therapy and gender. Check for goodness of fit of the model and interpret the effect estimates. Justify your choice of the model. (b) Fit the model to the binary response obtained by combining the first two response categories and combining the last two response categories. (c) What property of the model does the result in (b) reflect? (d) Compare the therapy effect of the model in (b) with the one computed in (a). (e) Fit the model as in (a), and include an interaction term. Interpret your results. (f) Using the results found in (e) compute the probability of complete recovery under the better chemotherapy treatment, each for male and for female patients. (g) Based on your analysis, what is your recommendation to the researchers? 14 Question Three [** marks] In a clinical trial for treatment of lung cancer, patients were randomly assigned to two chemotherapy treatment groups, namely the sequential and the alternating therapy groups. The following table shows the results of the clinical trial. Response to treatment Progressive No Partial Complete Therapy Gender Disease Change Recovery Recovery Sequential Male 30 47 31 28 Female 6 14 7 4 Alternating Male 43 46 22 22 Female 9 5 3 Suppose that you have been asked to assist in analyzing the data. (a) Fit a cumulative logit model with main effects for therapy and gender. Check for goodness of fit of the model and interpret the effect estimates. Justify your choice of the model. (b) Fit the model to the binary response obtained by combining the first two response categories and combining the last two response categories. (c) What property of the model does the result in (b) reflect? (d) Compare the therapy effect of the model in (b) with the one computed in (a). (e) Fit the model as in (a), and include an interaction term. Interpret your results. (f) Using the results found in (e) compute the probability of complete recovery under the better chemotherapy treatment, each for male and for female patients. (g) Based on your analysis, what is your recommendation to the researchers