(Problem 4.20 in [ICDA2] Revised ) The table below shows results of an eight-center clinical trial to compare a drug to placebo for curing an infection . At each center , subjects were randomly assigned to groups 1. Response Center Treatment Success Failure Drug Control 10 27 2 Drug 16 Control 10 3 Drug 14 5 Control 7 12 Drug to 14 Control 16 Drug 11 Control 12 6 Drug 10 Control 0 10 Drug 4 Control 8 8 Drug Control (a) Calculate and interpret the (sample) conditional odds ratios between the Treatment (drug v.s. placebo) and Response (success , failure ) for Center 1, Center 2, and Center 5, adding 0.5 to each cell to reduce the impact of the 0 cell count . (b) Find the partial tables between between Center (1 v.s. 2) and Response (success, failure), given Treatment = drug and given Treatment = drug. Calculate and interpret the (sample) conditional odds ratios. Do patients receiving the same treatment have different success rate in different centers? (c) Find the marginal table for the Treatment (drug , placebo ) and Response (success , failure ). Calculate and interpret the (sample ) marginal odds ratios of the marginal table . (d) Explain why it's not a good idea to test the independence of Treatment and Response using the marginal table of Treatment and Response and ignore Center. (e) Please test the conditional independence of Treatment and Response given Center using the Cochran- Mantel -Haenszel test . Please calculate the expected count and the variance for the cell (Drug , Success ) for each of the 8 centers, write down every term in the numerator and the denominator of the CMH statistic explicitly before evaluating them , and find the P-value. (f) Calculate and interpret Mantel - Haenszel's estimate of the common odds ratio between Treatment (drug v.s. placebo ) and Response ( success , failure ). Please write down every term in the numerator and the denominator of the estimate explicitly before evaluating it . (g) Verify your calculation in the previous two parts using the R command mantelhaen . test