Ii h 2 the log odds ratios associating treatment and

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ii. H 2 : The log odds ratios associating treatment and outcome are constant across categories of surgical risk. iii. H 3 : The log odds ratios associating treatment and outcome are linearly related to a continuous covariate, x 4 , which expresses surgical risk. iv. H 4 : The logit transform of the π is linearly related to x 4 , with a common slope for treatment and control groups. (b) Read the data into R and fit the logistic regression model with treatment status and surgical risk. Write down the regression equation for this model defining appropriate notations as needed. Provide the output of summary() function. (c) Carefully explain the findings in (b) regarding the effect of treatment. Incorporate an estimate of the odds ratio, a 95% confidence interval, and a statement regarding the overall significance of this finding. (d) Based on the model in (b), find an expression for the probability of surgical death for a control patient with a medium level of surgical risk. Provide a point estimate and a 95% confidence interval for your estimate. (e) Based on the model in (b), compute the deviance residual for the cell consisting of control patients at the low level of surgical risk. (f) Is there an association between surgical risk and mortality? Be sure to carefully state the null and alternative hypotheses in terms of the regression coefficients, provide the test statistic and its asymptotic distribution under the null. What is your conclusion?

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