Part I (2 points) The following is the output from R code. Please clearly state the null and the alternative hypotheses for the chisq test carried out by default in R, the test statistic, the rejection region, and the decision. > survdiff (Surv (burn$T3, burn$D3) zi, data=burn) Call: survdiff (formula = Surv (burn$T3, burn$D3) ~ zi, data = burn) N Observed Expected (0-E)^2/E (O-E)^2/V 21=0 70 28 21.4 3.79 2.07 21=1 84 20 26.6 3.79 1.66 Chisq= 3.8 on 1 degrees of freedom, p= 0.05 Part 11 Assume the following 4 models are fitted. The likelihood ratio test statistics for each of the model are listed. Model Model covariates Likelihood ratio test statistics for Ho: B = 0 versue H: at least one of the regression coefficient B, i=1, ... k, is not equal to 0. 3.73 4.70 11.54 12.95 Model 1 Model 2 Model 3 Model 4 Z1 Z1 Z2 Z1 Z3 Z1 Z2 Z3 (a) (2 points) Clearly specify your coding of covariates Z1, Z2 and Z3 and write out the equation of the Cox proportional hazard model to fit including all three variables (Model 4). (b) (1 point) Given the estimated regression coefficient for variable Z2 is 0.009 in Model 4. Interpret how a 20 units (20%) increase that is, Z2(new)=Z2(old) +20) in the total surface area burned affect the burn wound infection risk of a patient, assuming all the other conditions as the same. (0) (1 point) Is variable Z2 a significant risk factor for burn wound infection? Use a = 0.05. Justify your answer (d) (2 points) Given the following results for variable Z1 in Model 4. Construct a 95% Confidence interval for the relative risk between the body cleansing method and the routine bathing method, given all the other variables the same. Show you steps and Interpret the result. coef exp(coef) se(coef) z Pr(>1z1) 0.49543 1.64121 0.20910 2.369 0.0178 * z1 (e) (3 points) Physicians are particularly interested in checking if the Type of Burn is a significant risk factor for burn wound infections. Based on the results presented here, what is your conclusion? (1) (2 points) It is suspected that among the four types of burn, there does not exist statistically significant difference in the risk of infection for the chemical burn, the scald burn and the flame burn. Please clearly state your coding of covariates in order to test this statement and the model(s) to fit. Furthermore, please clearly state the null and alternative hypotheses, the test statistic, the rejection region, and the decision rule. Assume both Z1 and Z2 are included in all the models investigated