The data for this question consist of a sample of 50 persons from the 1967-1980 Evans County Study (Schoenbach et al. 1986). Two basic independent variables are of interest: AGE and chronic disease status (CHR), where CHR is coded as 0 = none and 1 = presence of chronic disease. A product term of the form AGE X CHR is also considered. The dependent variable is time until death, a continuous variable. The primary question of interest is whether CHR, considered as the exposure variable, is related to survival time, controlling for AGE. The computer results, based on ML estimation, 12 are as follows:
a. Assuming a regression model that contains the main effects of CHR and AGE, as well as the interaction effect between CHR and AGE, carry out a Wald test for significant interaction. (Specify the null hypothesis, the form of the test statistic, and its distribution under the null hypothesis.) What are the conclusions about interaction based on this test?
b. For the same model considered in part (a), how would one carry out an LR test for significant interaction? (Specify the null hypothesis, the form of the test statistic, and its distribution under the null hypothesis.) What are the conclusions about interaction based on this test? How do these results compare with those in part (a)?
c. Assuming no interaction, carry out a Wald test for the significance of the CHR variable, controlling for AGE. (As in the preceding parts of this problem, state the null hypothesis, the form of the test statistic, and its distribution under the null hypothesis.) What are the conclusions based on this test?
d. For the same no-interaction model considered in part (c), how would one carry out an LR test for significance of the CHR variable, controlling for AGE? (Specify the null hypothesis, the form of the test statistic, and its distribution under the null hypothesis.) Why can't one actually carry out this test given the output information provided earlier?
e. For the no-interaction model considered in part (c), compute a 95% confidence interval for the coefficient of the CHR variable, controlling for AGE. What does the computed confidence interval say about the reliability of the point estimate of the effect of CHR in this model?
f. What is the overall conclusion about the effect of CHR on survival time based on the computer results from this study?