Logistic Regression A Self Learning Text 3rd Edition David G. Kleinbaum, Mitchel Klein - Solutions

5.a. Is the deviance value of 159.2017 shown in the above output calculated using the deviance formula Devð^ bÞ¼2 lnðL^c=L^maxÞ; where L^c ¼ ML for current model and L^max ¼ ML for saturated model? Explain briefly.b. The deviance value of 159.2017 is obtained by comparing log likelihood
4. Is the model being fitted a saturated model? Explain briefly.
3. Is the model being fitted a fully parameterized model? Explain briefly.
2. How many covariate patterns are there for the model being fitted? Why are there so many?
1. Is data listing used for the above analysis in events trials (ET) format or in subject-specific format? Explain briefly.
10.a. What can you conclude from the Hosmer– Lemeshow statistic provided in the above output about whether the interaction model has lack of fit to the data? Explain briefly.b. What two models are actually being compared by the Hosmer–Lemeshow statistic of 0.0000? Explain briefly.c. Does the
9.a. Is the deviance value of 0.0000 shown in the above output calculated using the deviance formula Devðb^Þ¼2 lnðL^c=L^maxÞ; where L^c ¼ ML for current model and L^max ¼ ML for saturated model? Explain briefly.b. How can the deviance value of 0.0000 be calculated using the difference
8. Is the model being fitted a saturated model? Explain briefly.
7. Is the model being fitted a fully parameterized model? Explain briefly.
6.a. What can you conclude from the Hosmer- Lemeshow statistic provided in the above output about whether the model has lack of fit to the data? Explain briefly.b. Why does the output shown under "Partition for the Hosmer and Lemeshow Test" involve only 6 groups rather than 10 groups, and why is
5.a. Is the deviance value of 0.9544 shown in the above output calculated using the deviance formula Devðb^Þ¼2 lnðL^c=L^maxÞ; where L^c ¼ ML for current model and L^max ¼ ML for saturated model? Explain briefly.b. State the logit form of two logistic models that can be used to calculate the
4. Is the model being fitted a saturated model? Explain briefly.
3. Is the model being fitted a fully parameterized model? Explain briefly.
2. How many covariate patterns are there for the model being fitted? Describe them.
1. Is data listing described above in events trials (ET) format or in subject-specific (SS) format? Explain briefly.
8. Suppose the final model obtained from the cervical cancer study data is given by the following printout results:Describe briefly how you would use the above information to summarize the results of your study. (In your answer, you need only describe the information to be used rather than actually
7. Suppose the variable NS AS is dropped from the model based on the scenario described in Question 3. Describe how you would assess confounding and precision for any other V terms still eligible to be deleted from the model after interaction assessment.
6. Based again on the scenario described in Question 3, how would you assess whether the variable NS AS should be retained in the model? (In answering this question, consider both confounding and precision issues.)
5. Based again on the scenario described in Question 3, what is the expression for the odds ratio that describes the effect of SMK on cervical cancer status if the variable NS AS is dropped from the model that remains at the end of the interaction assessment stage?
4. Based on the scenario described in Question 3 (i.e., the only significant interaction term is SMK NS), what is the expression for the odds ratio that describes the effect of SMK on cervical cancer status at the end of the interaction assessment stage?
3. Assume that at the end of interaction assessment, the only interaction term found significant is the product term SMK NS. What variables are left in the model at the end of the interaction stage? Which of the V variables in the model cannot be deleted from any further models considered?
2. For the above model, list the steps you would take to assess interaction using a hierarchically backward elimination approach.
1. For the above model, which variables are interaction terms?
10. What problems are associated with the assessment of confounding and precision described in Exercises 8 and 9?
9. Suppose that the variable CT is determined to be a nonconfounder, whereas all other V variables in the model (of Exercise 1) need to be controlled. Describe briefly how you would assess whether the variable CT needs to be controlled for precision reasons.
8. Describe briefly how you would assess confounding for the model considered in Exercises 6 and 7.
7. For the scenario described in Example 6, and making use of the hierarchy principle, what V terms are eligible to be dropped as possible nonconfounders?
6. Suppose the interaction assessment stage finds that the interaction terms HT AGE and HT SEX are both significant. Based on this result, what is the formula for the odds ratio that describes the effect of HT on the prevalence of surgical wound infection?
5. Considering the scenario described in Exercise 4 (i.e., no interaction terms found significant), suppose you determine that the variables CT and AGE do not need to be controlled for confounding. Describe how you would consider whether dropping both variables will improve precision.
assessment stage? What V terms remain in the model at the end of interaction assessment? Describe how you would evaluate which of these V terms should be controlled as confounders.
4. Suppose the interaction assessment stage for the model in Example 1 finds no significant interaction terms. What is the formula for the odds ratio for the effect of HT on the prevalence of surgical wound infection at the end of the interaction
3. Briefly describe how to carry out interaction assessment for the model described in Exercise 1. (In answering this, it is suggested you make use of the tests described in Exercises 1 and 2.)
2. Using the model given in Exercise 1, describe briefly how to carry out a backward elimination procedure to assess interaction.
1. Suppose the following initial model is specified for assessing the effect of type of hospital (HT), considered as the exposure variable, on the prevalence of surgical wound infection, controlling for the other four variables on the above list: logit PðXÞ ¼ a þ bHT þ g1HS þ g2CT þ g3AGE
16. Assuming the scenario described in Question 15 (i.e., SMK NS AS is significant), what (reduced) model remains after the interaction assessment stage of the model? Are there any potential confounders that are still eligible to be dropped from the model? If so, which ones? If not, why not?
15. Suppose that the three-factor product term SMK NS AS is found significant during the interaction assessment stage of the analysis. Then, using the hierarchy principle, what other interaction terms must remain in any further model considered? Also, using the hierarchy principle, what
14. For the model in Question 11, briefly describe a hierarchical backward elimination procedure for obtaining a best model.
13. For the model in Question 11, is a test for the significance of the two-factor product term SMK NS dependent on the coding of SMK? If so, explain why; if not, explain why not.
12. For the model in Question 11, is a test for the significance of the three-factor product term SMK X NS x AS dependent on the coding of SMK? If so, explain why; if not explain, why not.
11. Consider the following E, V, W model that considers the effect of smoking, as the exposure variable, on cervical cancer status, controlling for the effects of the other four independent variables listed: logit P(X) =+ BSMK+V+NS+AS +73 NSX AS+ SMK X NS +8SMK AS+83SMK NS AS, where the V are dummy
10. If the variables E x A and E x A x B are found to be significant during interaction assessment, then a complete list of all components of these variables that must remain in any further models considered consists of E, A, B, E x A, Ex B, and A.
9. A model containing the variables E, A, B, C, A, A x B, E x A, E x A, E x A x B, and E x C is hierarchically well formulated.
8. During variable specification, the potential effect modifiers should be chosen by considering possible statistical problems that may result from the analysis.
7. During variable specification, the potential effect modifiers should be chosen by consider- ing prior research or theory about the risk factors measured in the study.
6. During variable specification, the potential confounders should be chosen based on analysis of the data under study.
5. Getting a precise estimate takes precedence over getting an unbiased answer.
4. The assessment of confounding may involve statistical testing.
3. The assessment of interaction may involve statistical testing.
2. The assessment of interaction should precede the assessment of confounding.
1. The three stages of the modeling strategy described in this chapter are interaction assess- ment, confounding assessment, and precision assessment.
10. Based on the results in Exercise 9, state the (reduced) model that is left at the end of the interaction assessment stage.
9. Suppose the interaction assessment stage for the model of Example 3 finds the following two-factor product terms to be significant: HT CT and HT SEX; the other two-factor product terms are not significant and are removed from the model. Using the hierarchy principle, what variables must be
8. Using the model of Exercise 3, describe briefly the hierarchical backward elimination procedure for determining the best model.
7. Suppose for the model described in Exercise 3 that a Wald test is carried out for the significance of the main effect term AGE. Why is this test inappropriate here?
6. Suppose for the model described in Exercise 3 that a Wald test is carried out for the significance of the twofactor product term HT AGE. Is this test dependent on coding? Explain briefly.
5. Suppose for the model described in Exercise 4 that a Wald test is carried out for the significance of the three-factor product term HT AGE SEX. Explain what is meant by the statement that the test result depends on the coding of the variable HT. Should such a test be carried out? Explain
4. Suppose the product term HT AGE SEX is added to the model described in Exercise 3. Is this new model still hierarchically well formulated? If so, state why; if not, state why not.
3. State the logit form of a hierarchically well-formulated E, V, W model for the above situation in which the Vs and the Ws are the Cs themselves. Why is this model hierarchically well formulated?
2. In defining an E, V, W model to describe the effect of HT on the development of surgical wound infection, describe how you would determine the W variables to go into the model. (In answering this question, you need to specify the criteria for choosing the W variables, rather than specifying the
1. In defining an E, V, W model to describe the effect of HT on the development of surgical wound infection, describe how you would determine the V variables to go into the model. (In answering this question, you need to specify the criteria for choosing the V variables, rather than the specific
11. Based on your answers to the above questions, which model, point estimate, and confidence interval for the effect of SMK on cervical cancer status are more appropriate, those computed for Model I or those computed for Model II? Explain.
10. Use your answer to Question 9 and the estimated variance–covariance matrix to carry out the computation of the 95% confidence interval described in Question 7.
9. Give a formula for the 95% confidence interval for the adjusted odds ratio described in Question 8 (when NS ¼ 1). In stating this formula, make sure to give an expression for the estimated variance portion of the formula in terms of variances and covariances obtained from the
8. Use the formula for the adjusted odds ratio in Question 7 to compute numerical values for the estimated odds ratios when NS ¼ 1 and when NS ¼ 0.
7. Using the output for Model II, give a formula for the point estimate of the odds ratio for the effect of SMK on cervical cancer status, which adjusts for the confounding effects of NS and AS and allows for the interaction of NS with SMK.
6. Carry out the Wald test for the effect of SMK NS, controlling for the other variables in Model II. In carrying out this test, provide the same information as requested in Question 3. Is the test significant? How does it compare to your results in Question 5?
5. Now consider Model II: Carry out the likelihood ratio test for the effect of the product term SMK NS on the outcome, controlling for the other variables in the model. Make sure to state the null hypothesis in terms of a model coefficient, give the formula for the test statistic and its
4. Using the printout for Model I, compute the point estimate and 95% confidence interval for the odds ratio for the effect of SMK controlling for the other variables in the model.
3. For Model I, test the hypothesis for the effect of SMK on cervical cancer status. State the null hypothesis in terms of an odds ratio parameter, give the formula for the test statistic, state the distribution of the test statistic under the null hypothesis, and, finally, carry out the test
2. Why are the variables, age and socioeconomic status, missing from the printout, even though these were variables matched on in the study design?
1. What method of estimation was used to obtain estimates of parameters for both models, conditional or unconditional ML estimation? Explain.
14. Give a formula for the 95% confidence interval for the adjusted odds ratio described in Exercise 12 when CHL ¼ 220. In stating this formula, make sure to give an expression for the estimated variance portion of the formula in terms of variances and covariances obtained from the
13. Use the formula for the adjusted odds ratio in Exercise 12 to compute numerical values for the estimated odds ratio for the following cholesterol values: CHL ¼ 220 and CHL ¼ 240.
12. Using the output for Model II, give a formula for the point estimate of the odds ratio for the effect of CAT on CHD, which adjusts for the confounding effects of AGE, CHL, ECG, SMK, and HPT and allows for the interaction of CAT with CHL.
11. Carry out the Wald test for the effect of CC on outcome, controlling for the other variables in Model II. In carrying out this test, provide the same information as requested in Exercise 10. Is the test result significant? How does it compare to your results in Exercise 10? Based on your
10. Now consider Model II: Carry out the likelihood ratio test for the effect of the product term CC on the outcome, controlling for the other variables in the model. Make sure to state the null hypothesis in terms of a model coefficient, give the formula for the test statistic and its
9. Using the printout for Model I, compute the point estimate and a 95% confidence interval for the odds ratio for the effect of CAT on CHD controlling for the other variables in the model.
8. For Model I, test the hypothesis for the effect of CAT on the development of CHD. State the null hypothesis in terms of an odds ratio parameter, give the formula for the test statistic, state the distribution of the test statistic under the null hypothesis, and, finally, carry out the test for a
7. Give a formula for a 95% confidence interval for the odds ratio describing the effect of HT controlling for the other variables in the no interaction model.Consider the following printout results that summarize the computer output for two models based on follow-up study data on 609 white males
6. Based on the study description preceding Exercise 1, do you think that the likelihood ratio and Wald test results will be approximately the same? Explain.
5. For the same question as described in Exercise 4, that is, concerning the effect of HT controlling for the other variables in the model, describe the Wald test for this effect by providing the null hypothesis, the formula for the test statistic, and the distribution of the test statistic under
4. Consider a test for the effect of hospital type (HT) adjusted for the other variables in the no interaction model. Describe the likelihood ratio test for this effect by stating the following: the null hypothesis, the for- mula for the test statistic, and the distribution and degrees of freedom
3. Suppose you want to carry out a (global) test for whether any of the two-way product terms (considered collectively) in your interaction model of Exercise 2 are significant. State the null hypothesis, the form of the appropriate (likelihood ratio) test statistic, and the dis- tribution and
2. State the logit form of a model that extends the model of Exercise 1 by adding all possible pairwise products of different variables.
1. State the logit form of a no interaction model that includes all of the above predictor variables.
20. For what purpose is the quantity denoted as MAX LOG LIKELIHOOD used?
19. The P-values given in the table correspond to Wald test statistics for each variable adjusted for the others in the model. The appropriate Z statistic is computed by dividing the estimated coefficient by its standard error. What is the Z statistic corresponding to the P-value of .086 for the
18. What is the 95% confidence interval for the odds ratio described in Question 16, and what parameter is being estimated by this interval?
17. State two alternative ways to describe the null hypothesis appropriate for testing whether the odds ratio described in Question 16 is significant.
16. What odds ratio is described by the value e to 0.24411? Interpret this odds ratio.
15. Describe how to compute the odds ratio for the effect of pill use in terms of an estimated regression coefficient in the model. Interpret the meaning of this odds ratio.
14. Why don’t the variables age and socioeconomic status appear in the printout?
13. What method of estimation should have been used to fit the logistic model for this data set? Explain.
11. The variance-covariance matrix printed out for a fitted logistic model gives the variances of each variable in the model and the covariances of each pair of variables in the model.
10. The Wald test and the likelihood ratio test of the same hypothesis give approximately the same results in large samples.
9. The likelihood ratio test is a chi-square test that uses the maximized likelihood value in its computation.
8. The nuisance parameter x is not estimated using an unconditional ML program.
7. The conditional likelihood function reflects the probability of the observed data configuration relative to the probability of all possible config- urations of the data.
6. If a likelihood function for a logistic model con- tains ten parameters, then the ML solution solves a system of ten equations in ten unknowns by using an iterative procedure.
5. In a matched case-control study involving 50 cases and 2-to-1 matching, a logistic model used to analyze the data will contain a small number of parameters relative to the total num- ber of subjects studied.

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Logistic Regression A Self Learning Text 3rd Edition David G. Kleinbaum, Mitchel Klein - Solutions

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