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

1. Matrix A is an example of which correlation structure?
12. Use the model in Question 9 to obtain the odds ratio for mild or no disease (D < 2) comparing hypertensive smokers vs. nonhypertensive nonsmokers, controlling for AGE and GENDER
11. Use the model in Question 9 to obtain the odds ratio for critical disease only (D 3) comparing hypertensive smokers vs. nonhypertensive nonsmokers, controlling for AGE and GENDER. Compare this odds ratio to that obtained for Question 10.
10. Use the model in Question 9 to obtain the odds ratio for the mild, severe, or critical stage of disease (i.e., D 1)] comparing hypertensive smokers vs. nonhypertensive nonsmokers, controlling for AGE and GENDER.
9. Suppose the following proportional odds model is specified assessing the effects of AGE (continuous), GENDER (female ¼ 0, male ¼ 1), SMOKE (nonsmoker ¼ 0, smoker ¼ 1), and hypertension status (HPT) (no ¼ 0, yes ¼ 1) on four progressive stages of disease (D ¼ 0 for absent, D ¼ 1 for
8. Suppose a four level outcome D coded D = 0, 1, 2, 3 is recoded D = 1, 2, 7, 29, then the choice of using D or D as the outcome in a propor- tional odds model has no effect on the parame- ter estimates as long as the order in the outcome is preserved.
7. If the outcome D has four categories coded D 0, 1, 2, 3, then the log odds of D 2 is greater than the log odds of D > 1.
6. If the outcome D has seven levels (coded 1, 2, ..., 7) and an exposure E has two levels (coded 0 and 1), then an assumption of the propor- tional odds model is that [P(D 3|E = 1)/ P(D
5. If the outcome D has seven levels (coded 1, 2, ..., 7), an assumption of the proportional odds model is that P(D 3)/P(D
4. If the outcome D has seven levels (coded 1, 2,..., 7), then P(D 4)/P(D < 4) is an example of an odds.
3. In an ordinal logistic regression in which the out- come variable has five levels, each independent variable will have four estimated coefficients.
2. In an ordinal logistic regression (using a propor- tional odds model) in which the outcome vari- able has five levels, there will be four intercepts.
1. The disease categories absent, mild, moderate, and severe can be ordinal.
8. Estimate the odds ratio for noncompliance vs. compliance. Consider the outcome comparison active tuberculosis vs. latent or no tuberculosis (D 2 vs. D < 2).
7. Estimate the odds of a compliant 20-year-old male, with an undetectable viral load and who has not progressed to AIDS, of having latent or active tuberculosis (D 1).
6. Estimate the odds of a compliant 20-year-old female, with an undetectable viral load and who has not progressed to AIDS, of having latent or active tuberculosis (D 1).
5. Estimate the odds of a compliant 20-year-old female, with an undetectable viral load and who has not progressed to AIDS, of having active tuberculosis (D 2).
4. Compute the estimated odds ratio for a 38-year-old noncompliant male with a detectable viral load, who has progressed to AIDS, compared with a similar female. Consider the outcome comparison active tuberculosis versus latent or none (D 2 vs. D < 2).
3. Compute the estimated odds ratio for a 25-year-old noncompliant male with a detectable viral load, who has progressed to AIDS, compared with a similar female. Consider the outcome comparison active or latent tuberculosis versus none (D 1 vs. D < 1).
2. For the above model, state the fitted model in terms of variables and estimated coefficients.
1. State the form of the ordinal model in terms of variables and unknown parameters.
10. Extend the model from Question 6 to allow for interaction between AGE and GENDER and between SMOKE and GENDER. How many additional parameters would be added to the model?
9. For the model in Question 6, describe how you would perform a likelihood ratio test to simultaneously test the significance of the SMOKE and HPT coefficients.State the null hypothesis, the test statistic, and the distribution of the test statistic under the null hypothesis.
8. Use the model in Question 6 to obtain the odds ratio for a 50-year-old vs. a 20-year-old subject, comparing severe disease to none, while controlling for GENDER, SMOKE, and HPT.
7. Use the model in Question 6 to obtain the odds ratio for male vs. female, comparing mild disease to none, while controlling for AGE, SMOKE, and HPT.
6. Suppose the following polytomous model is specified for assessing the effects of AGE (coded continuously), GENDER (male ¼ 1, female ¼ 0), SMOKE (smoker ¼ 1, nonsmoker ¼ 0), and hypertension status (HPT) (yes ¼ 1, no ¼ 0) on a disease variable with four outcomes (coded D ¼ 0 for none, D
5. In a polytomous model, the decision of which outcome category is designated as the reference has no bearing on the parameter estimates since the choice of reference category is arbitrary.
4. In a polytomous logistic regression in which the outcome variable has five levels, each indepen- dent variable will have one estimated coefficient. .
3. In a polytomous logistic regression in which the outcome variable has five levels, there will be four intercepts.
2. If an outcome has three levels (coded 0, 1, 2), then the ratio of P(D = 1)/P(D = 0) can be con- sidered an odds if the outcome is conditioned on only the two outcome categories being consid- ered (i.e., D = 1 and D = 0).
1. An outcome variable with categories North, South, East, and West is an ordinal variable.
10. Estimate the odds of having latent tuberculosis vs. none (D ¼ 1 vs. D ¼ 0) for a 20-year-old compliant female, with an undetectable viral load, who has not progressed to AIDS.
9. Estimate the odds ratio with a 95% confidence interval for the viral load suppression variable (detectable vs. undetectable), comparing active tuberculosis to none, controlling for the effect of the other covariates in the model.
8. Estimate the odds ratio(s) comparing a subject who has progressed to AIDS to one who has not, with the outcome comparison active tuberculosis vs. none (D ¼ 2 vs. D ¼ 0), controlling for viral suppression, age, and gender.
7. Use Wald statistics to assess the statistical significance of the interaction of AIDS and COMPLIANCE in the model at the 0.05 significance level.
6. Use the results from the previous two questions to obtain an estimated odds ratio for a 25-year-old noncompliant male, with a detectable viral load, who has progressed to AIDS, compared with a similar female, with the outcome comparison active tuberculosis vs. latent tuberculosis (D ¼ 2 vs. D
5. Compute the estimated odds ratio for a 25-year-old noncompliant male, with a detectable viral load, who has progressed to AIDS, compared with a similar female. Consider the outcome comparison active tuberculosis vs. none (D ¼ 2 vs. D ¼ 0).
4. Compute the estimated odds ratio for a 25-year-old noncompliant male, with a detectable viral load, who has progressed to AIDS, compared with a similar female. Consider the outcome comparison latent tuberculosis vs. none (D ¼ 1 vs. D ¼ 0).
3. Is there an assumption with this model that the outcome categories are ordered? Is such an assumption reasonable?
2. For the above model, state the fitted model in terms of variables and estimated coefficients.
1. State the form of the polytomous model in terms of variables and unknown parameters.
10. Explain how the confidence interval given in the printout is computed
9. How does the odds ratio obtained from the printout given in Question 8 compare with the odds ratio computed using McNemar’s formula X/Y?
8. The following printout results from using conditional ML estimation of an appropriate logistic model for analyzing the data:95% CI for OR Variable b sb P-value OR L U E 0.032 0.128 0.901 1.033 0.804 1.326 Use these results to compute the squared Wald test statistic for testing the significance
7. State the logit form of the logistic model that can be used to analyze the study data.
6. Consider the following McNemar’s table from the study analyzed by Donovan et al. (1984). This is a pair-matched case-control study, where the cases are babies born with genetic anomalies and controls are babies born without such anomalies. The matching variables are hospital, time period of
5. In a matched case-control study, logistic regres- sion can be used when it is desired to control for variables involved in the matching as well as variables not involved in the matching.
4. McNemar's test statistic is not appropriate when there is R-to-1 matching and R is at least 2.
3. If we do not match on an important risk factor for the disease, it is still possible to obtain an unbiased estimate of the odds ratio by doing an appropriate analysis that controls for the important risk factor.
2. An advantage of matching over not matching is that information may be lost when not matching.
1. In a category-matched 2-to-1 case-control study, each case is matched to two controls who are in the same category as the case for each of the matching factors.
that exchangeable d matched pairs are not unique.c. The pooled MORs assume that exchangeable d matched pairs are unique.d. None of the choicesa, b, and c above are correct.e. All of the choicesa, b, and c above are correct.
30. Which of the following helps explain why the pooled MOR should be preferred to the unpooled d MOR? (Cir- d cle the best answer)a. The pooled MORs are equal, whereas the unpooled d MORs d are different.b. The unpooled MORs assume
29. What are the values of MOR (unpooled) and d MOR d (pooled)?
28. What are the values for W, X, Y, and Z?
27. Which type of analysis should be preferred for these matched data (where smoking status is the only matched variable), pooled or unpooled?
26. What type of matched analysis is being used here, pooled or unpooled?
25. What is the estimated MOR from these data?
24. What type of matched analysis is being used with this table, pooled or unpooled? Explain briefly.SMK ¼ 1 E not E D 1 1 2 not D 0 2 2 4 SMK ¼ 0 E not E D 2 1 3 not D 2 1 3 6
23. What is the estimated MOR for these data?
22. How many discordant pairs are there where case is unexposed and the control is exposed?The table below summarizes the matched pairs information described in the previous questions. not D E not E D E 1 2 not E 1 1
21. How many discordant pairs are there where the case is exposed and the control is unexposed?
20. How many concordant pairs are there where both members are unexposed?
19. How many concordant pairs are there where both pair members are exposed?
18. For the model used in Exercise 16, describe the strategy you would use to arrive at a final model that controls for confounding and interaction. The data below are from a hypothetical pair-matched casecontrol study involving five matched pairs, where the only matching variable is smoking
17. Using the model given in Exercise 16, give an expression for the odds ratio for the effect of CON on HIV status, controlling for the confounding effects of AGE, RACE, NP, ASCM, and PAR, and for the interaction effect of PAR.
16. Based on the above scenario, state the logit form of a logistic model for assessing the effect of CON on HIV acquisition, controlling for NP, ASCM, and PAR as potential confounders and PAR as the only effect modifier.
15. If unconditional ML estimation had been used instead of conditional ML estimation, what estimate would have been obtained for the odds ratio of interest? Which estimation method is correct, conditional or unconditional, for this data set?
14. Use the information provided in Exercise 12 to compute a 95% confidence interval for the odds ratio, and interpret your result.
13. For the same situation as in Exercise 12, compute the Wald test for the significance of the exposure variable and compare its squared value and test conclusion with that obtained using McNemar’s test.
12. Consider again the pair-matched case-control data described in Exercise 10 (W ¼ 50, X ¼ 40, Y ¼ 20, Z ¼ 100). Using conditional ML estimation, a logistic model fitted to these data resulted in an estimated coefficient of exposure equal to 0.693, with standard error equal to 0.274. Using
11. For the pair-matched case-control study described in Exercise 10, let E denote the (0, 1) exposure variable and let D denote the (0, 1) disease variable. State the logit form of the logistic model that can be used to analyze these data. (Note: Other than the variables matched, there are no
10. Suppose in a pair-matched case-control study, that the number of pairs in each of the four cells of the table used for McNemar's test is given by W=50, X = 40, Y = 20, and Z = 100. Then, the computed value of McNemar's test statistic is given by 2.
9. When carrying out a Mantel-Haenszel chi-square test for 4-to-1 matched case-control data, the number of strata is equal to 5.
8. In a pair-matched case-control study, the Man- tel-Haenszel odds ratio (i.e., the MOR) is equiv- alent to McNemar's test statistic (X - Y)/ (X + Y). (Note: X denotes the number of pairs for which the case is exposed and the control is unexposed, and Y denotes the number of pairs for which the
7. A matched analysis can be carried out using a stratified analysis in which the strata consists of the collection of matched sets.
6. When in doubt, it is safer to match than not to match.
4. An advantage of matching over not matching is that a more precise estimate of the odds ratio may be obtained from matching. 5. One reason for deciding to match is to gain validity in estimating the odds ratio of interest.
3. In a 3-to-1 matched case-control study, the num- ber of observations in each stratum, assuming sufficient controls are found for each case, is four.
2. In a follow-up study, pair-matching on age is a procedure by which the age distribution of cases (i.e., those with the disease) in the study is constrained to be the same as the age distri- bution of noncases in the study.
1. In a case-control study, category pair-matching on age and sex is a procedure by which, for each control in the study, a case is found as its pair to be in the same age category and same sex cate- gory as the control.
7. A matched analysis can be carried out using a stratified analysis in which the strata consists of the collection of matched sets.
6. When in doubt, it is safer to match than not to match.
5. One reason for deciding to match is to gain validity in estimating the odds ratio of interest.
4. An advantage of matching over not matching is that a more precise estimate of the odds ratio may be obtained from matching.
3. In a 3-to-1 matched case-control study, the num- ber of observations in each stratum, assuming sufficient controls are found for each case, is four.
2. In a follow-up study, pair-matching on age is a procedure by which the age distribution of cases (i.e., those with the disease) in the study is constrained to be the same as the age distri- bution of noncases in the study.
1. In a case-control study, category pair-matching on age and sex is a procedure by which, for each control in the study, a case is found as its pair to be in the same age category and same sex cate- gory as the control.
4. Consider the following figure that superimposes the ROC curve within the rectangular area whose height is equal to the number of MRSA cases (114) and whose width is equal to the number of MRSA noncases (175).a. What is the area within the entire rectangle and what does it have in common with the
3. The ROC curve obtained for the model fitted to these data is shown below. a. Verify that the plots you produced to answer question 2 correspond to the appropriate points on the ROC curve shown here.b. Based on the output provided, what is the area under the ROC curve? How would you grade this
2. Using the following graph, plot the points on the graph that would give the portion of the ROC curve that corresponds to the following cut-points: 0.000, 0.200, 0.400, 0.600, 0.800, and 1.000 Sensitivity 1.0 + 0.8 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1-specificity
1. For a discrimination cut-point of 0.300 in the Classification Table provided above,a. fill in the table below to show the cell frequencies for the number of true positives (nTP), false positives (nFP), true negatives (nTN), and false negatives (nFN): True (Observed) Outcome cp ¼ 0.30 Y ¼ 1 Y
2. Based on the output,a. What is the area under the ROC curve? How would you grade this area in terms of the discriminatory power of the model being fitted?b. In the output provided under the heading “Association of Predicted Probabilities and Observed Responses,” the number of pairs is
1. Using the above output:a. Give a formula for calculating the estimated probability P^ðX*Þ of being a case (i.e., CHD ¼ 1) for a subject (X*) with the following covariate values: CAT ¼ 1, AGE ¼ 50, CHL ¼ 200, ECG ¼ 0, SMK ¼ 0, HPT ¼ 0? [Hint: P^ðX*Þ ¼ 1=f1 þ exp½logit P^ðX*Þg
11.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. Based on the Hosmer–Lemeshow test results for both the no-interaction and interaction models, can you determine which
10.a. Is the deviance value of 157.1050 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. Why cannot you use this deviance statistic to test whether the interaction
9. Is the model being fitted a saturated model? Explain briefly.
8. Is the model being fitted a fully parameterized model? Explain briefly.
7. Consider the information shown in the ouput under the heading “Partition for the Hosmer and Lemeshow Test.”a. Briefly describe how the 10 groups shown in the output under “Partition for the Hosmer and Lemeshow Test” are formed.b. Why does not each of the 10 groups have the same total
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. What two models are actually being compared by the Hosmer–Lemeshow statistic of 7.7793? Explain briefly.c. How can you choose

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

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