ࡱ> WYVq'` ,(bjbjLULU ..?.?glTlTlTlTLTtpx8VWWWW)YCYWY fphphphphphphp$_rhtpcYX^)YcYcYpWWpg\g\g\cY lWWfpg\cYfpg\g\gh,hW,V 0۩lToZgi|p0ph]u][]u hh]u~ilcYcYg\cYcYcYcYcYppK\cYcYcYpcYcYcYcYD+2d"2 FINAL EXAM REVIEW: ANSWER KEY Recall the psa dataset that we used in lab 4. I built a logistic regression model for predicting capsule=1 that included psa, age, and gleason in the model (model 1). Part of the resulting SAS output follows: Model 1: Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 514.289 411.208 SC 518.229 426.969 -2 Log L 512.289 403.208 Analysis of Maximum Likelihood Estimates Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -6.3896 1.4976 18.2045 <.0001 psa 1 0.0266 0.00894 8.8442 0.0029 age 1 -0.0208 0.0188 1.2351 0.2664 gleason 1 1.0790 0.1611 44.8373 <.0001 a. Write the resulting logistic regression equation for model 1 below:  b. What is the predicted probability of having capsule=1 for a 69-year old man with a psa level of 10 mg/ml and a gleason score of 5, according to model 1?  EMBED Equation.3  c. What does the intercept from the model tell you? Model 1: The log odds of capsule=1 for a man aged 0, with 0 psa and 0 gleason. d. Calculate the odds ratio and 95% confidence interval for psa from model 1. Interpret. Exp(0.0266)= 1.027 Exp(0.0266+1.96*0.00894)= 1.045 Exp(0.0266-1.96*0.00894)= 1.009 e. What would be different about the output if this was a conditional logistic regression? An ordinal logistic regression? Conditional = no intercept Ordinal = 2 or more intercepts 2. The following results are from a prospective study that considered predictors of mammography use in women. The investigators used logistic regression to analyze their data. Table 3 Results of a logistic regression predicting annual mammography use Variable name Parameter estimate (std error) Significance value  Family history-associated risk group .14 (.09) not sig. Age -.04 (.02) <0.05 Worry -.04 (.01) <0.05 Worryx family history-associated risk group -.05 (.02) <0.05  What is the odds ratio for getting a mammogram for every 10-year increase in age?  EMBED Equation.3  What is(are) the odds ratio(s) for every 1-unit increase in worry? Among women with no family history of breast cancer, the odds ratio for a 1-unit increase in worry is:  EMBED Equation.3  Among women with a family history of breast cancer, the odds ratio for worry a 1-unit increase in worry is:  EMBED Equation.3  What is(are) the odds ratio(s) for having a positive family history?  EMBED Equation.3  What do these results mean? 3. The following table came from a study on predictors of breastfeeding. The authors used ordinal logistic regression, where the outcome variable was coded 2=exclusive breastfeeding; 1=partial breastfeeding, and 0=no breastfeeding. Questions are based on the breastfeeding at 3 months after delivery column. Table3. Ordinal Logistic Regression Analysis of Factors Associated with Breastfeeding Variable Breastfeeding Initiation during Hospital Stay (n =2,064) OR (95% CI) Breastfeeding at 1 mo after Delivery (n =1,336) HYPERLINK "http://www3.interscience.wiley.com/cgi-bin/fulltext/118533598/main.html,ftx_abs" \l "t3n1#t3n1" * OR (95% CI) Breastfeeding at 3 mo after Delivery (n =1,453) HYPERLINK "http://www3.interscience.wiley.com/cgi-bin/fulltext/118533598/main.html,ftx_abs" \l "t3n2#t3n2" OR (95% CI)  Age (yr) < 20 0.49 (0.260.90) 0.28 (0.100.66) 0.28 (0.110.74) 2024 0.67 (0.480.94) 0.73 (0.481.12) 0.96 (0.631.47) 2529 0.80 (0.591.07) 1.05 (0.731.50) 0.94 (0.651.35) 3034 0.87 (0.641.18) 0.98 (0.681.41) 1.31 (0.901.90) Education Junior high school or lower 0.35 (0.250.49) 1.00 (0.641.57) 0.94 (0.631.42) Senior high school or vocational school 0.43 (0.350.53) 0.74 (0.580.95) 0.76 (0.590.97) Work status Full time 1.23 (1.031.48) 0.58 (0.460.72) 0.38 (0.300.48) Part time 1.00 (0.731.37) 1.12 (0.741.69) 1.03 (0.711.50) Father's support for breastfeeding 1.02 (1.011.03) 1.03 (1.021.04) 1.01 (0.9951.02) Method of delivery Cesarean 1.19 (0.9951.43) 0.69 (0.550.86) 0.70 (0.560.88) Assisted vaginal 0.88 (0.681.15) 0.75 (0.531.06) 0.67 (0.480.93) Initiation of breastfeeding within 30 min of delivery NA 1.47 (1.131.90) 1.57 (1.212.05)  The dependent variable was coded as exclusive breastfeeding (2), partial breastfeeding (1), and no breastfeeding (0). The reference group comprised mothers aged 35 years or more, who had an educational level of university or higher, who did not work, who had unassisted vaginal delivery, who did not initiate breastfeeding within 30 min of delivery, and who initiated breastfeeding during hospital stay. * Among mothers who initiated breastfeeding during hospital stay ; among mothers who breastfed at 1 mo after delivery. NA = not applicable.  What factors predicted a significantly higher level of breastfeeding at 3 months post-delivery? Age>=35 vs. Age<20. University educated vs. senior high school or vocational school. Stay at home moms vs. full time. Vaginal vs. other modes of delivery. And initiating breastfeeding within 30 min delivery vs. not. Among all the predictor variables shown in the table above, how many categorical predictors are there? Binary? Ordinal? Continuous? Cat: age, education, work status, method of delivery. Binary: intitation of BF within 30 min delivery; ordinal: none; cont: fathers support for breastfeeding. Among women who did not initiate breastfeeding within 30 minutes of delivery, 15% were still breastfeeding exclusively at 3 months and 30% were breastfeeding at all (partial or exclusive). The authors ran an ordinal logistic regression model with only initiation of breastfeeding within 30 minutes of delivery as the predictor and 3-month breastfeeding status as their outcome. The resulting unadjusted OR for initiation of breastfeeding within 30 minutes of delivery is 1.50. Write out the fitted logistic regression model/s. Intercepts: Logit (15%) = -1.7 Logit (30%) = -.85 Beta: Ln(1.5) = 0.4 4. The following data arose from a case-control study of coronary heart disease (CHD). Patients aged 30-79at presentation with suspected acute myocardial infarction (heart attack) were eligible if they had a sibling of the same sex and similar age (within 5years) who reported no history of coronary heart diseasethese siblings became the control group for the study. The following data describe the baseline characteristics of the cases and controls. Using these data and an appropriate statistical test, fill in the p-value for smokers below. CharacteristicCases (n=510)Controls (n=510)p-valueOdds RatioNo (%) of current smokers220 (43)139 (27)2.0No (%) with treated diabetes30 (6)22 (4) 1.5No (%) with treated hypertension155 (30)115 (23)3.0No (%) ended education <16 years385 (75)392 (77)0.5No (%) with household income <$50,000/year115 (25)98 (21)1.2 This is paired data; and you DO have enough information (using a bit of algebra) to reconstruct the paired 2x2 table. 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