1. PH6415 Review Questions

2. 2 Question 1 A journal article reports a 95%CI for the relative risk (RR) of an event (treatment versus control as (0.55, 0.97). What can be said of the p-value associated with testing Ho: RR=1 vs. Ha: RR not equal 1? A journal article reports a 95%CI for the relative risk (RR) of an event (treatment versus control as (0.55, 0.97). What can be said of the p-value associated with testing Ho: RR=1 vs. Ha: RR not equal 1? The p-value is < 0.01. The p-value is < 0.01. The p-value is < 0.05. The p-value is < 0.05. The p-value is > 0.05 The p-value is > 0.05 No statement can be said about the p-value. No statement can be said about the p-value.

3. 3 Question 2 If S (t) is the survival function and t is in years what is the meaning of S(3). If S (t) is the survival function and t is in years what is the meaning of S(3). The probability of dying at year 3. The probability of dying at year 3. The probability of surviving to year 3. The probability of surviving to year 3. The probability of dying by year 3 The probability of dying by year 3 The hazard of dying at year 3. The hazard of dying at year 3.

4. 4 Question 3 In logistic regression with a continuous variable age what is the meaning of  1 ? In logistic regression with a continuous variable age what is the meaning of  1 ? The difference in log odds between two persons 1 year apart in age The difference in log odds between two persons 1 year apart in age The relative odds between two persons 1 year apart in age The relative odds between two persons 1 year apart in age The difference in probabilities between two persons 1 year apart in age The difference in probabilities between two persons 1 year apart in age

5. 5 Question 4 If the probability of developing diabetes is 0.20 among Hispanics and 0.15 among whites, what is the relative odds (Hispanics v white) of developing diabetes. If the probability of developing diabetes is 0.20 among Hispanics and 0.15 among whites, what is the relative odds (Hispanics v white) of developing diabetes. 1.42 1.42 0.70 0.70 0.75 0.75 1.33 1.33

6. 6 Question 5 Suppose the logistic regression model: log odds =  0 +  1 X 1 +  2 X 2 +  3 X 1 *X 2 where X 1 is an indicator for treatment and X 2 is an indicator for male gender. The relative odds (treatment versus no treatment) for women is: Suppose the logistic regression model: log odds =  0 +  1 X 1 +  2 X 2 +  3 X 1 *X 2 where X 1 is an indicator for treatment and X 2 is an indicator for male gender. The relative odds (treatment versus no treatment) for women is: exp(  1 ) exp(  1 ) exp(  2 ) exp(  2 ) exp(  1 +  3 ) exp(  1 +  3 ) Exp(  1 -  3 ) Exp(  1 -  3 )

7. 7 Question 6 The probability and odds of an event will be nearly equal if: The probability and odds of an event will be nearly equal if: The probability of the event is small The probability of the event is small The probability of the event is large The probability of the event is large The probability of the event is 0.50 The probability of the event is 0.50

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9. 9 Cox Proportional Hazards Regression in SAS A Review Goto: www.biostat.umn.edu/~susant/PH6415DATA.html www.biostat.umn.edu/~susant/PH6415DATA.html C Read uis.readme file on website. Read uis.readme file on website. Input data from uis (SAS data set) Input data from uis (SAS data set) Use Proc Lifetest to plot the Kaplan-Meier Curve for each categorical predictor separately. Look to see if the survival curves are approximately parallel and if there appears to be a difference in survival. Use Proc Lifetest to plot the Kaplan-Meier Curve for each categorical predictor separately. Look to see if the survival curves are approximately parallel and if there appears to be a difference in survival. Use Proc PHREG to with model containing age, number of previous drug treatments, treatment and site. Use Proc PHREG to with model containing age, number of previous drug treatments, treatment and site.

10. 10 Cox Proportional Hazards Regression in SAS A Review C Consider the interaction between age and site. Is this interaction significant? Consider the interaction between age and site. Is this interaction significant? Consider the final model of age, number of previous drug treatments, site and age_site. Consider the final model of age, number of previous drug treatments, site and age_site.

11. 11 Questions About the Survival Curves What does the log-rank test of equality across strata indicate for the survival curves of the short and long treatment programs? What does the log-rank test of equality across strata indicate for the survival curves of the short and long treatment programs? What does the log-rank test of equality across strata indicate for the survival curves of the two different sites? Why might the p-value for the log-rank test be inflated? What does the log-rank test of equality across strata indicate for the survival curves of the two different sites? Why might the p-value for the log-rank test be inflated? What does the log-rank test of equality across strata indicate for the three combinations of heroine and cocaine use? Do the curves overlap? What does the log-rank test of equality across strata indicate for the three combinations of heroine and cocaine use? Do the curves overlap?

12. 12 Questions about Survival Data What is the median time to relapse for those at site A? What is the median time to relapse for those at site B? What is the median time to relapse for those at site A? What is the median time to relapse for those at site B? How many people relapsed at site A? What percent of site A relapsed? How many people relapse at site B? What percent of site B relapsed? How many people relapsed at site A? What percent of site A relapsed? How many people relapse at site B? What percent of site B relapsed? When did the first person relapse at site A? When did the first person relapse at site B? When did the first person relapse at site A? When did the first person relapse at site B?

13. 13 Questions about Censoring What percent of people where censored in the long treatment program compared to the short treatment? What percent of people where censored in the long treatment program compared to the short treatment? For both treatment groups, does that censoring appear to be patients who do not relapse or patients who are loss to follow-up? For both treatment groups, does that censoring appear to be patients who do not relapse or patients who are loss to follow-up?

14. 14 Questions about parameters in Cox Proportional Hazards What is the relative risk of relapse for a one unit increase in previous drug treatments if all other variables are held constant? This represents a ________ percent increase in rate of relapse. What is the relative risk of relapse for a one unit increase in previous drug treatments if all other variables are held constant? This represents a ________ percent increase in rate of relapse. If treatment length is altered from short(trt =0) to long (trt=1), while holding all other variables constant, the rate of relapse decreases by ______ percent. (RR of trt=1/trt=0). If treatment length is altered from short(trt =0) to long (trt=1), while holding all other variables constant, the rate of relapse decreases by ______ percent. (RR of trt=1/trt=0).

15. 15 Considering Interactions in Cox Proportional Hazards What is the relative risk of relapse for a person who is 30 compared to 25 if they are at site A (site=0) with all other variables held constant? This translates to a _____ percent decrease in rate of relapse. What is the relative risk of relapse for a person who is 30 compared to 25 if they are at site A (site=0) with all other variables held constant? This translates to a _____ percent decrease in rate of relapse. What is the relative risk of relapse for a person who is 30 compared to 25 if they are at site B (site=1) with all other variables held constant? This translates to a _____ percent decrease in relapse. What is the relative risk of relapse for a person who is 30 compared to 25 if they are at site B (site=1) with all other variables held constant? This translates to a _____ percent decrease in relapse. Is this difference in rate of relapse for a five year increase in age between the two sites significant? Is this difference in rate of relapse for a five year increase in age between the two sites significant?

16. 16 Logistic Regression Review Can age, educational level and gender (female=1) predict the odds that someone votes for a particular candidate? Let  = proportion of voters who vote for candidate “Superman”. Can age, educational level and gender (female=1) predict the odds that someone votes for a particular candidate? Let  = proportion of voters who vote for candidate “Superman”. Model: Model:

17. 17 Logistic Regression Review The following is a sample of logistic output: The following is a sample of logistic output: df bSE(b) X2X2X2X2P-value Intercept10.112.3481.103.748 Age10.002.0032..376.540 Education1-0.010.0184.299.585 Gender10.428.104016.95.001

18. 18 Questions for Logistic What is the equation of the estimated Log(odds)? What is the equation of the estimated Log(odds)? What do we predict the odds to be for a 35 year-old male with 16 years of school? What do we predict the odds to be for a 35 year-old male with 16 years of school? What is the probability a 35 year-old male with 16 years of school will vote for “Superman”? What is the probability a 35 year-old male with 16 years of school will vote for “Superman”? What is the odds a woman will vote for “Superman” compared to a man (all other covariates held fixed)? What is the odds a woman will vote for “Superman” compared to a man (all other covariates held fixed)?

19. 19 TOMHS Example Question: Does the effect of active blood pressure treatment on CVD differ for young versus older persons? Question: Does the effect of active blood pressure treatment on CVD differ for young versus older persons? Looking at an interaction effect (effect modification) Looking at an interaction effect (effect modification) Compare Compare Odds CVD (treatment/placebo) in younger patients Odds CVD (treatment/placebo) in younger patients Odds CVD (treatment/placebo) in older patients Odds CVD (treatment/placebo) in older patients

20. 20 Logistic Model For Interaction X1 = 1 for active treatment and 0 for placebo X2 = 1 for age ≥ 55 and 0 for age < 55 X3 = X1 * X2 So, X3 = 1 for active treatment and age > 55 X3 = all other combinations. X3 = all other combinations.

21. 21 Logistic Model For Interaction X1 = 1 for active treatment and 0 for placebo X2 = 1 for age ≥ 55 and 0 for age < 55 X3 = X1 * X2 Log Odds (placebo, young) =  0 Log Odds (active, young) =  0 +  1 Log Odds (placebo, old) =  0 +  2 Log Odds (active, old)=  0 +  1 +  2 +  3 Dif =  1 ; exp(  1 ) is odds (A v P) for young Dif =  1 +   ; exp(  1 +  3 ) is odds (A v P) for old

22. 22 Log Odds (placebo, young) =  0 Log Odds (active, young) =  0 +  1 Log Odds (placebo, old) =  0 +  2 Log Odds (active, old)=  0 +  1 +  2 +  3 exp(  1 ) is odds (A v P) for young exp(  1 +  3 ) is odds (A v P) for old What does  3 Mean? = Odds (A v P) for Oldexp(  1 +  3 ) Odds (A v P) for Youngexp (  1 ) exp (  3 ) = A ratio of ratios!!

23. 23 Interaction Hypothesis Q: Does the effect of active treatment on CVD differ for young versus older persons? Ho:  3 = 0 Ha:  3 ≠ 0 Test in SAS just like any other coefficient

24. The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -1.6843 0.2566 43.0730 <.0001 active 1 -0.8806 0.3301 7.1180 0.0076 old 1 0.0850 0.3549 0.0573 0.8108 active_old 1 0.7771 0.4395 3.1261 0.0770 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits active 0.415 0.217 0.792 old 1.089 0.543 2.183 active_old 2.175 0.919 5.147 b1 b2 b3 Odds CVD (A v P) for younger patients = exp(b1) = 0.415 Odds CVD (A v P) for older patients = exp(b1 + b3) = exp(-0.11) = 0.90 2.175 = 0.90/.415 Ratio of Odds Ratios

25. 25 In patients < age 55 the CVD risk was 58% lower in the active treatment (OR: 0.42) – Exp(b1) For patients over 55 years of age the CVD risk was only 10% lower (OR:.90). - Exp(b1+b3) The test for interaction between treatment and age approached significance (p=.07). Description of Findings