SURVIVAL ANALYSIS

STATISTICS

(3.2) STATA code and output for fitting the Cox proportional hazards model on the variables smoking and age is the following: xi: stcox i. smoking age, nolog i . smoking Ismoking 0-1 (naturally coded; _Ismoking_0 omitted) failure d: dead analysis time t: t Cox regression -- Breslow method for ties No. of subjects = 80 Number of obs 80 No. of failures = 58 Time at risk 1257.07 LR chil (2) 113. 34 Log likelihood = -167.57034 Prob > chi2 0. 0000 t | Haz. Ratio Std. Err. Z P>IZI [95% Conf. Interval] Ismoking 1 | 2. 498235 . 7755781 2.95 0.003 1. 359494 4. 590808 age 1. 193037 . 0221666 9.50 0.000 1. 150372 1. 237283 (a) Is age significantly associated with the hazard of death for breast cancer patients? Explain your answer by interpreting the hazard ratio and its 95% confidence interval. (2) (b) Does the hazard of death significantly differ between smokers and nonsmokers for breast cancer pa- tients? Explain your answer by interpreting the hazard ratio and its 95% confidence interval. (2) (c) Explain why, for the data in this question, age is a confounder for smoking. (2)QUESTION 3 The dataset be, on breast cancer, is installed with STATA and can be retrieved by typing webuse be in the command window. The dataset has the following variables: age, smoking, dietfat, t, and dead where t is the time variable and dead is the event variable. (3.1) STATA code and output for fitting the Cox proportional hazards model on the variable smoking is the fol- lowing: xi: stcox i. smoking, nolog i . smoking Ismoking 0-1 (naturally coded; _Ismoking_0 omitted) failure d: dead analysis time t: t Cox regression -- Breslow method for ties No. of subjects = 80 Number of obs S 80 No. of failures = 58 Time at risk 1257.07 LR chi2 (1) 1. 38 Log likelihood = -223 . 55236 Prob > chil 0. 2407 t | Haz. Ratio Std. Err. Z P>|ZI [953 Conf. Interval] Ismoking 1 | 1. 407848 . 4011162 1. 20 0.230 8054452 2. 460794 Does the hazard of death significantly differ between smokers and nonsmokers for breast cancer patients? Explain your answer by interpreting the hazard ratio and its 95% confidence interval. (2) [TURN OVER](3.3) STATA code and output for fitting the Cox proportional hazards model on the variables smoking and dietfat is the following: xi: stcox i. smoking dietfat, nolog i . smoking Ismoking_0-1 (naturally coded; _Ismoking_0 omitted) failure d: dead analysis time t: t Cox regression -- Breslow method for ties No. of subjects = 80 Number of obs 80 No. of failures = 58 Time at risk = 1257.07 LR chi2 (2) = 6.73 Log likelihood = -220.87645 Prob > chi2 0. 0346 t | Haz. Ratio Std. Err. Z P>IZI [95% Conf. Interval] Ismoking 1 | 1. 404309 . 4003418 1.19 0.234 8031583 2 . 45541 dietfat | 1. 337665 . 1657453 2.35 0. 019 1. 049248 1. 705363 (a) Is the variable dietfat significantly associated with the hazard of death for breast cancer patients? Ex- plain your answer by interpreting the hazard ratio and its 95% confidence interval. (2) (b) Does the hazard of death significantly differ between smokers and nonsmokers for breast cancer pa- tients? Explain your answer by interpreting the hazard ratio and its 95% confidence interval. (2) (c) Is dietfat a confounder for smoking? Explain your answer by interpreting the appropriate hazard ratio and its 95% confidence interval. (2)(3.4) STATA code and output for fitting the Cox proportional hazards model on the three variables smoking, age and dietfat is the following: xi: stcox i . smoking age dietfat, nolog i . smoking Ismoking 0-1 (naturally coded; _Ismoking_0 omitted) failure d: dead analysis time t: t Cox regression -- Breslow method for ties No. of subjects = 80 Number of obs 80 No. of failures = 58 Time at risk 1257.07 LR chi2 (3) 240.30 Log likelihood = -104. 09039 Prob > chil = 0. 0000 t | Haz. Ratio Std. Err. Z P>|ZI [95% Conf. Interval] Ismoking 1 | 6.195222 2.399872 4.71 0.000 2. 899499 13. 23704 age | 1 . 838246 . 1239863 9.03 0.000 1. 610615 2. 098049 dietfat | 10. 92422 3. 16937 8. 24 0.000 6.186391 19.29052 (a) Does the hazard of death significantly differ between smokers and nonsmokers for breast cancer pa- tients when smoking is adjusted for age and dietfat? Explain your answer by interpreting the hazard ratio and its 95% confidence interval. (2) (b) By how much times does the hazard of death for breast cancer increase when dietfat increases by one unit after adjusting for age? Show your calculations. (2) (c) Write down the Cox proportional hazards model with smoking, age and dietfat as predictor variables. (2)