hw9key - BIOST/EPI 513 Spring Quarter 2011 Dr. McKnight...

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Unformatted text preview: BIOST/EPI 513 Spring Quarter 2011 Dr. McKnight HOMEWORK 9 KEY See Appendix I for STATA commands and Appendix II for output. 1. (a) O Kaplan-Meier survival estimates 0- ‘ W LO [\I _ O O LQ _ 0 L0 (\i _ O O Q _ O _|—|—i—i—i_ O 200 400 600 800 Days since beginning of follow up rx = Placebo rx = ZDV Figure l. Kaplan-Meier survival curves for the two treatment groups. The ZDV group appears to have a better prognosis. (b) Test statistic: 5.48 Reference distribution: Chi-squared distribution with 1 df P-Value: 0.019 Reject the null hypothesis of no treatment difference in disease progression. (C) 0.51 (95% CI: 0.29-0.91) (d) Test statistic: -2.30 Reference distribution: standard Normal distribution P-value: 0.022 Reject the null hypothesis of no treatment difference in disease progression. (6) Test statistic: 5.66 Reference distribution: Chi-squared distribution with 1 df P-value: 0.017 Reject the null hypothesis of no treatment difference in disease progression. (0 There was strong evidence that treatment was associated with abated disease progression. The relative risk comparing ZDV to placebo was 0.51 (95% CI: 0.29-0.91; P = 0.02). 2. Using the data in actg019.dta, examine the effect of adjusting the treatment comparison for baseline CD4 count. (81) 0.46 (95% CI: 0.26-0.81) (b) Test statistic: -2.68 Reference distribution: standard Normal distribution P-value: 0.007 Reject the null hypothesis of no adjusted treatment difference in disease progression. (0) There was strong evidence that treatment was associated with abated disease progression. Adjusted for CD4 count, the relative risk comparing ZDV to placebo was 0.46 (95% CI: 0.26-0.81, P = 0.007). (Note: it would also be valid to present the unadjusted hazard ratio and P-value). (d) Test statistic: -5.3l Reference distribution: standard Normal distribution P-Value: <0.00l Reject the null hypothesis of no association between baseline CD4 and disease progression after adjusting for treatment. (6) The estimated hazard ratio obtained in part (a) of this question (0.46) is farther from 1, because this model included a precision variable that is strongly associated with the outcome. (1) Est. coef. SE Unadjusted model -0.671 0.292 Adjusted model -0.785 0.293 The estimated coefficient from the adjusted model has a slightly higher standard error due to the addition of a precision variable that is strongly associated with the outcome. (g) The P-value in part (b) of this question is smaller, because including a precision variable that is strongly associated with the outcome increased the power of the test of whether the coefficient is zero. (a) Table 1. Summary of disease progression by CD4 group. 0-199 200-399 400-500 I Total Not progressed 87 469 268 I 824 Progressed 22 24 9 55 Total 109 493 277 879 % progressed 20.2% 4.9% 3.3% I 6.3% 3 (b) (C) (d) 0.459 (95% Cl: 0.258-0.815) 0.456 (95% CI: 0.257-0.810) i. The adjusted hazard ratio comparing ZDV to placebo can be obtained via exponentiation of the coefficient of interest using both methods. Estimates and confidence intervals for the hazard ratio based on these two types of adjustment are virtually identical for these data. ii. The baseline hazard function is allowed to differ across strata of the adjustment variable under true stratification adjustment, whereas under dummy variable adjustment, the baseline hazard function is constrained to be the same across all strata of the adjustment variable. iii. In general, my preference would depend on my background knowledge of the adjustment variable. If I had reason to believe the strata have baseline survival curves that do not have parallel relationships, then I would choose a stratified model for its flexibility. ***************************Appendix I: commands**************************** *** Useful commands: stset <timevar> <censorvar> (declares data to be survival—time data) * stci, by(<groupvar>) (gives 95% CI for median survival time for each group) * sts test <groupvar> (performs the log rank test) * stcox <groupvar> (performs Cox regression) * stcox <groupvar>, strata(<var>) (performs stratified Cox regression) * change working directory to where you save the data ** Ql: Association between treatment and disease progression stset days cens sts graph, by(rx) sts test rx stcox rx test rx stcox rx ** Q2: Adjusted association between treatment and disease progression stcox rx cd4 stcox rx, nohr stcox rx cd4, nohr capture drop cd4group egen cd4group = cut(cd4), at (O, 200, 400, 600) tab cd4group cens, row ** Q3: Dummy variable and true stratification adjustment stcox rx i.cd4group stcox rx, strata(cd4group) ****************************Appendix output ***************************** l. failur v nt: c ns 1— 0 & c ns < obs. time interval: (0, days] exit on or before: failure 880 total obs. 0 exclusions 880 obs. remaining, representing 55 failures in single record/single failure data 354872 total analysis time at risk, at risk from t = O earliest observed entry t = 0 last observed exit t = 746 failure d: cens analysis :ime t: days Log—rank tes: for equality of survivor functions \ Events Events rx \ observed expected _ _ _ _ _ _ __+_________________________ Placebo \ 38 29 36 ZDV \ 17 25 64 _ _ _ _ _ _ __+_________________________ Total \ 55 55 00 chi2(l) = 5.48 Pr>chi2 = 0.0192 failure d: cens analysis time t: days Cox regression —— Breslow method for ties No. of subjects 2 880 Number of obs = 880 No. of failures = 55 r‘ime at risk 2 354872 LR chi2(l) = 5.66 Jog likelihood = —328.57534 Prob > chi2 = 0.0174 _t | Haz. Ratio Std. Err. z P>\z\ [95% Conf. Interval] _ _ _ _ _ _ _ _ _ _ _ __+________________________________________________________________ rx | .5109554 .1493189 —2.30 0.022 .2881592 .9060112 2. Cox regression —— Breslow method for ties No. of subjects = 880 Number of obs = 880 No. of failures 2 55 r‘ime at risk = 354872 LR chi2(2) = 34.46 Jog likelihood = —3l4.l7559 Prob > chi2 = 0.0000 it | Haz Ratio Std er z P>\z\ [95% Conf Interval] _ _ _ _ _ _ _ _ _ _ _ __+________________________________________________________________ rx | .456067l .l3365l2 —2.68 0.007 .2567927 .8099809 cd4 | .9934464 .0012295 —5.3l 0.000 .9910395 .9958591 Cox regression —— Breslow method for ties No. of subjects 2 880 Number of obs = 880 No. of failures = 55 r‘ime at risk 2 354872 LR chi2(1) = 5.66 Jog likelihood = —328.57534 Prob > chi2 = 0.0174 _t | Coef. Std. Err. z P>]z] [95% Conf. Interval] _ _ _ _ _ _ _ _ _ _ _ __+________________________________________________________________ rx | —.6714729 .2922346 —2 30 0 022 —1.244242 —.O987036 Cox regression —— Breslow method for ties No. of subjects = 880 Number of obs = 880 No. of failures 2 55 r‘ime at risk = 354872 LR chi2(2) = 34.46 Jog likelihood = —314.l7559 Prob > chi2 = 0.0000 it | Coef Std Err z P>]z] [95% Conf Interval] _ _ _ _ _ _ _ _ _ _ _ __+________________________________________________________________ rx | —.7851153 .2930517 —2.68 0.007 —1.359486 —.2107446 cd1 | —.0065752 .0012376 —5.31 0.000 —.0090009 —.0041495 Event Indicator cd4group Censored AIDS/Beat Total 0 87 22 109 79 82 20.18 100 00 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __+__________ 200 469 24 493 95 13 4 87 100 00 400 268 9 277 96 75 3.25 100 00 Total 824 55 879 93 74 6 26 100 00 3. Cox regression —— Breslow method for ties No. of subjects 2 879 Number of obs = 879 No. of failures = 55 r‘ime at risk 2 354172 LR chi2(3) = 36.50 Jog likelihood 2 —313.0085 Prob > chi2 = 0.0000 _t | Haz. Ratio Std. Err. z P>]z] [95% Conf. Interval] _ _ _ _ _ _ _ _ _ _ _ __+________________________________________________________________ rx | .4588707 .134435 —2.66 0.008 .2584131 .8148285 | cd4group | 200 | .2161258 .0641403 —5.16 0.000 .1208072 .386652 400 | .1446965 .0575267 —4.86 0.000 .0663816 .3154049 Stratified Cox regr. —— no ties No. of subjects 2 880 Number of obs = 879 No. of failures = 55 r‘ime at risk 2 354872 LR chi2(1) = 7.73 Jog likelihood = —256.32572 Prob > Chi2 = 0.0054 _t | Haz. Ratio Std. Err. z P>lzl [95% Conf. Interval] _ _ _ _ _ _ _ _ _ _ _ __+________________________________________________________________ rx | .4560441 .1337879 —2.68 0.007 .2566215 .8104396 Stratified by Cd4group ...
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hw9key - BIOST/EPI 513 Spring Quarter 2011 Dr. McKnight...

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