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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 KaplanMeier 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. KaplanMeier survival curves for the two treatment groups. The ZDV group appears to have a better prognosis. (b) Test statistic: 5.48
Reference distribution: Chisquared distribution with 1 df PValue: 0.019
Reject the null hypothesis of no treatment difference in disease progression. (C) 0.51 (95% CI: 0.290.91) (d) Test statistic: 2.30
Reference distribution: standard Normal distribution Pvalue: 0.022
Reject the null hypothesis of no treatment difference in disease progression. (6) Test statistic: 5.66 Reference distribution: Chisquared distribution with 1 df
Pvalue: 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: 0.290.91; 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: 0.260.81) (b) Test statistic: 2.68
Reference distribution: standard Normal distribution Pvalue: 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:
0.260.81, P = 0.007). (Note: it would also be valid to present the unadjusted hazard ratio
and Pvalue). (d) Test statistic: 5.3l Reference distribution: standard Normal distribution PValue: <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 Pvalue 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.
0199 200399 400500 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: 0.2580.815) 0.456 (95% CI: 0.2570.810) 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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 Spring '11
 BarbaraMc.Knight

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