San Diego City College Statistics Worksheet

DescriptionPM 510 Homework 13 (Week 14)
Problems marked with [SPSS] are intended to be done with SPSS. For these problems, please
provide the edited output Word document.
1. A clinical trial was conducted to test the efficacy of different vitamin supplements in
preventing visual loss in patients with retinitis pigmentosa. Visual loss was measured by loss
of retinal function as characterized by a 50% decline in the electrical activity in the retina.
Patients were randomized to 15,000 IU of vitamin A or 75 IU of vitamin A. Patients were
enrolled in 1984-87 and follow-up was terminated in September 1991. Failure was defined as
visual loss. ”Censored” was defined as dropouts due to death, other disease, side effects
possibly due to the study medications, or unwillingness to comply.
15,000 IU of vitamin A
t
Dt
Ct
Rt
0
0
0
172
1
3
4
172
2
6
0
165
3
15
1
159
4
21
26
143
5
15
35
96
6
5
41
46
t
0
1
2
3
4
5
6
75 IU of vitamin A
Dt
Ct
0
0
8
0
13
3
21
2
21
28
13
31
13
29
Rt
182
182
174
158
135
86
42
t = time in years
Dt = number of deaths during year t
Ct = number of censored during year t
Rt = number surviving to beginning of interval t
The following life tables for each treatment group contain the probability of dying and
surviving in each interval, and the cumulative probability of survival.
Qt = probability of dying in interval t = Dt / Qt
1 – Qt = probability of surviving in interval t
̂( ) = cumulative probability of surviving in interval t = ̂( − 1) * (1 – Qt)
15,000 IU of vitamin A
Dt
Ct
Rt
t
0
0
0
172
1
3
4
172
2
6
0
165
3
15
1
159
4
21
26
143
5
15
35
96
6
5
41
46
Qt
1 – Qt
0.000
0.017
0.036
0.094
0.147
0.156
0.109
1.000
0.983
0.964
0.906
0.853
0.844
0.891
̂( )
1.000
0.983
0.947
0.858
0.732
0.617
0.550
t
0
1
2
3
4
5
6
75 IU of vitamin A
Dt
Ct
0
0
8
0
13
3
21
2
21
28
13
31
13
29
Rt
182
182
174
158
135
86
42
Qt
1 – Qt
0.000
0.044
0.075
0.133
0.156
0.151
0.310
1.000
0.956
0.925
0.867
0.844
0.849
0.690
̂( )
1.000
0.956
0.885
0.767
0.648
0.550
0.380
(a) What are ̂(2), the estimated probability of survival at 2 months for each treatment group? What
about ̂(4)? and ̂(6)?
(b) Below is the Kaplan-Meier curve for each treatment group. What is the median survival
for each group?
(c) How would you test if there is a difference in the time to visual loss in patients receiving
15,000 IU of Vitamin A vs those receiving 75 IU of Vitamin A. State the null and
alternative hypothesis and name the test statistic.
2. [SPSS] In the 1980s, a study was conducted to examine the effects of the drug ganciclovir on
AIDS patients suffering from disseminated cytomegalovirus infection. Two groups of patients
were followed; 18 were treated with the drug and 11 were not. The results of this study are
contained in the data set cyto.sav. Survival time in months after diagnosis are saved under
the variable name time, and indicators of censoring status—where 0 designates that an
observation was censored and 1 that a death occurred—under the name censor. Values of
treatment group, where 1 indicates that a patient took the drug and 2 that he or she did not, are
saved under the name group.
(a) Construct Kaplan-Meier curves for each group based on the product-limit estimate.
(b) Does it appear that individuals in one group survive longer than those in the other group?
Is there any indication of non-proportional hazards?
(c) Test the null hypothesis that the distributions of death times are identical in the two
treatment groups using the Log-rank test. What do you conclude?
(d) Estimate the hazard ratio for ganciclovir vs. placebo and give a 95% confidence interval
for the population hazard ratio.
3. Answer the following questions from the Gamis, et al., JCO paper.
(a) Consider the Kaplan-Meier curves in Figure 2 on pg. 3028 and focus on the EFS (eventfree survival) curves.
i) Which two panels show evidence of non-proportional hazards?
ii) Estimate the median EFS for the GO patients in each of the four analyses (Panels AD).
(b) Consider Table 3 on p. 3027 and focus on the “Outcomes from Study Entry” section.
i) Compare the estimated EFS hazard ratios and p-values for GO vs. no-GO patients for
low-risk patients and for intermediate-risk patients. Which set of patients shows a
greater estimated difference between the GO and no-GO patients? Which test is
statistically significant at the α = 0.10 level? Is there any discrepancy when you compare
the p-values instead of the estimated hazard ratios? If you answered yes, can you explain
the apparent discrepancy?

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