Biost 536, Fall 2014
Homework #1
September 26, 2014, Page 1 of 5
Biost 536: Categorical Data Analysis in Epidemiology
Emerson, Fall 2014
Homework #1
September 26, 2014
Written problems: To be submitted as a MS-Word compatible file to the class Catalyst dropbox by 1:30
pm on Thursday, September 26, 2014. See the instructions for peer grading of the homework that are
posted on the web pages.
On this (as all homeworks) Stata / R code and unedited Stata / R output is TOTALLY
unacceptable. Instead, prepare a table of statistics gleaned from the Stata output. The table
should be appropriate for inclusion in a scientific report, with all statistics rounded to a
reasonable number of significant digits. (I am interested in how statistics are used to answer the
scientific question.)
In all problems requesting “statistical analyses” (either descriptive or inferential), you should
present both
 Methods: A brief sentence or paragraph describing the statistical methods you used.
This should be using wording suitable for a scientific journal, though it might be a
little more detailed. A reader should be able to reproduce your analysis. DO NOT
PROVIDE Stata OR R CODE.
 Inference: A paragraph providing full statistical inference in answer to the question.
Please see the supplementary document relating to “Reporting Associations” for
details.
Keys to past homeworks from quarters that I taught Biost 517 (e.g. HW #8 from 2012) or Biost
518 (e.g., HW #1 from 2014) or Biost 536 (e.g. HW #3 from 2013) might be consulted for the
presentation of inferential results. Note that the requirement to provide a paragraph describing
your statistical methods was new this year in Biost 518, and other past keys do not give explicit
examples of a separate paragraph. However, many past keys provide this information as an
introductory sentence.
All questions of treatment benefit relate to any benefit of idarubicin to more frequently induce complete
remission in patients with acute myelogenous leukemia (AML) relative to daunorubicin. The data can be
found on the class web page (follow the link to Datasets) in the file labeled leukemia.txt. Documentation
is in the file leukemia.doc. The data is in free-field format. The file initleuk.txt contains Stata and R code
that might be useful in
reading in the file.
In this homework, we are ultimately interested in inference for the primary endpoint (induction of
complete remission) by treatment and sex. We will ignore the sequential aspect of the clinical trial and
just analyze the data as if we had always planned on getting data on 130 subjects. We will use an intent to
treat approach that analyzes all subjects according to how they were randomized.
1. Provide suitable descriptive statistics for this dataset as might be presented in Table 1 of a
manuscript appearing in the medical literature.
Methods: Dichotomous variables were created for attainment of complete remission
(Complete Remission), status at follow-up (Alive at Follow-Up), and whether subjects
received a bone marrow transplant (Bone Marrow Transplant). Descriptive statistics are
restricted to the treatment arm of the study (Idarubicin), the control arm (Daunorubicin),
Biost 536, Fall 2014
Homework #1
September 26, 2014, Page 2 of 5
and finally presented overall. For continuous and ordered categorical variables (age,
French American British classification of acute myeloid leukemia (FAB classification of
AML), Karnofsky score, white blood cell count, platelet count, hemoglobin, chemotherapy
courses to complete remission, and observation time) we include the mean, standard
deviation, minimum and maximum. For binary variables (sex and indicators of complete
remission, status at follow up, and bone marrow transplant) we present percentages.
Results: Data is available on 130 subjects; however, data is missing on FAB AML Subtype
for 8 subjets on the daunorubicin arm and 4 subjects on the idarubicin arm. Additionally
one subject has missing data for white blood cell count, platelet count, and hemoglobin at
baseline in the daunorubicin arm. Since none of these covariates will be adjusted for in this
initial analysis, this won’t be an immediate problem but should we should take care to note
how this may affect further analyses.
This randomized control trial has 65 of the 130 subjects assigned to each arm. Gender is
fairly evenly distributed with males making up about 54% of the arm receiving
daunorubicin treatment and 46% of the idarubicin arm, age distribution was similarly
evenly distributed ranging from late teens to early 60s with subjects on the daunorubicin
arm having an average age of 40 and subjects on the idarubicin arm averaging 38 years of
age. Among indicators of health and outcomes, subjects on the daunorubicin arm tended to
have higher baseline white blood cell and platelet counts, subects on the idarubicin arm
had a higher proportion achieving complete remission (78-59%), a higher proportion were
alive at follow up (42-25%) and had a longer mean observation time (574-421).
Treatment Arm
Daunorubicin
Idarubicin
Total
N=65
N=65
N=130
Male (%)
53.8%
46.2%
50.0%
40(13.4; 19 38(12.5; 17 39(12.9; 17 Age (yrs)1
60)
61)
61)
FAB Classification of AML
3(1.5; 0 - 6)
3(1.5; 1 - 6)
3(1.5; 0 - 6)
Subtype1
80(12.6; 40 80(11.6; 30 80(12.1; 30 Karnofsky Score
100)
100)
100)
Baseline White Blood
43(55.0; 0.7 - 29(36.3; 0.4 36(46.9; 0.4 Cells (103/mm3)1
215)
154.1)
215)
Baseline Platelets
94(92.4;11 67(57.8; 11 80(77.8; 11 (103/mm3)1
457)
370)
457)
Baseline Hemoglobin
9.6(1.5; 6.4 9.2(1.8; 2.8 9.4(17; 2.8 1
(g/dl)
13.9)
13.7)
13.9)
Complete Remission (%)
58.5%
78.46%
68.5%
Chemotherapy Courses
to Complete Remission2
1.5(0.5; 1 - 2)
1.3(0.5; 1 - 2)
1.4(0.5;1 - 2)
24.6%
41.5%
33.1%
9.2%
12.3%
10.8%
Alive at Follow-Up (%)
Bone Marrow Transplant
(%)
Biost 536, Fall 2014
Homework #1
September 26, 2014, Page 3 of 5
Observation Time
421(322.2; 3 - 574(445.2; 9 - 497.5(394.6; 3 (Days)1
1848)
1800)
1848)
1 Summary statistics are of the form Mean(SD; Min-Max)
2This only applies to subjects achieving complete
remission, so the sample sizes are as follows: Daunorubicin
Arm=38, Idarubicin Arm=51, Total=89
2. Perform an analysis to assess whether subjects taking idarubicin have better primary
clinical outcomes than patients on daunorubicin.
Methods: The proportion of subjects achieving complete remission was compared
between groups receiving the idarubicin treatment and those receiving the
daunorubicin treatment. Because Wald-based statistics behave the worst at more
extreme proportions than were observed by treatment arm in table 1, I felt
comfortable using a chi-square test and taking a 95% confidence interval using
Wald-based statistics.
Results: The proportion of subjects on the idarubicin treatment arm that achieved
complete remission was .78 compared to .58 on the daunoribicin arm. The observed
20% absolute difference in remission is one that would not be surprising if the true
difference were between 4.4% and 35.6% with the idarubicin arm having the more
favorable outcomes. With a one sided chi-square p-value of 0.014, we can assert with
confidence that we can reject the null hypothesis of no difference in outcomes in
favor of the hypothesis that subjects taking idarubicin have more favorable clinical
outcomes.
3. Is the analysis of treatment effect confounded by sex? Provide your reasoning.
One would not expect there to be confounding by sex, as this is a randomized
control trial. We do see a higher proportion of males in the daunorubicin arm than
in the idarubicin arm but the difference in proportions is pretty small. In the
analyses that follow; however, we will see that males have worse remission rates
than females independent of treatment so the concern about confounding is nonnegligible.
4. Perform an analysis to assess any treatment benefit of idarubicin over daunorubicin
adjusted for sex.
Methods: Odds of achieving complete remission were compared between subjects
taking idarubicin and subjects taking daunorubicin using logistic regression holding
sex constant and allowing for unequal variances.
Results: Subjects, controlling for sex who took idarubicin were observed to have
odds of complete remission 2.5 times higher than those taking daunorubicin. This
observed odds ratio would not be surprising if the true odds ratio comparing
subjects in the treatment group and the control group were between 1.14 and 5.53.
With a one-sided p-value of 0.022 we can reject with confidence the hypothesis that
the odds of achieving complete remission do not differ between treatment arms
when holding sex constant.
Biost 536, Fall 2014
Homework #1
September 26, 2014, Page 4 of 5
5. Perform an analysis to assess whether males taking idarubicin have more frequent
complete remission than males taking daunorubicin.
Methods: Odds of achieving complete remission were compared between male
subjects taking idarubicin and subjects taking daunorubicin using logistic
regression allowing for unequal variances.
Results: Male subjects who took idarubicin were observed to have odds of complete
remission 2.5 times higher than those taking daunorubicin. This observed odds ratio
would not be surprising if the true odds ratio comparing subjects in the treatment
group and the control group were between 0.89 and 6.88. With a one-sided p-value
of 0.084 and a 95% confidence interval that includes an odds ratio of 1, we cannot
reject the hypothesis that the odds of achieving complete remission do not differ
between treatment arms for males.
6. Repeat problem 5 for females.
Methods: Odds of achieving complete remission were compared between female
subjects taking idarubicin and subjects taking daunorubicin using logistic
regression allowing for unequal variances.
Results: Female subjects who took idarubicin were observed to have odds of
complete remission 2.6 times higher than those taking daunorubicin. This observed
odds ratio would not be surprising if the true odds ratio comparing subjects in the
treatment group and the control group were between 0.75 and 8.77. With a onesided p-value of 0.131 and a 95% confidence interval that includes an odds ratio of
1, we cannot reject the hypothesis that the odds of achieving complete remission do
not differ between treatment arms for males.
7. Perform an analysis to assess whether any treatment benefit of idarubicin over
daunorubicin differs by sex.
Methods: Odds ratios of achieving complete remission between subjects taking
idarubicin and subjects taking daunorubicin were compared by sex using logistic
regression controlling for sex, including an interaction term, and allowing for
unequal variances.
Results: Male subjects who took idarubicin were observed to have odds ratios of
complete remission compared to their daunorubicin treated counterparts that was
4% less than the odds ratio comparing idarubicin and daunorubicin taking females.
This difference in odds ratios would not be surprising if the difference in odds ratio
for males was between one fifth (20%) that for females and 4.8 times larger than
that for females. With a one-sided p-value of 0.961 and a 95% confidence interval
that includes a no difference, we cannot reject the hypothesis that the treatment
effect of idarubicin compared to daunorubicin is the same between men and women.
8. Use the analysis you performed in problem 7 to answer the question of whether
idarubicin use is associated with more frequent induction of remission.
Using a logistic regression comparing odds of remission between subjects treated
with idarubicin and daunorubicin that controlled for sex and allowed for a
differential effect between men and women, we find an estimated odds ratio for
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Homework #1
September 26, 2014, Page 5 of 5
women of 2.57 that would not be atypical if the true odds ratio were between 0.75
and 8.81. Additionally, the estimated odds ratio for males of 2.47 could easily occur
if the true odds ratio were between 0.5 and 12.3. Given that these all contain the
null hypothesis of no difference, we cannot confidently say that idarubicin is
associated with more frequent induction of remission.
9. For each of the analysis models used in problems 4 and 7, provide estimates of the
probability of inducing a complete remission by all combinations of treatment group and
sex. How do these estimates compare to descriptive statistics for those groups?
Methods: Odds are simply p/(1-p) where p is the probability of event. To get
probabilities from odds we simply take the odds estimated by multiplying the
baseline odds (females on the daunoribicin arm) by whichever treatment or gender
effects apply and applying the interaction term for males for the model that employs
it and take the resulting odds/(1+odds).
Results: The table below shows the predicted probability of inducing a complete
remission by sex and treatment arm.
Probability of Remission
Idarubicin
Daunorubicin
Males
Females
Males
Females
Model Type
No Interaction
Interaction
0.702
0.700
0.855
0.857
0.484
0.476
0.702
0.700
Observed
0.700
0.857
0.486
0.700
Both the model that does not include interaction and the model that does include an
interaction term predict the clinical outcomes in the dataset reasonably well. Each is
within 1% absolute difference from the observed probabilities of remission.
10. Which of the above analyses should be used to decide whether idarubicin should be
approved for the indication of AML? What problems exist with the use of the other
analyses you performed?
If I were asked to perform a single analysis to determine whether idarubicin should
be used for AML I would have used the analysis that controls for sex. As mentioned
before, we have different proportions of males and females in each arm with a
difference in baseline remission rates that would make the uncontrolled model
susceptible to confounding. In addition, without performing any statistical analyses
beyond summary statistics, we can see a substantial difference in treatment effects.
Ignoring this would be scientifically dishonest and would lead to reporting an
aggregate effect that we cannot confidently state is uniform between sexes.