Biost 536, Fall 2014
Homework #1
September 26, 2014, Page 1 of 4
Biost 536: Categorical Data Analysis in Epidemiology
Emerson, Fall 2014
Homework #1
September 26, 2014
Student # 1704
1. Provide suitable descriptive statistics for this dataset as might be presented in Table 1 of a manuscript
appearing in the medical literature.
Methods: I created the following table to provide descriptive statistics for patients categorized by treatment
with either daunorubicin or idarubicin. Relevant variables include demographic factors, classification of
disease into subtypes, and measurements of disease severity and patient condition.
Results: There were 65 patients treated with daunorubicin and 65 patients treated with idarubicin.
Measurements of FAB were missing for 12 patients, and an additional patient was omitted from analysis due to
an improbable FAB value of 0. One patient was missing data on baseline white blood cells, one patient was
missing data on baseline platelets, and one patient was missing data on baseline hemoglobin. Patients on
daunorubicin had trends toward higher baseline white blood cells and platelets.
Descriptive
Statistics
Daunorubicin
Idarubicin
All patients
Mean (SD: Min Mdn Max; n)
Mean (SD: Min Mdn Max; n)
Mean (SD: Min Mdn Max; n)
n (%)
n (%)
n (%)
39.8 (13.4; 19, 40, 60; n=65)
38.0 (12.5; 17, 36, 61; n=65)
38.9 (12.9; 17, 37 , 61 ;n= 130)
Female
30 (46%)
35 (54%)
65 (50%)
Male
35 (54%)
30 (46%)
65 (50%)
3.3 (1.4; 1, 3, 6; n=56)
2.9 (1.5; 1, 3, 6; n=61)
3.1 (1.5; 1, 3, 6; n=117)
1
6 (11%)
13 (21%)
19 (16%)
2
15 (27%)
15 (25%)
30 (25%)
3
9 (16%)
11 (18%)
20 (17%)
4
12 (21%)
8 (13%)
20 (17%)
5
13 (23%)
12 (20%)
25 (21%)
6
1 (2%)
2 (3%)
3 (3%)
8*
4
12*
79.5 (12.6; 40, 80, 100; n=65)
79.5 (11.6; 30, 80, 100; n=65)
79.5 (12.1; 30, 80, 100; n=130)
43.3 (55.0; 0.7, 16.7, 215; n=64)
29.0 (36.3; 0.4, 11.8, 154.1; n=65)
36.1 (46.9; 0.4, 13.8, 215; n=129)
Age (years)
Sex
FAB classification
Missing
Karnovsky score
Baseline white
blood cellsA
B
Baseline platelets
93.6 (92.4; 11, 62, 457; n=64)
66.6 (57.8; 11, 50, 370; n=65)
Baseline
hemoglobin C
9.6 (1.5; 6.4, 9.5, 13.9; n=64)
9.2 (1.8; 2.8, 9.2, 13.7; n=65)
*In addition to the 12 missing values for FAB, one implausible value of 0 for FAB in the
daunorubicin group was omitted.
A
One person in the daunorubicin group was missing data on baseline white blood cells.
B
One person in the daunorubicin group was missing data on baseline platelets.
C
One person in the hemoglobin group was missing data on baseline hemoglobin.
80.0 (77.8; 11, 57, 457; n=129)
9.4 (1.7; 2.8, 9.3, 13.9; n=129)
Biost 536, Fall 2014
Homework #1
September 26, 2014, Page 2 of 4
2. Perform an analysis to assess whether subjects taking idarubicin have better primary clinical outcomes
than patients on daunorubicin.
Methods: I used an unadjusted logistic regression model to assess the association of complete remission and
treatment. Both treatment (idarubicin vs. daunorubicin) and complete remission (yes vs. no) were binary
variables.
Results: There was evidence that patients taking idarubicin had better primary clinical outcomes than patients
taking daunorubicin (two-sided p=0.016). Those taking idarubicin were 2.59 times as likely to go into
complete remission than those taking daunorubicin. Based on a 95% confidence interval, I found that the
precision of the study was such that the result would not be unusual if the odds ratio of complete remission in
the idarubicin group as compared to the daunorubicin group ranged between 1.20 and 5.59.
3. Is the analysis of treatment effect confounded by sex? Provide your reasoning.
Methods: I assessed whether confounding was possible in this study design. In order to be a confounder, the
causal model must include an association between the potential confounding factor (PCF) and the exposure
(treatment), as well as the PCF and the outcome (complete remission), with the additional condition that the
PCF cannot be in the causal pathway.
Results: This is a randomized clinical trial, and so there should not be an association between sex and the
treatment, which is necessary for confounding to be present. Table 1 shows relatively balanced sex
distribution between the daunorubicin and idarubicin groups, so there is no evidence that randomization failed.
4. Perform an analysis to assess any treatment benefit of idarubicin over daunorubicin adjusted for sex.
Methods: I used a logistic regression model to assess the association of complete remission and treatment
adjusted for sex. Treatment (idarubicin vs. daunorubicin), complete remission (yes vs. no), and sex (male vs.
female) were binary variables.
Results: There was evidence that patients taking idarubicin have better primary clinical outcomes than patients
taking daunorubicin, after adjustment for sex (two-sided p=0.016). Those taking idarubicin were 2.59 times as
likely to go into complete remission than those taking daunorubicin. Based on a 95% confidence interval, I
found that the precision of the study was such that the result would not be unusual if the odds ratio of complete
remission in the idarubicin group as compared to the daunorubicin group, adjusted for sex, ranged between
1.20 and 5.60.
5. Perform an analysis to assess whether males taking idarubicin have more frequent complete remission
than males taking daunorubicin.
Methods: I used a logistic regression model to assess the association of complete remission and treatment in
males. Treatment (idarubicin vs. daunorubicin) and complete remission (yes vs. no) were binary variables.
Results: There was not strong evidence that male patients taking idarubicin had better primary clinical
outcomes than male patients taking daunorubicin (two-sided p=0.084). Males who took idarubicin were 2.47
times as likely to go into complete remission as males taking daunorubicin; however, based on a 95%
confidence interval, I found that the precision of the study was such that the result would not be unusual if the
odds ratio of complete remission in the idarubicin group as compared to the daunorubicin group ranged
between 0.89 and 6.88. Since I was limiting analysis to males, the sample size was smaller, which made the
confidence interval less precise.
6. Repeat problem 5 for females.
Methods: I used a logistic regression model to assess the association of complete remission and treatment in
females. Treatment (idarubicin vs. daunorubicin) and complete remission (yes vs. no) were binary variables.
Results: There was not strong evidence that female patients taking idarubicin had better primary clinical
outcomes than female patients taking daunorubicin (two-sided p=0.084). Females taking idarubicin were 2.57
times as likely to go into complete remission as females taking daunorubicin; however, based on a 95%
Biost 536, Fall 2014
Homework #1
September 26, 2014, Page 3 of 4
confidence interval, I found that the precision of the study was such that the result would not be unusual if the
odds ratio of complete remission in the idarubicin group as compared to the daunorubicin group ranged
between 0.75 and 8.77. Since I was limiting analysis to females, the sample size was smaller, which made the
confidence interval less precise.
7. Perform an analysis to assess whether any treatment benefit of idarubicin over daunorubicin differs by
sex.
Methods: I used a logistic regression model with an interaction term for sex and treatment to assess whether
the treatment benefit of idarubicin over daunorubicin differed by sex. I used the p-value for the interaction
term to test the null hypothesis of no interaction. Treatment (idarubicin vs. daunorubicin), complete remission
(yes vs. no), and sex (male vs. female) were binary variables.
Results: There was not evidence that the treatment benefit of idarubicin over daunorubicin differed by sex (p
for interaction=0.961). Since I was considering the treatment benefit separately for males and females, the
sample sizes were smaller. This lowered the precision, which could have been the reason for not seeing an
interaction, or there truly may have been no interaction effect.
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.
Methods: In order to test the null hypothesis of no effect of treatment on complete remission, I performed an ftest, using a logistic regression model with an interaction term for sex and treatment. Treatment (idarubicin vs.
daunorubicin), complete remission (yes vs. no), and sex (male vs. female) were binary variables.
Results: There was evidence that patients taking idarubicin had better primary clinical outcomes than patients
taking daunorubicin after accounting for potential effect modification by sex (p=0.016).
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: I used the adjusted logistic regression model (from question 4) and the logistic regression model with
an interaction term (from question 7) to estimate the probability of inducing a complete remission for all
combinations of sex and treatment group. I got the coefficients for these models using a statistical analysis
package and then had to plug these numbers into the appropriate model for the given treatment and sex groups.
Because I had used logistic regression, I then had to convert odds to probability.
Results: The estimates for the adjusted model were the same as those for the descriptive statistics for females in
both treatment groups and males who took idarubicin (at least with the two significant digits I presented).
Males using daunorubicin were very similar, with a 48% probability of complete remission in the adjusted
model and a 49% probability of complete remission in the descriptive statistics. The estimates from the
interaction model were the same as the descriptive statistics for all combinations of sex and treatment.
Descriptive Statistics for Probability of Complete Remission
Daunorubicin
Idarubicin
Count (percent)
Count (percent)
Males
17 (49%)
21 (70%)
Females
21 (70%)
30 (86%)
Probability of Complete Remission
Adjustment Model (Question 4)
Daunorubicin
Idarubicin
Males
48%
70%
Females
70%
86%
Biost 536, Fall 2014
Homework #1
September 26, 2014, Page 4 of 4
Probability of Complete Remission
Interaction Model (Question 7)
Daunorubicin
Idarubicin
Males
49%
70%
Females
70%
86%
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?
The appropriate model is the crude model without a term for adjustment or interaction, used in problem 2. As
stated in problem 3, this is a randomized clinical trial, and so there should not be an association between sex and
the treatment, which is necessary for confounding to be present. Table 1 shows relatively balanced sex
distribution between the daunorubicin and idarubicin groups, so there is no evidence that randomization failed.
Therefore, a sex-adjusted model is not appropriate. In order for an interaction term to be warranted, there
would need to be an a priori hypothesis that the effect of treatment on complete remission is biologically
different between men and women. I do not believe this is likely, and so a model with an interaction term is not
appropriate.