The document describes a hypothetical study examining the effect of maternal exposure to the 9/11 attacks on low birthweight. The study included 3,360 women in NYC who gave birth from 2001-2010. Exposure data and birth outcome data were collected. Several analyses were conducted: 1) A logistic regression found maternal exposure was associated with low birthweight (OR 1.35). 2) An interaction model found the effect of exposure on low birthweight was stronger for births within 2 years of 9/11 (OR 2.29) compared to later births (OR 1.09). 3) Stratification by birth period found significant effect modification. 4) Separate analyses by birth period found a significant association of exposure with low birthweight for

1. BS835 Class 6 HW exercises
Questions 1 and 2 are from the in-class exercises
(Hypothetical data based broadly on Maslow et.al.,
Reproductive Outcomes Following Maternal Exposure to the
Events of September 11, 2001, at the World Trade Center, in
New York City, AJPH.) To determine the effect of exposure to
the events of 9/11 (including both environmental exposures and
stress-related exposures), exposure data was collected on
n=3,360 women who gave birth to a singleton child in NYC
between Oct. 2001 and December 2010. We will look at any
exposure (categorized as exposed vs. not exposed; the study
looked at different types of exposures as well), and focus on
low birthweight as the adverse outcome potentially related to
exposure. We expect the effect of exposure to be stronger for
babies born in the two years following 9/11, and so we are
interested in potential effect modification.
Hypothetical data are saved in the file ‘WTC Births.xlsx’.
Variables in the data set are:
1) idnum, a study ID number
2) momage, mother’s age at 9/11, categorized and coded as 1
for those under 30 years, 2 for those aged 30 to 35 years, and 3
for those older than 35
3) college, maternal education coded 1 for those with a 4 year
college degree, 0 for those with less than a college degree
4) earlyperiod, coded 1 for births that occurred within 2 years
of 9/11, and 0 for those that occurred more than 2 years after
9/11
5) exposure, maternal exposure to the events from 9/11
6) LBW, low birthweight, coded 1 for infants weighing less than
2,000 grams, 0 for those weighing 2,000 grams or more.

2. Question 1. Our broad research question is whether a woman’s
exposure to the events of 9/11 had an adverse effect on the
outcome of her pregnancy.
As a preliminary check on the data, 5.2% of the mom’s in the
study had a low birthweight infant.
As a first analysis, fit a multiple logistic regression model with
low birthweight as the outcome variable and exposure, time
period (the earlyperiod variable), maternal age, and maternal
education as predictors. I’ve summarized results in the
following table (you can check to see that your results match
the results in the table):
Variable
aOR
95% CI
Exposed to events of 9/11
Birth within 2 yrs of 9/11
Maternal age
<30 yrs
30 – 35 yrs
>35 yrs
College degree
1.35
1.15
Ref
0.90
0.82
0.43
0.99, 1.84
0.82, 1.61
--

3. 0.62, 1.29
0.53, 1.27
0.31, 0.58
Run a Hosmer-Lemeshow test to check on the fit of the model,
and interpret the results of this Hosmer-Lemeshow test.
Discuss these findings for the exposure variable – was there an
effect of exposure on low birthweight? Explain.
Question 2. The study sample included births from the 10 years
following 9/11. The investigators believe that the effect of
exposure would be strong for women pregnant at the time of
9/11 or shortly after, but that the effect of exposure may weaken
over time. To investigate, run a model including the covariates
from Question 1, but adding an interaction term between
exposure and the ‘earlyperiod’ (birth within 2 years of 9/11)
variable.
Results from the interaction model are given in the table below
(Note this table asks for slopes, not odds ratios).
Check these results using the SAS or R code given
below:
Results of a logistic regression interaction model predicting low
birthweight
Variable

4. Slope
p-value
for slope
Intercept
Exposed to events of 9/11
Birth within 2 yrs of 9/11
Exposure x Birth within 2 yrs
Maternal age
<30 yrs
30 – 35 yrs
>35 yrs
College degree
-2.360
0.083
-0.227
0.747
Ref
-0.108
-0.196
-0.845
<0.001
0.663
0.376
0.035
--
0.561
0.377
<0.001
The table below focuses on the effect of exposure, during the

5. early period and during the late period for the study (effect
modification of the effect of exposure by time), from the above
interaction model. See the SAS and R code below. While
results age given by R and SAS
, I think you can calculate the two odds ratios by hand
(with a calculator) from the slopes above – check these
calculations. I think we need to use the computer to get the
confidence intervals for these odds ratios.
Effect of exposure to the events of 9/11 on low birthweight, by
time period of delivery
Time Period
aOR
95% CI for aOR
Birth within 2 years of 9/11
2.29
1.28, 4.12
Birth more than 2 years after 9/11
1.09
0.75, 1.58
Is there effect modification here? Explain (address significance
as well as size of the effect).
Some SAS and R help follow:
SAS code for the interaction model in Question 2
proclogistic;
class momage (ref='1') / param=ref;
model lowBW (event='1') = exposure earlyperiod

6. exposure*earlyperiod
momage college;
estimate 'Exposure OR early period' exposure
1 exposure*earlyperiod
1
/ exp cl;
estimate 'Exposure OR late period' exposure
1 exposure*earlyperiod
0
/ exp cl;
run;
R code for the interaction model in Question 2
# for later period (earlyperiod = 0)
log.out <- glm(lowBW ~ exposure + earlyperiod +
exposure:earlyperiod +
relevel(factor(momage),ref='1') +
college,family=binomial(link='logit') )
summary(log.out)
exp(coef(log.out))
exp(confint(log.out))
# For contrasts of exposure and interaction terms load
‘multcomp’ package
# R gives slopes and standard error for the early and late effects
# need to convert to ORs and CIs ‘by hand’
library(multcomp)
exp.early <- matrix(c(0,1,0,0,0,0,1),1)
summary(glht(log.out, linfct=exp.early))

7. exp.late <- matrix(c(0,1,0,0,0,0,0),1)
summary(glht(log.out, linfct=exp.late))
Question 3. We can also test for effect modification through
classical epidemiologic stratification methods, although these
methods don’t allow for controlling for other variables. I used
the Mantel-Haenszel stratification methods (see Class 4
homework, using ‘proc freq’ in SAS and ‘epi.2by2’ in R) to
examine the association between exposure to the events of 9/11
and low-birthweight, controlling for (stratifying by) the
earlyperiod variable. Results are given below:
Results: From SAS, the Breslow-Day test gives chi-square (1
df) of 4.83, p=0.028.
The stratified results for the effect of exposure on low
birthweight were
Early Period: OR = 2.32 (1.30, 4.16)
Late Period: OR = 1.08 (0.74, 1.56).
From R, the Woolf’s test (labeled ‘M-H test of homogeneity of
ORs) gives chi-square (1 df) 4.67, p=0.030.
The stratified results were:
Early Period: OR = 2.31 (1.30, 4.22)
Late Period: OR = 1.08 (0.74, 1.56)
Is there significant evidence of effect modification? Explain.
SAS code:
procfreq; table earlyperiod*exposure*lowBW / all;
run;
R code:
# M-H analysis

8. epi.2by2(tab.out,method='cohort.count')
# stratified results
oddsratio(table(exposure[earlyperiod==0],lowBW[earlyperiod=
=0]))
oddsratio(table(exposure[earlyperiod==1],lowBW[earlyperiod=
=1]))
Question 4. (I’ve done the computer work and summarized
results in the table below. SAS code and R code that I used is
given at the end of the question.) Significant effect
modification indicates that the association of interest is
different for different subgroups in the study. So, when there is
significant interaction, another way to account for the
interaction is to run separate analyses for the different
subgroups. One nice consequence of this approach is that it
avoids presenting results from interaction models (which can be
more complicated to present).
Run two logistic regressions (I’ve done this, see table), one for
mothers who gave birth within 2 years of 9/11 (earlyperiod=1),
the other for mothers who gave birth after 2 years from 9/11.
Both regressions should predict low birthweight from exposure,
mom’s age, and mom’s college education. (Note that
‘earlyperiod’ and the interaction term are not included in these
models, since the analysis is being done stratified by
earlyperiod.) Some SAS and R help is given below.
Results are summarized in the following table:
Results of separate logistic regressions predicting low-

9. birthweight, for women giving birth within 2 years of 9/11 and
for women giving birth more than 2 years after 9/11
Birth within 2 years of 9/11
(n=840)
Birth more than 2 years after 9/11
(n=2520)
Variable
aOR
95% CI
aOR
95% CI
Exposed to events of 9/11
Maternal age
<30 yrs
30 – 35 yrs
>35 yrs
College degree
2.30
Ref
0.72
0.82
0.44
1.29, 4.19
--
0.37, 1.42
0.36, 1.77
0.25, 0.79
1.09
Ref
0.98
0.83
0.42

10. 0.74, 1.57
--
0.64, 1.54
0.49, 1.40
0.29, 0.61
Based on these analyses, describe the effect of exposure, for
mothers giving birth either within 2 years or after 2 years from
9/11.
SAS code and R code are below.
Some SAS help:
There are several ways to run a sub-group analysis in SAS. I’ll
use the ‘where’ statement, which can be used with most procs,
to restrict the analysis to a subgroup.
title ‘Analysis for births within 2 years of 9/11’;
proclogistic; where earlyperiod=1;
class momage (ref='1') / param=ref;
model lowBW (event='1') = exposure momage college;
run;
title ‘Analysis for births after 2 years of 9/11’;
proclogistic; where earlyperiod=0;
class momage (ref='1') / param=ref;
model lowBW (event='1') = exposure momage college;
run;
The ‘where’ statement restricts an analysis to the subset of

11. subjects who satisfy the stated condition.
Some R help:
There are several ways to run a sub-group analysis in R. I’ll
use what I think of as a ‘select if’ statement, parallel to the
‘where’ statement in SAS. R uses square brackets following a
variable name to indicate that only subjects who satisfy the
condition in the square brackets should be included in the
analysis. One somewhat awkward consequence of this is that
the square brackets need to be included with every variable
referenced in the procedure.
log.out1 <- glm(lowBW[earlyperiod==1] ~
exposure[earlyperiod==1] +
relevel(factor(momage[earlyperiod==1]),ref='1') +
college[earlyperiod==1],
family=binomial(link='logit') )
summary(log.out1)
exp(coef(log.out1))
exp(confint(log.out1))
log.out0 <- glm(lowBW[earlyperiod==0] ~
exposure[earlyperiod==0] +
relevel(factor(momage[earlyperiod==0]),ref='1') +
college[earlyperiod==0],
family=binomial(link='logit') )
summary(log.out0)
exp(coef(log.out0))
exp(confint(log.out0))Note that two equal signs, ‘==’ are
needed to specify an equality in the ‘select if’ statement in the
square brackets.