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 â€˜WTC Births.xlsxâ€™. Variables in the data set are:
1) idnum, a study ID number
2) momage, motherâ€™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.
Question 1. Our broad research question is whether a womanâ€™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 momâ€™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. Iâ€™ve summarized results in the following table (you can check to see that your results match the results in the table):
|Exposed to events of 9/11
Birth within 2 yrs of 9/11
30 â€“ 35 yrs
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 â€“ was there an effect of exposure on low birthweight? Explain.
Question 2.Â 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 â€˜earlyperiodâ€™ (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).Â Check these results using the SAS or R code given below:
Results of a logistic regression interaction model predicting low birthweight
Exposed to events of 9/11
Birth within 2 yrs of 9/11
Exposure x Birth within 2 yrs
30 â€“ 35 yrs
The table below focuses on the effect of exposure, during the 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 SASÂ , I think you can calculate the two odds ratios by hand (with a calculator) from the slopes above â€“ 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? ExplainÂ (address significance as well as size of the effect).
Some SAS and R help follow:
SAS code for the interaction model in Question 2
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