Simulation Data Set

These are simulated data without any identifying information or informative birth-level covariates. We also standardize the pollution exposures on each week by subtracting off the median exposure amount on a given week and dividing by the interquartile range (IQR) (as in the actual application to the true NC birth records data). The dataset that we provide includes weekly average pregnancy exposures that have already been standardized in this way while the medians and IQRs are not given. This further protects identifiability of the spatial locations used in the analysis. This dataset is not publicly accessible because: EPA cannot release personally identifiable information regarding living individuals, according to the Privacy Act and the Freedom of Information Act (FOIA). This dataset contains information about human research subjects. Because there is potential to identify individual participants and disclose personal information, either alone or in combination with other datasets, individual level data are not appropriate to post for public access. Restricted access may be granted to authorized persons by contacting the party listed. It can be accessed through the following means: File format: R workspace file; “Simulated_Dataset.RData”.

Metadata (including data dictionary)
•	y: Vector of binary responses (1: adverse outcome, 0: control)
•	x: Matrix of covariates; one row for each simulated individual
•	z: Matrix of standardized pollution exposures
•	n: Number of simulated individuals
•	m: Number of exposure time periods (e.g., weeks of pregnancy)
•	p: Number of columns in the covariate design matrix
•	alpha_true: Vector of “true” critical window locations/magnitudes (i.e., the ground truth that we want to estimate)

Code
Abstract
We provide R statistical software code (“CWVS_LMC.txt”) to fit the linear model of coregionalization (LMC) version of the Critical Window Variable Selection (CWVS) method developed in the manuscript. We also provide R code (“Results_Summary.txt”) to summarize/plot the estimated critical windows and posterior marginal inclusion probabilities.

Description
“CWVS_LMC.txt”: This code is delivered to the user in the form of a .txt file that contains R statistical software code. Once the “Simulated_Dataset.RData” workspace has been loaded into R, the text in the file can be used to identify/estimate critical windows of susceptibility and posterior marginal inclusion probabilities.

“Results_Summary.txt”: This code is also delivered to the user in the form of a .txt file that contains R statistical software code. Once the “CWVS_LMC.txt” code is applied to the simulated dataset and the program has completed, this code can be used to summarize and plot the identified/estimated critical windows and posterior marginal inclusion probabilities (similar to the plots shown in the manuscript). 

Optional Information (complete as necessary) 
Required R packages:
•	For running “CWVS_LMC.txt”:
•	msm: Sampling from the truncated normal distribution
•	mnormt: Sampling from the multivariate normal distribution
•	BayesLogit: Sampling from the Polya-Gamma distribution
•	For running “Results_Summary.txt”:
•	plotrix: Plotting the posterior means and credible intervals
Instructions for Use
Reproducibility (Mandatory)
What can be reproduced: The data and code can be used to identify/estimate critical windows from one of the actual simulated datasets generated under setting E4 from the presented simulation study.

How to use the information: 
•	Load the “Simulated_Dataset.RData” workspace
•	Run the code contained in “CWVS_LMC.txt”
•	Once the “CWVS_LMC.txt” code is complete, run “Results_Summary.txt”. Format: Below is the replication procedure for the attached data set for the portion of the analyses using a simulated data set:

Data
The data used in the application section of the manuscript consist of geocoded birth records from the North Carolina State Center for Health Statistics, 2005-2008. In the simulation study section of the manuscript, we simulate synthetic data that closely match some of the key features of the birth certificate data while maintaining confidentiality of any actual pregnant women.

Availability
Due to the highly sensitive and identifying information contained in the birth certificate data (including latitude/longitude and address of residence at delivery), we are unable to make the data from the application section publically available. However, we will make one of the simulated datasets available for any reader interested in applying the method to realistic simulated birth records data. This will also allow the user to become familiar with the required inputs of the model, how the data should be structured, and what type of output is obtained. While we cannot provide the application data here, access to the North Carolina birth records can be requested through the North Carolina State Center for Health Statistics, and requires an appropriate data use agreement.

Description
Permissions: These are simulated data without any identifying information or informative birth-level covariates. We also standardize the pollution exposures on each week by subtracting off the median exposure amount on a given week and dividing by the interquartile range (IQR) (as in the actual application to the true NC birth records data). The dataset that we provide includes weekly average pregnancy exposures that have already been standardized in this way while the medians and IQRs are not given. This further protects identifiability of the spatial locations used in the analysis. 

This dataset is associated with the following publication:
Warren, J., W. Kong, T. Luben, and H. Chang. Critical Window Variable Selection: Estimating the Impact of Air Pollution on Very Preterm Birth.   Biostatistics. Oxford University Press, OXFORD,  UK,  1-30, (2019).

Tags: bayesian-variable-selection, critical-windows, linear-model-of-coregionalization
Organization: U.S. Environmental Protection Agency