RVCM4GT

This repository contains R codes (for reproducibility) along with simulation results for "Varying Coefficient Regression for Group Testing Data". Our model is try to estimate an individual-level regression model based on group testing data that can capture the age-varying impact on the Chlamydia risk with selection. To relate available information, we consider

$$ \text{logit}(\text{Pr}(\widetilde Y_i=1\mid \boldsymbol x_i, u_i))=\underbrace{\psi_0(u_i)+\sum_{d=1}^p x_{id}\psi_d(u_i)}_{\text{Age-varying Effects}} + \underbrace{\sum_{\ell=1}^L r_\ell(i)\gamma_\ell}_{\text{Random Effect}} \quad\text{for }i=1,\ldots,N, $$

where $\widetilde Y_i$ is the hidden chlamydia status for $i^{th}$ patient, age $u_i$, $\boldsymbol x_i=(x_{i1},\ldots,x_{ip})^\top$ are covariates, and $\psi_d(u_i)=\delta_{1d}(\alpha_d+\delta_{2d}\beta_d(u_i))$ for binary indicators $\delta_{1d},\delta_{2d}$; see more details in the paper. In short, our stochastic search variable selection categorize each of covariates into one of three groups:

• $\delta_{1d}=0\longrightarrow$ insignificant effects.
• $\delta_{1d}=1$
  • $\delta_{2d}=0\longrightarrow$ age-independent effects.
  • $\delta_{2d}=1\longrightarrow$ age-varying effects.

To reproduce the results in the paper, we provide implementation details as follows.

username@login001 ~$ git clone git@github.com:yizenglistat/rvcm4gt.git
username@login001 ~$ cd rvcm4gt

In addition, for the privacy of the Iowa SHL group testing data, we create a simulated fake Iowa group testing data (under /data/simulated_fake_data.csv) for illustration. As we will see the code running on the fake data set successfully below

Arguments

# A demo example to run 500 repetitions in one machine.
task_id <- 1	
nreps <- 500
Ns <- c(3000, 5000)
pool_sizes <- c(5, 10)
model_names <- c("m1", "m2")
testings <- c("AT", "DT", "IT")
N_test <- 600
sigma <- 0.5

• task_id

The machine id. For example, 1,...,100 if running on the cluster. In this way, we will run 5 simulations independently on 100 nodes to have a total of 500 repetitions.

• nreps

The repetitions.

• Ns

A vector of sample sizes.

• pool_sizes

A vector of pool sizes.

• model_names

A vector of model names. Different model names corresponds to different varying function sets.

• testings

A vector of testing protocols such as AT (array testing), DT (Dorfman Testing) or IT (Individual Testing).

• N_test

Number of knots values in inference for estimated varying functions.

• sigma

True random effect standard deviation

Simulation Reproduction

After setting up the environment (requirement.txt) and arguments, one should be able to run the following code in R to reproduce simulation results in the paper.

# R version 4.4.0 or above

> source('run.r')

After collecting .RData files under output/, one should be able to reproduce the results subsequently. The following demo figure and demo table show that $\textcolor{red}{\textbf{red}}$ means the $\textcolor{red}{\textbf{age-varying effects}}$, $\textcolor{blue}{\textbf{blue}}$ means the significant but $\textcolor{blue}{\textbf{age-independent effects}}$ and $\textbf{black}$ means the $\textbf{insignificant effects}$ can be both correctly identified and estimated; see details in the paper.

IP: the inclusion probability of the any significant effect, i.e., $\alpha_d$ or $\beta_d(u)$.

IPF: the inclusion probability of the age-independent effect, i.e., $\alpha_d$ only.

IPV: the inclusion probability of the age-varying effect, i.e., $\beta_d(u)$ only.

Application Reproduction

We include a simulated (fake) group testing data that closely emulate the structure of Iowa group testing data under the folder data/fake/. To reproduce the simulated data analysis results in the Supplementary Masterials, one can run the following script.

# R version 4.4.0 or above

> source('run_fake.r')

Significant and age-varying coefficients

Significant but age-independent coefficients

Insignificant coefficients

Authors

• Yizeng Li
• Dewei Wang - the corresponding author
• Joshua M. Tebbs

License

This project is licensed under the MIT License - see the License file for details.