yizenglistat / rvcm4gt

Regularized Bayesian varying coefficient regression for group testing data

RVCM4GT

This repository contains R codes (for reproducibility) along with simulation results for "Regularized Bayesian varying coefficient regression models 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 [e-mail]: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

Reproduce

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 3.6.0+

> source('main.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.

Parameter	Summary	IT	c=5		c=10
			DT	AT	DT	AT
	IP	0.007	0.007	0.007	0.007	0.007
	IP	0.007	0.007	0.008	0.007	0.007
	Bias(CP95)	-0.008(0.962)	-0.015(0.940)	-0.004(0.942)	-0.034(0.912)	-0.013(0.932)
	SSD(ESE)	0.066(0.069)	0.072(0.072)	0.068(0.067)	0.095(0.083)	0.077(0.074)
	Bias(CP95)	-0.007(0.942)	-0.008(0.936)	-0.002(0.938)	-0.012(0.938)	-0.001(0.938)
	SSD(ESE)	0.064(0.063)	0.067(0.063)	0.067(0.062)	0.072(0.068)	0.066(0.065)
	Bias(CP95)	0.047(0.950)	0.044(0.952)	0.039(0.964)	0.059(0.924)	0.048(0.960)
	SSD(ESE)	0.062(0.079)	0.062(0.080)	0.058(0.078)	0.067(0.084)	0.062(0.081)
	Bias(CP95)		-0.032(0.902)	0.000(0.954)	-0.038(0.914)	0.002(0.964)
	SSD(ESE)		0.081(0.053)	0.024(0.021)	0.084(0.062)	0.041(0.034)
	Bias(CP95)		-0.008(0.974)	-0.001(0.988)	-0.019(0.972)	-0.006(0.996)
	SSD(ESE)		0.021(0.024)	0.016(0.017)	0.050(0.046)	0.021(0.033)
	Bias(CP95)		0.002(0.990)	0.000(0.920)	-0.014(0.992)	-0.010(0.990)
	SSD(ESE)		0.011(0.014)	0.012(0.011)	0.032(0.052)	0.027(0.033)
	Bias(CP95)		0.000(0.966)	-0.003(0.974)	-0.003(0.922)	-0.003(0.966)
	SSD(ESE)		0.008(0.007)	0.012(0.013)	0.011(0.009)	0.012(0.011)
Cost	AVGtest	5000	2943.15	2971.33	3567.84	2943.73
Savings	Percent	00.00%	41.14%	40.57%	28.64%	41.12%

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.

Authors

• Dewei Wang - the corresponding author

License

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