Merge pull request #86 from NSAPH-Software/iss79

Address comments regarding available packages

paper/paper.md

@@ -29,11 +29,13 @@ bibliography: paper.bib
 
 # Summary
 
-We present the GPCERF R package, which employs a novel Bayesian approach based on Gaussian Process (GP) to estimate the causal exposure-response function (CERF) for continuous exposures, along with associated uncertainties. R packages that target causal effects under a binary exposure setting exist [e.g., @MatchIt_R], as well as in the continuous exposure setting [e.g., @CausalGPS_R]. However, they often rely on a separate resampling stage to quantify uncertainty of the estimates, which can be computationally demanding. GPCERF provides a two-step end-to-end solution for causal inference with continuous exposures that is equipped with automatic and efficient uncertainty quantification. During the first step (the design phase), the algorithm searches for optimal hyperparameters (using the exposures and covariates) that achieve optimal covariate balance in the induced pseudo-population, i.e., that the correlation between the exposure and each covariate is close to zero. The selected hyperparameters are then used in the second step (the analysis phase) to estimate the CERF on the balanced data set and its associated uncertainty using two different types of GPs: a standard GP and a nearest-neighbor GP (nnGP). The standard GP offers high accuracy in estimating CERF but is also computationally intensive. The nnGP is a computationally efficient approximation of the standard GP and is well-suited for the analysis of large-scale datasets. 
+We present the GPCERF R package, which employs a novel Bayesian approach based on Gaussian Process (GP) to estimate the causal exposure-response function (CERF) for continuous exposures, along with associated uncertainties. R packages that target causal effects under a binary exposure setting exist [e.g., @MatchIt_R], as well as in the continuous exposure setting [e.g., @CausalGPS_R]. However, they often rely on a separate resampling stage to quantify uncertainty of the estimates. GPCERF provides a two-step end-to-end solution for causal inference with continuous exposures that is equipped with automatic and efficient uncertainty quantification. During the first step (the design phase), the algorithm searches for optimal hyperparameters (using the exposures and covariates) that achieve optimal covariate balance in the induced pseudo-population, i.e., that the correlation between the exposure and each covariate is close to zero. The selected hyperparameters are then used in the second step (the analysis phase) to estimate the CERF on the balanced data set and its associated uncertainty using two different types of GPs: a standard GP and a nearest-neighbor GP (nnGP). The standard GP offers high accuracy in estimating CERF but is also computationally intensive. The nnGP is a computationally efficient approximation of the standard GP and is well-suited for the analysis of large-scale datasets. 
 
 # Statement of need
 
-Existing R packages for estimating causal exposure-response functions with continuous exposures typically require resampling approaches, such as bootstrap, to determine the uncertainty of the estimates [e.g., @CausalGPS_R]. However, these resampling-based algorithms can become computationally burdensome when handling large datasets. To bridge this gap, we have developed a unique Bayesian methodology that employs a Gaussian Processes (GPs) prior for counterfactual outcome surfaces, thereby enabling more flexible estimation of the CERF. While various R packages, like GauPro [@GauPro_2023], mlegp [@mlegp_2022], and GPfit [@GPfit_2019], offer Gaussian process regression capabilities, we chose not to use them. The primary reason is that these packages rely on traditional techniques for hyper-parameter tuning, such as sampling from the hyper-parameters' posterior distributions or maximizing the marginal likelihood function. Our approach, in contrast, aims to achieve optimal covariate balancing. By utilizing the posterior distributions of model parameters, we can automatically assess the uncertainty in our CERF estimates [for further details, see @Ren_2021_bayesian]. Since standard GPs are infamous for their scalability issues—particularly due to operations involving the inversion of covariance matrices—we adopt a nearest-neighbor GP (nnGP) prior to ensure computationally efficient inference of the CERF in large-scale datasets.
+Existing R packages designed for estimating causal exposure-response functions with continuous exposures, like CausalGPS [@CausalGPS_R], generally use resampling methods such as bootstrap to ascertain the uncertainty of their estimates. In response to the challenges encountered with large datasets in these resampling-based algorithms, we have introduced a novel Bayesian approach. This method utilizes Gaussian Processes (GPs) as a prior for counterfactual outcome surfaces, offering a more flexible way to estimate the CERF.
+
+While various R packages, like GauPro [@GauPro_2023], mlegp [@mlegp_2022], and GPfit [@GPfit_2019], offer Gaussian process regression capabilities, we chose not to use them. The primary reason is that these packages rely on traditional techniques for hyper-parameter tuning, such as sampling from the hyper-parameters' posterior distributions or maximizing the marginal likelihood function. Our approach, in contrast, aims to achieve optimal covariate balancing. By utilizing the posterior distributions of model parameters, we can automatically assess the uncertainty in our CERF estimates [for further details, see @Ren_2021_bayesian]. Since standard GPs are infamous for their scalability issues—particularly due to operations involving the inversion of covariance matrices—we adopt a nearest-neighbor GP (nnGP) prior to ensure computationally efficient inference of the CERF in large-scale datasets.
 
 # Overview