Improving large-scale estimation and inference for profiling health care providers

Abstract

Provider profiling has been recognized as a useful tool in monitoring health care quality, facilitating inter-provider care coordination, and improving medical cost-effectiveness. Existing methods often use generalized linear models with fixed provider effects, especially when profiling dialysis facilities. As the number of providers under evaluation escalates, the computational burden becomes formidable even for specially designed workstations. To address this challenge, we introduce a serial blockwise inversion Newton algorithm exploiting the block structure of the information matrix. A shared-memory divide-and-conquer algorithm is proposed to further boost computational efficiency. In addition to the computational challenge, the current literature lacks an appropriate inferential approach to detecting providers with outlying performance especially when small providers with extreme outcomes are present. In this context, traditional score and Wald tests relying on large-sample distributions of the test statistics lead to inaccurate approximations of the small-sample properties. In light of the inferential issue, we develop an exact test of provider effects using exact finite-sample distributions, with the Poisson-binomial distribution as a special case when the outcome is binary. Simulation analyses demonstrate improved estimation and inference over existing methods. The proposed methods are applied to profiling dialysis facilities based on emergency department encounters using a dialysis patient database from the Centers for Medicare & Medicaid Services.

Keywords: Poisson-binomial distribution; divide-and-conquer; emergency department encounters; exact test; parallel computing.

FIGURE 1

(1) Runtime of SerBIN and glm with provider counts varying from 100 to 2000 (left). To accommodate large provider counts for glm, experiments were conducted on an Intel® Xeon® Gold 6254 quad‐processor with base frequency 3.1GHz and RAM 576GB. SerBIN was implemented using Rcpp and RcppArmadillo., , Three covariates were included in model fitting with $\mathit{\beta }={[1,0.5,-1]}^{\top }$. The vertical axis is set as the base‐10 log scale. (2) Runtime of SerBIN and BAN with provider counts varying from 2000 to 8000 (middle). Experiments conducted on an Intel® Core^TM i9‐9900K processor with base frequency 3.6GHz and RAM 16GB. BAN was implemented using Rcpp and RcppArmadillo. A design matrix of 100 covariates was drawn based on (6), and then dichotomized column‐wise according to the column median. Regression parameters $\mathit{\beta }$ were jointly sampled from a standard multivariate normal distribution. (3) Speedup of DACBIN relative to SerBIN with various thread and provider counts (right). Speedup with a given number of threads is defined as the ratio of the runtime of SerBIN to the runtime of DACBIN. Experiments conducted on the Intel^® Core^TM i9‐9900K processor with 100 covariates generated as in (2). DACBIN was implemented using Rcpp and RcppArmadillo

FIGURE 2

Type I error rates and powers of exact, score and Wald tests. All values were calculated based on 1000 independent replicates with $m=100$, ${\sigma }^2=0.16$, and significance level $\alpha =0.05$. With correlation $\rho$ varying from 0 to 0.9, rates in Panel A were obtained assuming ${\gamma }_1={\gamma }_{\mathrm{M}}=\mu =\log (4/11)$. In Panel B, correlation was fixed at $\rho =0.5$, whereas ${\gamma }_1$ is allowed to vary in terms of relative deviation $({\gamma }_1-\mu )/\sigma$

FIGURE 3

Coverage probability (CP) vs correlation $\rho$ with varying levels of provider effect ${\gamma }_1$. In each scenario, 1000 data sets are simulated with $m=100$ providers, with the first provider having $n_1=11$ subjects

FIGURE 4

A matrix of histograms and scatter plots of test statistics using 2018‐2019 ED visits data. Facilities are stratified by ED visit rate or discharge count. Dashed lines represent 2.5% and 97.5% quantiles of the standard normal distribution. 45‐degree lines are in solid black