Joint Indirect Standardization When Only Marginal Distributions are Observed in the Index Population

<p>It is a common interest in medicine to determine whether a hospital meets a benchmark created from an aggregate reference population, after accounting for differences in distributions of multiple covariates. Due to the difficulties of collecting individual-level data, however, it is often the case that only marginal distributions of the covariates are available, making covariate-adjusted comparison challenging. We propose and evaluate a novel approach for conducting indirect standardization when only marginal covariate distributions of the studied hospital are known, but complete information is available for the reference hospitals. We do this with the aid of two existing methods: iterative proportional fit, which estimates the cells of a contingency table when only marginal sums are known, and synthetic control methods, which create a counterfactual control group using a weighted combination of potential control groups. The proper application of these existing methods for indirect standardization would require accounting for the statistical uncertainties induced by a situation where no individual-level data are collected from the studied population. We address this need with a novel method which uses a random Dirichlet parameterization of the synthetic control weights to estimate uncertainty intervals for the standard incidence ratio. We demonstrate our novel methods by estimating hospital-level standardized incidence ratios for comparing the adjusted probability of computed tomography examinations with high radiations doses, relative to a reference standard and we evaluate out methods in a simulation study. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.</p

Tobacco smoke induced damage to the lung.

<p>Cigarette smoke-induced damage was evaluated in hematoxylin stained lung tissue sections (top). Cigarette smoke-induced neutrophil infiltration was evaluated using myeloperoxidase staining of lung tissue sections to confirm the location of neutrophils in the vasculature and lung tissues (bottom). Tissue sections are from SH rats exposed to 6 hours of tobacco smoke per day for 3 days, 4 weeks or 12 weeks.</p

Adhesion molecule and chemokine expression at specific locations correlate with leukocytes recovered from the BALF.

<p>Adhesion molecule and chemokine expression at specific locations correlate with leukocytes recovered from the BALF.</p

Leukocytes recovered from the BALF of SH rats after 3 days, 4 weeks, or 12 weeks of tobacco smoke exposure.

<p>Total leukocytes, monocyte/macrophages neutrophils, and lymphocytesrecovered from the BALF after 3 days, 4 weeks, or 12 weeks of tobacco smoke exposure.</p

Smoke increases neovasculization.

<p>Bronchial blood vessels per mm airway lumen at 3 days, 4 weeks and 12 weeks smoke exposure.</p

Mean linear intercept.

<p>Mean linear intercept is reported as a measurement of alveolar airspace enlargement within the lung parenchyma after 3 days, 4 weeks or 12 weeks of filtered air or tobacco smoke exposure.</p

Adhesion molecule and chemokine expression in and around the bronchial blood vessels following 3 days, 4 weeks, or 12 weeks of tobacco smoke exposure.

<p>Top) Representative pictures of immunohistochemical staining of E-selectin in the bronchial wall of SH rats exposed to filtered air or tobacco smoke for 3 days, 4 weeks, or 12 weeks. Arrows indicate bronchial blood vessels. Bottom) IHC staining intensity of E-selectin, VCAM, ICAM, MCP-1, and MIP-2 after 3 days, 4 weeks, or 12 weeks of tobacco smoke as scored by blinded ranking. The difference from control staining is reported as mean ± SEM, where the mean control staining at each location is set to zero. * <i>p</i> value<0.05 vs. filtered air. Brackets indicate comparisons between 3 days, 4 weeks and 12 weeks of smoke exposure. (staining scores were reranked prior to analysis changing the scale, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033304#s2" target="_blank">methods</a>).</p

Tobacco smoke induced chemokine expression.

<p>Top) Representative pictures of immunohistochemical (IHC) staining of MCP-1 and MIP-2 in the bronchial wall of SH rats exposed to filtered air or 3 days of tobacco smoke. Bottom) IHC staining intensity of the chemokines MCP-1 and MIP-2 after 3 days of tobacco smoke as scored by blinded ranking. Br BV: bronchial blood vessel; Br Epi: bronchial epithelial cells; Alv. Mac: alveolar macrophages; Br Mac: macrophages in the bronchial wall. Brackets indicate comparisons between filtered air exposure and tobacco smoke exposure. (Note: Adhesion molecules and chemokine staining scores were reranked putting them on a 1–12 scale. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033304#s2" target="_blank">methods</a>).</p

Tobacco smoke induced adhesion molecule expression.

<p>Top) Representative pictures of immunohistochemical (IHC) staining of E-selectin, VCAM, and ICAM in the bronchial wall of SH rats exposed to filtered air or 3 days of tobacco smoke. Arrows indicate bronchial blood vessels. Bottom) IHC staining intensity of the adhesion molecules E-selectin, VCAM, and ICAM after 3 days of tobacco smoke as scored by blinded ranking. Br BV: bronchial blood vessel; Par BV: parenchymal blood vessel. Brackets indicate comparisons between filtered air exposure and tobacco smoke exposure. (Note: Adhesion molecules and chemokine staining scores were reranked putting them on a 1–12 scale. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033304#s2" target="_blank">methods</a>).</p

Neutrophil specific adhesion molecule and chemokine expression at specific locations correlate with neutrophils recovered from the BALF.

<p>Neutrophil specific adhesion molecule and chemokine expression at specific locations correlate with neutrophils recovered from the BALF.</p