\documentclass[11pt]{article}

\usepackage[top=0.85in,left=0.75in,right=0.75in,footskip=0.75in]{geometry}

% Citations
\usepackage[numbers,sort&compress]{natbib}
\setcitestyle{authoryear,open={(},close={)}}
\setcitestyle{numbers,square}

% Fonts and formatting
\usepackage{stix}
\usepackage{setspace}

% Tables
\usepackage{threeparttable}
\usepackage{multirow}
\usepackage{booktabs}
\usepackage{tabularx}
\usepackage{float}

% Landscape tables
\usepackage{rotating}

% Links
\usepackage[colorlinks=true,citecolor=blue,linkcolor=magenta]{hyperref}

\begin{document}

\doublespacing

\begin{center}
\textbf{Additional File 1: U.S. Regional Subgroup Analyses}
\end{center}

\section*{U.S. Regional Subgroup Analyses}

%To understand variation across the United States, we included a separate analysis which stratified the population into ten regional sub-groups based on CMS regional locations and offices: New England (Boston office), New York/New Jersey (New York office), Mid-Atlantic (Philadelphia office), South (Atlanta office), Midwest (Chicago office), Central (Kansas City office), South Central (Dallas office), Mountain (Denver office), Pacific Northwest (Seattle office), and Pacific (San Francisco office) \citep{CMSRegionalOffices}. Alaska is considered part of the Pacific Northwest region, and Hawaii is grouped with the Pacific region. Due to the number of regions and the small sample-sizes in some regions, the complete model with region interactions demonstrated issues with convergence, so we limited this preliminary statistical analysis to the New York/New Jersey, South, and Pacific regions.


The population subgroups for all ten regions are detailed in Table \ref{tab:region_stats_1} and Table \ref{tab:region_stats_2}. Among the New England cohort, 64.96\% of beneficiaries used hospice. The New York/New Jersey region had the lowest rate of hospice use with 54.83\% using hospice. In the Mid-Atlantic region, 68.51\% of beneficiaries used hospice. The South and Midwest regions had the highest rate of hospice use with 72.65\% in the South and 71.20\% in the Midwest. In the Pacific region, 65.72\% used hospice. In the Pacific Northwest, 62.28\% used hospice, despite 35.77\% of beneficiaries living within 15 minutes of a hospice--the smallest percentage among all the regions. 69.42\% of beneficiaries in the Mountain region, 68.54\% of beneficiaries in the Central region, and 70.67\% in the South Central region used hospice. 

\begin{table}[h!]
\centering
\begin{tabular}{lrrrrr}
\hline
 & \textbf{New England} & \textbf{New York/New Jersey} & \textbf{Mid-Atlantic} & \textbf{South} & \textbf{Midwest} \\
 & (N=6,041) & (N=12,268) & (N=12,244) & (N=24,452)& (N=18,769) \\
\hline
\textbf{Sex} & & & & & \\
\hspace{1em}Male (1) & 51.37\% & 48.20\% & 50.68\% & 51.90\% & 50.48\% \\
\hspace{1em}Female (2) & 48.63\% & 51.80\% & 49.32\% & 48.10\% & 49.52\% \\
\textbf{Age Group} & & & & & \\
\hspace{1em}65-69 years (1) & 12.81\% & 12.54\% & 15.49\% & 15.79\% & 15.78\% \\
\hspace{1em}70-74 years (2) & 19.19\% & 19.30\% & 21.92\% & 22.47\% & 21.29\% \\
\hspace{1em}75-79 years (3) & 21.29\% & 20.38\% & 20.66\% & 21.55\% & 21.43\% \\
\hspace{1em}80-84 years (4) & 18.72\% & 18.87\% & 18.13\% & 18.78\% & 18.53\% \\
\hspace{1em}85+ years (5) & 27.99\% & 28.91\% & 23.80\% & 21.41\% & 22.97\% \\
\textbf{Race} & & & & & \\
\hspace{1em}White (1) & 92.57\% & 81.54\% & 77.59\% & 85.04\% & 85.22\% \\
\hspace{1em}Black (2) & 3.67\% & 9.41\% & 18.82\% & 11.05\% & 11.04\% \\
\hspace{1em}Hispanic (5) & 2.65\% & 5.45\% & 1.68\% & 3.05\% & 2.54\% \\
\hspace{1em}Asian (4) & 1.11\% & 3.59\% & 1.91\% & 0.85\% & 1.20\% \\
\textbf{RUCA Codes} & & & & & \\
\hspace{1em}Urban (2) & 95.02\% & 96.04\% & 90.92\% & 84.47\% & 84.49\% \\
\hspace{1em}Suburban (1) & 4.15\% & 3.55\% & 6.36\% & 11.29\% & 12.45\% \\
\hspace{1em}Rural (0) & 0.83\% & 0.42\% & 2.72\% & 4.24\% & 3.06\% \\
\textbf{Distance to Hospice} & & & & & \\
\hspace{1em}< 15 mins & 71.06\% & 55.08\% & 64.24\% & 44.01\% & 71.69\% \\
\hspace{1em}15-30 mins & 25.01\% & 39.75\% & 30.10\% & 39.09\% & 24.63\% \\
\hspace{1em}> 30 mins & 3.92\% & 5.17\% & 5.65\% & 16.90\% & 3.68\% \\
\textbf{Hospice Use} & & & & & \\
\hspace{1em}No (0) & 35.04\% & 45.17\% & 31.49\% & 27.35\% & 28.80\% \\
\hspace{1em}Yes (1) & 64.96\% & 54.83\% & 68.51\% & 72.65\% & 71.20\% \\
\hline
\end{tabular}
\caption{Descriptive statistics by CMS region (Part 1).}
\label{tab:region_stats_1}
\vspace{-0.1in}
\end{table}

\begin{table}[h!]
\centering
\begin{tabular}{lrrrrr}
\hline
 & \textbf{Pacific} & \textbf{PNW} & \textbf{Mountain} & \textbf{Central} & \textbf{South Central} \\
 & (N=13,261) & (N=3,221) & (N=1,851) & (N=4,526) & (N=10,288) \\
\hline
\textbf{Sex} & & & & & \\
\hspace{1em}Male (1) & 52.70\% & 53.77\% & 52.73\% & 50.31\% & 52.26\% \\
\hspace{1em}Female (2) & 47.30\% & 46.23\% & 47.27\% & 49.69\% & 47.74\% \\
\textbf{Age Group} & & & & & \\
\hspace{1em}65-69 years (1) & 15.13\% & 15.46\% & 15.83\% & 16.08\% & 16.94\% \\
\hspace{1em}70-74 years (2) & 21.70\% & 21.67\% & 22.37\% & 21.92\% & 23.13\% \\
\hspace{1em}75-79 years (3) & 20.81\% & 22.29\% & 19.56\% & 22.60\% & 21.82\% \\
\hspace{1em}80-84 years (4) & 18.73\% & 18.26\% & 18.96\% & 17.19\% & 17.66\% \\
\hspace{1em}85+ years (5) & 23.62\% & 22.32\% & 23.28\% & 22.21\% & 20.44\% \\
\textbf{Race} & & & & & \\
\hspace{1em}White (1) & 73.65\% & 92.98\% & 94.00\% & 93.24\% & 79.18\% \\
\hspace{1em}Black (2) & 5.20\% & 1.89\% & 1.35\% & 4.95\% & 9.76\% \\
\hspace{1em}Hispanic (5) & 10.71\% & 2.14\% & 3.78\% & 1.10\% & 9.40\% \\
\hspace{1em}Asian (4) & 10.44\% & 2.98\% & 0.86\% & 0.71\% & 1.66\% \\
\textbf{RUCA Codes} & & & & & \\
\hspace{1em}Urban (2) & 91.67\% & 76.09\% & 75.47\% & 66.15\% & 76.34\% \\
\hspace{1em}Suburban (1) & 7.47\% & 20.58\% & 18.21\% & 25.43\% & 17.26\% \\
\hspace{1em}Rural (0) & 0.85\% & 3.32\% & 6.32\% & 8.42\% & 6.40\% \\
\textbf{Distance to Hospice} & & & & & \\
\hspace{1em}< 15 mins & 66.39\% & 35.77\% & 53.27\% & 75.63\% & 63.74\% \\
\hspace{1em}15-30 mins & 17.82\% & 29.09\% & 20.69\% & 16.28\% & 24.59\% \\
\hspace{1em}> 30 mins & 15.79\% & 35.14\% & 26.04\% & 8.09\% & 11.66\% \\
\textbf{Hospice Use} & & & & & \\
\hspace{1em}No (0) & 34.28\% & 37.72\% & 30.58\% & 31.46\% & 29.33\% \\
\hspace{1em}Yes (1) & 65.72\% & 62.28\% & 69.42\% & 68.54\% & 70.67\% \\
\hline
\end{tabular}
\caption{Descriptive statistics by CMS region (Part 2).}
\label{tab:region_stats_2}
\vspace{-0.1in}
\end{table}


In the model including regional interactions, we faced challenges with model convergence due to the large number of factors and the relatively small sample-sizes in some regions. As a result, we sampled three regions--New York/New Jersey, South, and Pacific--to simplify the model and produce preliminary results. Then, we ran ANOVA Type III Wald tests to measure effects across different regions, Table \ref{tab:region_stratified_marginal_effects_interactions}. 

When comparing a baseline model without region interactions to the model including region interactions, we found that regional heterogeneity improved the model fit ($\chi^2$ = 78.18, df = 28, p < 0.001). This finding suggests that at least one of the predictors is involved in statistically significant interactions with geographic region. While we were not able to produce results for all ten subregions, the results from the subgroup indicates that we could expect the three-region (New York/New Jersey, South, and Pacific) sub-analysis to show heterogeneous results if we were to get the analysis on the full dataset to run.


\begin{sidewaystable}[htbp]
\centering
\setlength{\tabcolsep}{4pt}
\renewcommand{\arraystretch}{1.25}
\begin{tabular}{lcccc}
\toprule
 & \textbf{New York/New Jersey} & \textbf{South} & \textbf{Pacific} & \textbf{Type III p-value} \\
\textbf{Variable} & \textbf{Marg. Eff. [95\% CI]} & \textbf{Marg. Eff. [95\% CI]} & \textbf{Marg. Eff. [95\% CI]} &  \\
\midrule

Female & 6.51 [4.76, 8.26]*** & 5.75 [4.70, 6.80]*** & 5.32 [3.66, 6.97]*** & 0.519 \\

Age (5-year group) & 1.85 [1.21, 2.49]*** & 1.71 [1.48, 1.94]*** & 1.95 [1.37, 2.53]*** & 0.768 \\

Race & -- & -- & -- & 0.049 \\
\hspace{3mm}Black & -4.64 [-8.29, -0.99]* & -6.36 [-8.16, -4.55]*** & -6.32 [-10.33, -2.32]** & -- \\
\hspace{3mm}Hispanic & 4.12 [-0.04, 8.27] & 0.44 [-3.06, 3.94] & -3.57 [-6.39, -0.76]* & -- \\
\hspace{3mm}Asian & -5.55 [-10.50, -0.59]* & -6.28 [-11.67, -0.88]* & -6.47 [-9.47, -3.48]*** & -- \\

Distance to Hospice & -- & -- & -- & $<0.001$ \\
\hspace{3mm}$<$15 min & 3.86 [-1.70, 9.41] & -2.93 [-4.74, -1.12]** & -1.06 [-6.18, 4.07] & -- \\
\hspace{3mm}15--30 min & 0.29 [-5.30, 5.89] & -0.94 [-2.74, 0.86] & 0.98 [-2.17, 4.12] & -- \\

ZIP \% Black & 4.91 [-2.12, 11.94] & -1.13 [-4.86, 2.60] & -3.44 [-6.78, -0.11]* & 0.164 \\

ZIP \% White & 6.26 [-0.47, 12.98] & -0.97 [-4.73, 2.79] & -0.41 [-3.06, 2.24] & 0.099 \\

ZIP \% Hispanic & 4.50 [-2.11, 11.13] & -0.67 [-4.39, 3.04] & -1.88 [-4.38, 0.62] & 0.242 \\

ZIP \% Asian & 4.59 [-2.18, 11.36] & 1.42 [-3.04, 5.87] & -2.47 [-5.24, 0.31] & 0.207 \\

Suburban & 5.74 [-11.63, 23.13] & 1.40 [-1.75, 4.54] & 5.05 [-0.13, 10.22] & 0.924 \\

Urban & 12.29 [-4.92, 29.50] & 5.95 [2.77, 9.12]*** & 18.42 [7.23, 29.62]** & 0.852 \\

Income (log) & 0.38 [-1.06, 1.82] & 0.87 [-0.03, 1.76] & -1.46 [-2.79, -0.13]* & 0.004 \\

\bottomrule
\end{tabular}

\caption{Marginal effects (percentage points) and associated 95\% confidence intervals from a generalized linear mixed model predicting hospice use, stratified by three CMS geographic regions: New York/New Jersey, South, and Pacific. Type III Wald tests measure whether effects differ across regions. Significance codes: *** $p<0.001$, ** $p<0.01$, * $p<0.05$, . $p<0.1$.}

\label{tab:region_stratified_marginal_effects_interactions}
\end{sidewaystable}


In the interaction model, the neighborhood-level predictors demonstrated varying statistical significance across all three regions. The Type III p-values indicate that beneficiary race, distance to hospice, and income are the only predictors that interact significantly with region. This finding proves that the effects of these factors on hospice use differ across regions. 

Across all three regions, beneficiaries who identify as Black or Asian had decreased odds of hospice use. Only in the Pacific region were Hispanic beneficiaries 3.57 percentage points less likely to use hospice; the other regions showed no significant effect. While the effect of being Black or Asian had a similar direction across all three regions, the Type III p-values indicate that the magnitude of this effect differs depending on which region a beneficiary lives in. Furthermore, considering the statistically significant result for Hispanic beneficiaries in the Pacific region, we found that racial identity alone does not uniformly predict hospice use across the United States. Rather, interactions between race and geographic region produce heterogeneous results. 

In the South, beneficiaries living within 15 minutes from a hospice had decreased odds of hospice use by -2.93 percentage points compared to their counterparts living 30 minutes or more from a hospice. However, distance from a hospice had no significant effect on hospice use in the other two regions, indicating heterogeneous effects on hospice use across geographic regions. 

Finally, neighborhood income levels were also significantly associated with hospice use only in the Pacific region. Higher income levels were negatively associated with hospice use by -4.25 and -1.46 percentage points. However, the other two regions produced no statistically significant result, further demonstrating the varying impact of predictors in different geographic regions.

These preliminary results support our findings that geographic availability of hospice does not fully account for hospice utilization patterns. Rather, a patient's CMS geographic region could be one contextual factor in the broader hospice decision-making process. Future research should incorporate regional analyses into a pathway-based model to understand how geographic region and regional-level differences can shape structural conditions surrounding hospice care and ultimately shape end-of-life care trajectories. 




\end{document}