# Appendices

## Appendix A: Summary Statistics Tables {#AppendixA}

```{r appendA}

readmit_cci_org %>%

kbl(caption = "Readmission Empirical Statistics by CCI Score", digits=3,

col.names = c("CCI Score", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_classic_2(full_width = F)

readmit_lace_org %>%

kbl(caption = "Readmission Empirical Statistics by LACE Score", digits=3,

col.names = c("LACE Score", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_classic_2(full_width = F)

readmit_hos_org %>%

kbl(caption = "Readmission Empirical Statistics by HOSPITAL Score", digits=3,

col.names = c("HOS Score", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_classic_2(full_width = F)

```

## Appendix B: Plots of Empirical Logits by Year, Score {#AppendixB}

```{r appendB}

readmit_yr <- bind_rows(readmit_yr_cci, readmit_yr_lace, readmit_yr_hos)

readmit_plot <- readmit_yr %>% na_if(-Inf)

ggplot(readmit_plot, aes(x = Value, y = logit.Readmit, shape = Score)) +

geom_point(alpha = 0.4, size = 3) + geom_line() +

facet_wrap(vars(Year)) +

theme_minimal() +

labs(x = "Acuity Score", y = "Empirical Logit", shape = "Score") +

ggtitle("Empirical Logit by Calculated Score, Year")

yr_cci_plot <- readmit_yr_cci %>% na_if(-Inf)

ggplot(yr_cci_plot, aes(x = Value, y = logit.Readmit, col= as.factor(Year))) +

geom_point(alpha = 0.4, size = 3) + geom_line() +

theme_minimal() +

labs(x = "CCI Score", y = "Empirical Logit", col = "Year") +

ggtitle("Empirical Logit by CCI Score, Year")

yr_lace_plot <- readmit_yr_lace %>% na_if(-Inf)

ggplot(yr_lace_plot, aes(x = Value, y = logit.Readmit, col= as.factor(Year))) +

geom_point(alpha = 0.4, size = 3) + geom_line() +

theme_minimal() +

labs(x = "LACE Score", y = "Empirical Logit", col = "Year") +

ggtitle("Empirical Logit by LACE Score, Year")

yr_hos_plot <- readmit_yr_hos %>% na_if(-Inf)

ggplot(yr_hos_plot, aes(x = Value, y = logit.Readmit, col= as.factor(Year))) +

geom_point(alpha = 0.4, size = 3) + geom_line() +

theme_minimal() +

labs(x = "HOSP Score", y = "Empirical Logit", col = "Year") +

ggtitle("Empirical Logit by HOSPITAL Score, Year")

```

## Appendix C: Demographic EDA Tables, Plots {#AppendixC}

```{r appendc_cci}

readmit_cci_gen %>%

select(!Demo) %>%

kbl(caption = "Readmission Empirical Statistics by CCI Score, Gender", digits=3,

col.names = c("CCI Score", "Gender", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_minimal(full_width = F) %>%

column_spec(1, bold=T)

readmit_cci_re %>%

select(!Demo) %>%

kbl(caption = "Readmission Empirical Statistics by CCI Score, Race/Ethnicity", digits=3,

col.names = c("CCI Score", "Race/Ethnicity", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_minimal(full_width = F) %>%

column_spec(1, bold=T)

readmit_cci_ins %>%

select(!Demo) %>%

kbl(caption = "Readmission Empirical Statistics by CCI Score, Insurance", digits=3,

col.names = c("CCI Score", "Insurance", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_minimal(full_width = F) %>%

column_spec(1, bold=T)

cci_gen_plot <- readmit_cci_gen %>% na_if(-Inf)

ggplot(cci_gen_plot, aes(x = CCI, y=logit.Readmit, shape=Value, label=CCI)) +

geom_point(alpha = 0.3, size = 5) + geom_line(alpha = 0.3) +

geom_text() +

labs(x = "CCI Score", y = "Empirical Logit", shape = "Gender") +

theme_minimal() + ggtitle("Empirical Logit by CCI Score, Gender")

cci_re_plot <- readmit_cci_re %>% na_if(-Inf)

ggplot(cci_re_plot, aes(x = CCI, y=logit.Readmit, shape=Value, label=CCI)) +

geom_point(alpha = 0.3, size = 5) + geom_line(alpha = 0.3) +

geom_text() +

labs(x = "CCI Score", y = "Empirical Logit", shape = "Race/Ethnicity") +

theme_minimal() + ggtitle("Empirical Logit by CCI Score, Race/Ethnicity")

cci_ins_plot <- readmit_cci_ins %>% na_if(-Inf)

ggplot(cci_ins_plot, aes(x = CCI, y=logit.Readmit, shape=Value, label=CCI)) +

geom_point(alpha = 0.3, size = 5) + geom_line(alpha = 0.3) +

geom_text() +

labs(x = "CCI Score", y = "Empirical Logit", shape = "Insurance") +

theme_minimal() + ggtitle("Empirical Logit by CCI Score, Insurance")

```

```{r appendc_lace}

readmit_lace_gen %>%

select(!Demo) %>%

kbl(caption = "Readmission Empirical Statistics by LACE Score, Gender", digits=3,

col.names = c("LACE Score", "Gender", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_minimal(full_width = F) %>%

column_spec(1, bold=T)

readmit_lace_re %>%

select(!Demo) %>%

kbl(caption = "Readmission Empirical Statistics by LACE Score, Race/Ethnicity", digits=3,

col.names = c("LACE Score", "Race/Ethnicity", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_minimal(full_width = F) %>%

column_spec(1, bold=T)

readmit_lace_ins %>%

select(!Demo) %>%

kbl(caption = "Readmission Empirical Statistics by LACE Score, Insurance", digits=3,

col.names = c("LACE Score", "Insurance", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_minimal(full_width = F) %>%

column_spec(1, bold=T)

lace_gen_plot <- readmit_lace_gen %>% na_if(-Inf)

ggplot(lace_gen_plot, aes(x = LACE, y=logit.Readmit, shape=Gender, label=LACE)) +

geom_point(alpha = 0.3, size = 5) + geom_line(alpha = 0.3) +

geom_text() +

labs(x = "LACE Score", y = "Empirical Logit", shape = "Gender") +

theme_minimal() + ggtitle("Empirical Logit by LACE Score, Gender")

lace_re_plot <- readmit_lace_re %>% na_if(-Inf)

ggplot(lace_re_plot, aes(x = LACE, y=logit.Readmit, shape=Value, label=LACE)) +

geom_point(alpha = 0.3, size = 5) + geom_line(alpha = 0.3) +

geom_text() +

labs(x = "LACE Score", y = "Empirical Logit", shape = "Race/Ethnicity") +

theme_minimal() + ggtitle("Empirical Logit by LACE Score, Race/Ethnicity")

lace_ins_plot <- readmit_lace_ins %>% na_if(-Inf)

ggplot(lace_ins_plot, aes(x = LACE, y=logit.Readmit, shape=Value, label=LACE)) +

geom_point(alpha = 0.3, size = 5) + geom_line(alpha = 0.3) +

geom_text() +

labs(x = "LACE Score", y = "Empirical Logit", shape = "Insurance") +

theme_minimal() + ggtitle("Empirical Logit by LACE Score, Insurance")

```

```{r appendc_hos}

readmit_hos_gen %>%

select(!Demo) %>%

kbl(caption = "Readmission Empirical Statistics by HOSPITAL Score, Gender", digits=3,

col.names = c("HOSP Score", "Gender", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_minimal(full_width = F) %>%

column_spec(1, bold=T)

readmit_hos_re %>%

select(!Demo) %>%

kbl(caption = "Readmission Empirical Statistics by HOSPITAL Score, Race/Ethnicity", digits=3,

col.names = c("HOSP Score", "Race/Ethnicity", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_minimal(full_width = F) %>%

column_spec(1, bold=T)

readmit_hos_ins %>%

select(!Demo) %>%

kbl(caption = "Readmission Empirical Statistics by HOSPITAL Score, Insurance", digits=3,

col.names = c("HOSP Score", "Insurance", "Mean Age", "N", "Readmit No.", "Readmit Prop", "Readmit Odds", "Readmit Logit")) %>%

kable_minimal(full_width = F) %>%

column_spec(1, bold=T)

hos_gen_plot <- readmit_hos_gen %>% na_if(-Inf)

ggplot(hos_gen_plot, aes(x = HOSPITAL, y=logit.Readmit, shape=Gender, label=HOSPITAL)) +

geom_point(alpha = 0.3, size = 5) + geom_line(alpha = 0.3) +

geom_text() +

labs(x = "HOSP Score", y = "Empirical Logit", shape = "Gender") +

theme_minimal() + ggtitle("Empirical Logit by HOSPITAL Score, Gender")

hos_re_plot <- readmit_hos_re %>% na_if(-Inf)

ggplot(hos_re_plot, aes(x = HOSPITAL, y=logit.Readmit, shape=Value, label=HOSPITAL)) +

geom_point(alpha = 0.3, size = 5) + geom_line(alpha = 0.3) +

geom_text() +

labs(x = "HOSP Score", y = "Empirical Logit", shape = "Race/Ethnicity") +

theme_minimal() + ggtitle("Empirical Logit by HOSPITAL Score, Race/Ethnicity")

hos_ins_plot <- readmit_hos_ins %>% na_if(-Inf)

ggplot(hos_ins_plot, aes(x = HOSPITAL, y=logit.Readmit, shape=Value, label=HOSPITAL)) +

geom_point(alpha = 0.3, size = 5) + geom_line(alpha = 0.3) +

geom_text() +

labs(x = "HOSP Score", y = "Empirical Logit", shape = "Insurance") +

theme_minimal() + ggtitle("Empirical Logit by HOSPITAL Score, Insurance")

```

## Appendix D: CCI Model Comparison and Diagnostics {#AppendixD}

Since the base CCI model showed no evidence of a relationship between readmission risk and CCI score, expanded covariate models were not considered.

```{r cci_diag}

CCI_eq <- "$B_0 + B_1*CCI$"

CCI_est <- round(CCI_mod0$coefficients[2], 3)

CCI_confint <- paste(round(cci_confint[2,1], 3),

round(cci_confint[2,2], 3), sep = ", ")

CCI_dev <- round(CCI_mod0$deviance)

CCI_df <- CCI_mod0$df.residual

CCI_aic <- round(AIC(CCI_mod0))

cci_mod_tab <- data.frame(cbind(CCI_eq,

CCI_est,

CCI_confint,

CCI_dev,

CCI_df,

CCI_aic))

colnames(cci_mod_tab) <- c("$log(\\frac{p_{CCI_i}}{1-p_{CCI_{i}}})$",

"$B_1$ Estimate", "$B_1$ 95% CI",

"Residual Deviance", "Degrees of Freedom",

"AIC")

rownames(cci_mod_tab) <- NULL

cci_models <- kbl(cci_mod_tab, caption = "CCI Model Summary", escape = FALSE) %>%

kable_classic_2(full_width = FALSE)

cci_models

```

## Appendix E: LACE Model Comparisons {#AppendixE}

```{r lace_models}

lace_eq <- c("$B_0 + B_1*LACE$", "$B_0 + B_1*LACE + B_2*Gender$",

"$B_0 + B_1*LACE + B_2*Age + \\\\ \\ \\ \\ \\ B_3*Year + B_4*Gender + B5*Insurance$",

"$B_0 + B_1*LACE * B_2*Age * \\\\ \\ \\ \\ \\ B_3*Year * B_4*Gender * B5*Insurance$")

lace_est <- c(round(lace_mod0$coefficients[2], 3),

round(lace_gen_mod$coefficients[2], 3),

round(lace_add_mod$coefficients[2], 3),

round(lace_sat_mod$coefficients[2], 3))

lace_mod0_confint <- round(confint(lace_mod0)[2,], 3)

lace_gen_confint <- round(confint(lace_gen_mod)[2,], 3)

lace_add_confint <- round(confint(lace_add_mod)[2,], 3)

lace_sat_confint <- round(confint(lace_sat_mod)[2,], 3)

lace_ci <- c(paste(lace_mod0_confint[1], lace_mod0_confint[2], sep = ", "),

paste(lace_gen_confint[1], lace_gen_confint[2], sep = ", "),

paste(lace_add_confint[1], lace_add_confint[2], sep = ", "),

paste(lace_sat_confint[1], lace_sat_confint[2], sep = ", "))

lace_dev <- c(round(lace_mod0$deviance), round(lace_gen_mod$deviance),

round(lace_add_mod$deviance), round(lace_sat_mod$deviance))

lace_df <- c(round(lace_mod0$df.residual), round(lace_gen_mod$df.residual),

round(lace_add_mod$df.residual), round(lace_sat_mod$df.residual))

lace_aic <- c(round(AIC(lace_mod0)), round(AIC(lace_gen_mod)),

round(AIC(lace_add_mod)), round(AIC(lace_sat_mod)))

lace_mod_tab <- data.frame(cbind(lace_eq, lace_est, lace_ci,

lace_dev, lace_df, lace_aic))

colnames(lace_mod_tab) <- c("$log(\\frac{p_{LACE_i}}{1-p_{LACE_{i}}})$",

"$B_1$ Estimate", "$B_1$ 95% CI",

"Residual Deviance", "Degrees of Freedom",

"AIC")

rownames(lace_mod_tab) <- NULL

lace_models <- kbl(lace_mod_tab, caption = "LACE Model Comparison",

linesep = "\\addlinespace", escape = FALSE) %>%

kable_classic_2(full_width = FALSE)

lace_models

```

## Appendix F: HOSPITAL Model Comparisons {#AppendixF}

```{r stayduration_models}

hos_eq <- c("$B_0 + B_1*HOSPITAL$", "$B_0 + B_1*HOSPITAL + B_2*Gender$",

"$B_0 + B_1*HOSPITAL + B_2*Age + \\\\ \\ \\ \\ \\ B_3*Year + B_4*Gender + B5*Insurance$",

"$B_0 + B_1*HOSPITAL * B_2*Age * \\\\ \\ \\ \\ \\ B_3*Year * B_4*Gender * B5*Insurance$")

hos_est <- c(round(hos_mod0$coefficients[2], 3),

round(hos_gen_mod$coefficients[2], 3),

round(hos_add_mod$coefficients[2], 3),

round(hos_sat_mod$coefficients[2], 3))

hos_mod0_confint <- round(confint(hos_mod0)[2,], 3)

hos_gen_confint <- round(confint(hos_gen_mod)[2,], 3)

hos_add_confint <- round(confint(hos_add_mod)[2,], 3)

hos_sat_confint <- round(confint(hos_sat_mod)[2,], 3)

hos_ci <- c(paste(hos_mod0_confint[1], hos_mod0_confint[2], sep = ", "),

paste(hos_gen_confint[1], hos_gen_confint[2], sep = ", "),

paste(hos_add_confint[1], hos_add_confint[2], sep = ", "),

paste(hos_sat_confint[1], hos_sat_confint[2], sep = ", "))

hos_dev <- c(round(hos_mod0$deviance), round(hos_gen_mod$deviance),

round(hos_add_mod$deviance), round(hos_sat_mod$deviance))

hos_df <- c(round(hos_mod0$df.residual), round(hos_gen_mod$df.residual),

round(hos_add_mod$df.residual), round(hos_sat_mod$df.residual))

hos_aic <- c(round(AIC(hos_mod0)), round(AIC(hos_gen_mod)),

round(AIC(hos_add_mod)), round(AIC(hos_sat_mod)))

hos_mod_tab <- data.frame(cbind(hos_eq, hos_est, hos_ci, hos_dev, hos_df, hos_aic))

colnames(hos_mod_tab) <- c("$log(\\frac{p_{HOSPITAL_i}}{1-p_{HOSPITAL_{i}}})$",

"$B_1$ Estimate", "$B_1$ 95% CI",

"Residual Deviance", "Degrees of Freedom",

"AIC")

rownames(hos_mod_tab) <- NULL

hos_models <- kbl(hos_mod_tab, caption = "HOSPITAL Model Comparison",

linesep = "\\addlinespace", escape = FALSE) %>%

kable_classic_2(full_width = FALSE)

hos_models

```

## Appendix G: LOS Follow Up Analysis {#AppendixG}

```{r filter_readmits}

snf_readmits <- snf_data_fit %>% filter(Readmit == "Y")

```

```{r los_plots}

los_cci_plot <- snf_readmits %>%

group_by(CCI, Gender) %>%

summarize(mean.stay = mean(StayDurationDays))

ggplot(los_cci_plot, aes(x = CCI, y = mean.stay, lty = Gender)) +

geom_line() +

theme_minimal() +

scale_x_continuous(breaks = seq(0, 14, 2), limits = c(0, 14)) +

scale_y_continuous(breaks = seq(0, 16, 2), limits = c(0, 16)) +

labs(y = "Average LOS") +

ggtitle("Average Length of Stay by CCI Score, Gender")

los_lace_plot <- snf_readmits %>%

group_by(LACE, Gender) %>%

summarize(mean.stay = mean(StayDurationDays))

ggplot(los_lace_plot, aes(x = LACE, y = mean.stay, lty = Gender)) +

geom_line() +

theme_minimal() +

scale_x_continuous(breaks = seq(4, 18, 2), limits = c(4, 18)) +

scale_y_continuous(breaks = seq(0, 16, 2), limits = c(0, 16)) +

labs(y = "Average LOS") +

ggtitle("Average Length of Stay by LACE Score, Gender")

los_hos_plot <- snf_readmits %>%

group_by(HOSPITAL, Gender) %>%

summarize(mean.stay = mean(StayDurationDays))

ggplot(los_hos_plot, aes(x = HOSPITAL, y = mean.stay, lty = Gender)) +

geom_line() +

theme_minimal() +

scale_x_continuous(breaks = seq(0, 11, 2), limits = c(0, 11)) +

scale_y_continuous(breaks = seq(0, 16, 2), limits = c(0, 16)) +

labs(y = "Average LOS") +

ggtitle("Average Length of Stay by HOSPITAL Score, Gender")

```

```{r los_mods}

# Linear Models

cci_los_mod <- lm(StayDurationDays ~ CCI, data = snf_data_fit)

lace_los_mod <- lm(StayDurationDays ~ LACE + Gender, data = snf_data_fit)

hos_los_mod <- lm(StayDurationDays ~ HOSPITAL + Gender, data = snf_data_fit)

# Pearson's correlation coef

cors <- c(round(cor(snf_data_fit$CCI, snf_data_fit$StayDurationDays), 3),

round(cor(snf_data_fit$LACE, snf_data_fit$StayDurationDays), 3),

round(cor(snf_data_fit$HOSPITAL, snf_data_fit$StayDurationDays), 3))

los_ests <- c(round(cci_los_mod$coefficients[2], 3),

round(lace_los_mod$coefficients[2], 3),

round(hos_los_mod$coefficients[2], 3))

los_ci <- c(paste(round(confint(cci_los_mod)[2,1], 3),

round(confint(cci_los_mod)[2,2], 3), sep = ", "),

paste(round(confint(lace_los_mod)[2,1], 3),

round(confint(lace_los_mod)[2,2], 3), sep = ", "),

paste(round(confint(hos_los_mod)[2,1], 3),

round(confint(hos_los_mod)[2,2], 3), sep = ", "))

score <- c("CCI", "LACE", "HOSPITAL")

los_tab <- data.frame(cbind(score, cors, los_ests, los_ci))

colnames(los_tab) <- c("Score", "Pearson's Corr", "LM Est", "95% CI")

los_models <- kbl(los_tab, caption = "Length of Stay by Score",

linesep = "\\addlinespace", escape = FALSE) %>%

kable_classic_2(full_width = FALSE)

los_models

```