02_adjusted_models.Rmd

---
title: "SARS-CoV-2 vs Influenza: Adjusted modeling of outcomes"
author: "Patrick G. Lyons, MD, MSc"
output: html_document
date: "2022-08-26"
---

This script performs adjusted modeling of outcomes (death/hospice discharge, invasive mechanical ventilation, ventilator free days) in data from patients with SARS-CoV-2 and influenza.

# Load libraries
```{r libraries, include = FALSE}
library(data.table)
library(tidyverse)
library(tidytable)
library(here)
library(tableone)
```

# Load cleaned data
```{r load data}
df <- fread(here("covflu_combined_deidentified.csv"))

# create binary COVID indicator and drop multistate model variables (not needed in this script)
df <-
  df %>%
  mutate.(
    covid = case_when.(
      virus == "SARS-CoV-2" ~ 1,
      virus == "Influenza"  ~ 0,
      TRUE                  ~ NA_integer_
    )
  ) %>%
  select.(
    -c(max_o2_12h, hours_in_hosp, hours_12)
  ) %>%
  distinct.() # one row per encounter
```

# Fit a mixed-effects logistic regression to determine the independent relationship between virus and outcomes.
```{r multilevel model - primary outcome}
library(lme4)

clustered_model <- 
  lme4::glmer(
      dead_or_hospice ~
      covid + 
      age_years + 
      bmi + 
      race_nonwhite + 
      female + 
      elix_chf +
      elix_arrhythmia +
      elix_valvular_disease  +
      elix_pulmonary_circulation_disorders +
      elix_peripheral_vascular_disorders +  
      elix_hypertension_combined +
      elix_paralysis +
      elix_neuro_other +
      elix_chronic_pulmonary_disease +
      elix_dm_combined +
      elix_hypothyroidism +
      elix_renal_failure +
      elix_liver_disease +
      elix_pud +
      elix_hiv +
      elix_lymphoma +
      elix_metastatic_cancer +
      elix_solid_tumor_without_metastasis +
      elix_ra_cvd +
      elix_coagulopathy +
      elix_obesity +
      elix_weight_loss +
      elix_fluid_and_electrolye_disorders +
      elix_blood_loss_anemia +
      elix_deficiency_anemias +
      elix_alcohol_abuse +
      elix_drug_abuse +
      elix_psychoses +
      elix_depression + 
      (1 | hospital),
    family  = binomial,
    data    = df,
    control = glmerControl(optimizer = "bobyqa"),
    nAGQ    = 10
  )

se <- sqrt(diag(vcov(clustered_model)))
# table of estimates with 95% CI
(tab <- 
    cbind(
      Est = fixef(clustered_model), 
      LL = fixef(clustered_model) - 1.96 * se, 
      UL = fixef(clustered_model) + 1.96 *se
    )
)

exp(tab)
```

```{r multilevel model - ventilator}
library(lme4)

clustered_model <- 
  lme4::glmer(
      imv_enc_01 ~
      covid + 
      age + 
      bmi + 
      race_nonwhite + 
      female + 
      elix_chf +
      elix_arrhythmia +
      elix_valvular  +
      elix_phtn +
      elix_pvd +  
      elix_htn +
      elix_paralysis +
      elix_neuro_other +
      elix_pulmonary +
      elix_dm +
      elix_d_mcx +
      elix_hypothyroid +
      elix_renal +
      elix_liver +
      elix_pud +
      elix_hiv +
      elix_lymphoma +
      elix_mets +
      elix_tumor +
      elix_rheumatic +
      elix_coagulopathy +
      elix_obesity +
      elix_weight_loss +
      elix_fluids_lytes +
      elix_blood_loss +
      elix_anemia +
      elix_alcohol +
      elix_drugs +
      elix_psychoses +
      elix_depression + 
      (1 | hospital),
    family  = binomial,
    data    = df,
    control = glmerControl(optimizer = "bobyqa"),
    nAGQ    = 10
  )

se <- sqrt(diag(vcov(clustered_model)))
# table of estimates with 95% CI
(tab <- 
    cbind(
      Est = fixef(clustered_model), 
      LL  = fixef(clustered_model) - 1.96 * se, 
      UL  = fixef(clustered_model) + 1.96 *se
    )
)

exp(tab)
```

# Fine-Gray model adjusted for length of stay
```{r Fine-Gray model for LOS}
library(cmprsk)

q <- 
  df %>%
  rename.(covid01 = covid) |>
  mutate.(
    hospital     = factor(hospital),
    outcome_surv = case_when.(
      dead_or_hospice == 1 ~ 0,
      dead_or_hospice == 0 ~ 1,
      TRUE                 ~ 2,
    )
  ) 

q <- mltools::one_hot(as.data.table(q)) # dummies for FG

x <- 
  q[,
    c(
    "covid01",
    "hospital_amh",
    "hospital_bjsph",
    "hospital_bjwch",
    "hospital_boone",
    "hospital_ch",
    "hospital_mbmc",
    "hospital_mbsh",
    "hospital_parkland",
    "hospital_pwh",
    "age",
    "bmi",
    "female",
    "race_nonwhite",  
    "elix_chf",
    "elix_arrhythmia",
    "elix_valvular",
    "elix_phtn",
    "elix_pvd",  
    "elix_htn", 
    "elix_paralysis",
    "elix_neuro_other",
    "elix_pulmonary",
    "elix_dm",
    "elix_d_mcx", 
    "elix_hypothyroid",
    "elix_renal",
    "elix_liver", 
    "elix_pud",
    "elix_hiv",
    "elix_lymphoma",
    "elix_mets",
    "elix_tumor",
    "elix_rheumatic",
    "elix_coagulopathy",
    "elix_obesity",
    "elix_weight_loss",
    "elix_fluids_lytes",
    "elix_blood_loss",
    "elix_anemia",
    "elix_alcohol",
    "elix_drugs",
    "elix_psychoses",
    "elix_depression"
    )
  ]
  
x <- as.matrix(x)

q %>%
  select_if(is.numeric) %>%
  cor(use = "complete.obs") %>% 
  corrplot::corrplot()

null_mod <- 
  glm(
    dead_or_hospice ~
      covid + 
      hospital_amh +
      hospital_bjsph +
      hospital_bjwch +
      hospital_boone +
      hospital_ch +
      hospital_mbmc +
      hospital_mbsh +
      hospital_parkland +
      hospital_pwh +
      elix_chf +
      elix_arrhythmia +
      elix_valvular_disease  +
      elix_pulmonary_circulation_disorders +
      elix_peripheral_vascular_disorders +  
      elix_hypertension_combined +
      elix_paralysis +
      elix_neuro_other +
      elix_chronic_pulmonary_disease +
      elix_dm_combined +
      elix_hypothyroidism +
      elix_renal_failure +
      elix_liver_disease +
      elix_pud +
      elix_hiv +
      elix_lymphoma +
      elix_metastatic_cancer +
      elix_solid_tumor_without_metastasis +
      elix_ra_cvd +
      elix_coagulopathy +
      elix_obesity +
      elix_weight_loss +
      elix_fluid_and_electrolye_disorders +
      elix_blood_loss_anemia +
      elix_deficiency_anemias +
      elix_alcohol_abuse +
      elix_drug_abuse +
      elix_psychoses +
      elix_depression,
    family = "binomial",
    data   = q
  )

q_step <- stats::step(null_mod, direction = "backward")

los_fg <- crr(
  ftime     = q$los_hosp_hours,
  fstatus   = q$outcome_surv,
  cov1      = x,
  na.action = na.omit,
  failcode  = 1,
  cencode   = 2,
  maxiter   = 100
)

summary(los_fg)
```

# Negative binomial model for 28-day VFD
```{r vfd}
library(pscl)
library(MASS)
library(boot)
library(lmtest)

df <- 
  df %>%
  mutate.(vfd_28 = as.integer(vfd_28))

m1 <- zeroinfl(
  vfd_28 ~ 
    covid + 
    hospital +
    age_years + 
    bmi + 
    female + 
    race_nonwhite + 
    elix_chf +
    elix_arrhythmia + 
    elix_valvular_disease + 
    elix_pulmonary_circulation_disorders + 
    elix_peripheral_vascular_disorders + 
    elix_hypertension_combined +
    elix_paralysis + 
    elix_neuro_other + 
    elix_chronic_pulmonary_disease + 
    elix_dm_combined +
    elix_hypothyroidism + 
    elix_renal_failure + 
    elix_liver_disease + 
    elix_pud +
    elix_hiv + 
    elix_lymphoma + 
    elix_metastatic_cancer + 
    elix_solid_tumor_without_metastasis + 
    elix_ra_cvd +
    elix_coagulopathy + 
    elix_obesity + 
    elix_weight_loss + 
    elix_fluid_and_electrolye_disorders +
    elix_blood_loss_anemia + 
    elix_deficiency_anemias + 
    elix_alcohol_abuse + 
    elix_drug_abuse + 
    elix_psychoses +
    elix_depression | 
    covid + 
    hospital +
    age_years + 
    bmi + 
    female + 
    race_nonwhite + 
    elix_chf +
    elix_arrhythmia + 
    elix_valvular_disease + 
    elix_pulmonary_circulation_disorders + 
    elix_peripheral_vascular_disorders + 
    elix_hypertension_combined +
    elix_paralysis + 
    elix_neuro_other + 
    elix_chronic_pulmonary_disease + 
    elix_dm_combined +
    elix_hypothyroidism + 
    elix_renal_failure + 
    elix_liver_disease + 
    elix_pud +
    elix_hiv + 
    elix_lymphoma + 
    elix_metastatic_cancer + 
    elix_solid_tumor_without_metastasis + 
    elix_ra_cvd +
    elix_coagulopathy + 
    elix_obesity + 
    elix_weight_loss + 
    elix_fluid_and_electrolye_disorders +
    elix_blood_loss_anemia + 
    elix_deficiency_anemias + 
    elix_alcohol_abuse + 
    elix_drug_abuse + 
    elix_psychoses +
    elix_depression,
   dist = 'negbin',
   link = 'logit',
   data = df
  )
# variables after | indicate the logit model predicting excessive zeros

summary(m1)

exp(coef(m1))

# bootstrap CIs

f <- function(data, i) {
  require(pscl)
  m <- 
    zeroinfl(
        vfd_28 ~ 
          covid + 
          hospital +
          age_years + 
          bmi + 
          female + 
          race_nonwhite + 
          elix_chf +
          elix_arrhythmia + 
          elix_valvular_disease + 
          elix_pulmonary_circulation_disorders + 
          elix_peripheral_vascular_disorders + 
          elix_hypertension_combined +
          elix_paralysis + 
          elix_neuro_other + 
          elix_chronic_pulmonary_disease + 
          elix_dm_combined +
          elix_hypothyroidism + 
          elix_renal_failure + 
          elix_liver_disease + 
          elix_pud +
          elix_hiv + 
          elix_lymphoma + 
          elix_metastatic_cancer + 
          elix_solid_tumor_without_metastasis + 
          elix_ra_cvd +
          elix_coagulopathy + 
          elix_obesity + 
          elix_weight_loss + 
          elix_fluid_and_electrolye_disorders +
          elix_blood_loss_anemia + 
          elix_deficiency_anemias + 
          elix_alcohol_abuse + 
          elix_drug_abuse + 
          elix_psychoses +
          elix_depression | 
          covid + 
          hospital +
          age_years + 
          bmi + 
          female + 
          race_nonwhite + 
          elix_chf +
          elix_arrhythmia + 
          elix_valvular_disease + 
          elix_pulmonary_circulation_disorders + 
          elix_peripheral_vascular_disorders + 
          elix_hypertension_combined +
          elix_paralysis + 
          elix_neuro_other + 
          elix_chronic_pulmonary_disease + 
          elix_dm_combined +
          elix_hypothyroidism + 
          elix_renal_failure + 
          elix_liver_disease + 
          elix_pud +
          elix_hiv + 
          elix_lymphoma + 
          elix_metastatic_cancer + 
          elix_solid_tumor_without_metastasis + 
          elix_ra_cvd +
          elix_coagulopathy + 
          elix_obesity + 
          elix_weight_loss + 
          elix_fluid_and_electrolye_disorders +
          elix_blood_loss_anemia + 
          elix_deficiency_anemias + 
          elix_alcohol_abuse + 
          elix_drug_abuse + 
          elix_psychoses +
          elix_depression,
    data  = df[i, ], 
    dist  = "negbin"
  )
  as.vector(t(do.call(rbind, coef(summary(m)))[, 1:2]))
}

set.seed(10)
(res <- boot(df, f, R = 10000, parallel = "multicore", ncpus = 7))

## basic parameter estimates with percentile and bias adjusted CIs
parms <- t(sapply(seq(1, 145, 2), function(i) {
  out <- boot.ci(res, index = c(i, i + 1), type = c("perc", "bca"))
  with(out, c(Est = t0, pLL = percent[4], pUL = percent[5],
    bcaLL = bca[4], bcaUL = bca[5]))
}))

## add row names
row.names(parms) <- names(coef(m1))
## print results
parms

expparms <- t(sapply(c(1, 3, 5, 7, 9), function(i) {
  out <- boot.ci(res, index = c(i, i + 1), type = c("perc", "bca"), h = exp)
  with(out, c(Est = t0, pLL = percent[4], pUL = percent[5],
    bcaLL = bca[4], bcaUL = bca[5]))
}))


# dispersion statistic
E2 <- resid(m1, type = "pearson")
N <- nrow(df)
p <- length(coef(m1)) + 1 # +1 is due to theta
sum(E2^2) / (N-p) # 0.825

# compare to null model
m0 <- update(m1, . ~ 1)
pchisq(2 * (logLik(m1) - logLik(m0)), df = 3, lower.tail = FALSE) # m1 model is statistically significant

# compare to standard negative binomial regression
m2 <- MASS::glm.nb(vfd_28 ~ hospital + age_years + bmi + female + race_nonwhite + elix_chf +
                       elix_arrhythmia + elix_valvular_disease + elix_pulmonary_circulation_disorders +
                       elix_peripheral_vascular_disorders + elix_hypertension_combined +
                       elix_paralysis + elix_neuro_other + 
                       elix_chronic_pulmonary_disease + elix_dm_combined +
                       elix_hypothyroidism + elix_renal_failure + elix_liver_disease + elix_pud +
                       elix_hiv + elix_lymphoma + elix_metastatic_cancer + 
                       elix_solid_tumor_without_metastasis + elix_ra_cvd +
                       elix_coagulopathy + elix_obesity + elix_weight_loss + 
                       elix_fluid_and_electrolye_disorders +
                       elix_blood_loss_anemia + elix_blood_loss_anemia + elix_alcohol_abuse + 
                       elix_drug_abuse + elix_psychoses + elix_depression + covid, data = df)
# leave out any of the variables that were after | in the m1 model

summary(m2)

# test to compare zero-inflated neg binom to standard neg binom
lmtest::lrtest(m1, m2)

#sd = se(sqrt(n)) 
# 0.0072719*69.17369 // count - 0.5030242
# ci for count -- -0.0428 to -0.0142
# exponentiate -- 0.96 / 0.99
```