03-results.Rmd

---
editor_options:
  chunk_output_type: console
output:
  pdf_document: default
  word_document: default
---
# Results {-}


```{r setup, include=FALSE, cache=F}
knitr::opts_chunk$set(echo = FALSE, warning=FALSE, message = FALSE, results = TRUE, cache = F, fig.align = "center", out.width = "100%", cache.lazy = FALSE)


# https://stackoverflow.com/questions/46080853/why-does-rendering-a-pdf-from-rmarkdown-require-closing-rstudio-between-renders/46083308#46083308
library(kableExtra)
if (knitr::is_latex_output()) {
  usepackage_latex("booktabs")
  usepackage_latex("longtable")
  usepackage_latex("array")
  usepackage_latex("multirow")
  usepackage_latex("wrapfig")
  usepackage_latex("float")
  usepackage_latex("colortbl")
  usepackage_latex("pdflscape")
  usepackage_latex("tabu")
  usepackage_latex("threeparttable")
  usepackage_latex("threeparttablex")
  usepackage_latex("ulem", "normalem")
  usepackage_latex("makecell")
}


# format = 'html'
# synth_data = FALSE

library(tidyverse)
library(stringr)
library(tableone)
library(nlme)
library(boot)

# Real data ---------
if(synth_data == FALSE) {
  #df <- read_csv('Data/final_wi_dataset-2020-03-03.csv') %>%
  df <- read_csv('Data/final_wi_dataset-with_rp_id_2020-05-26.csv') %>%
    mutate(
      intervention = ifelse(monthsSinceIntervention > 0, "Post", "Pre"),
      rot_paras = ifelse(rp == 1, "Rotational Paramedics", "Control"),
      rp_table = ifelse(rp == 1, "Intervention", "Control"),
      age = ordered(age, levels = c("[0,5]", "(5,10]", "(10,15]", "(15,20]", "(20,25]", "(25,30]", "(30,35]", "(35,40]", "(40,45]", "(45,50]", "(50,55]", "(55,60]", "(60,65]","(65,70]","(70,75]", "(75,80]", "(80,85]", "(85,90]", "(90,95]", "(95,100]", "(100,105]", "(105,110]")),
      risk = ordered(risk, levels=c("Low", "Low-Medium","Medium", "High")),
      los = ordered(los, levels=c("<1 year", "1 to 5 years", ">5 years")),
      ltc = ordered(ltc, levels=c("[0,4]", "(4,8]", "(8,12]","(12,16]")),
      `non-conveyed` = ifelse(conveyed == 1, 0, 1),
      `safe non-conveyance` = case_when(
          conveyed == 1 ~ 0,
          recontact == 1 ~ 0,
          TRUE ~ 1
        ),
      newTimeElapsed = ifelse(timeElapsedMonths < 13, timeElapsedMonths + 1, timeElapsedMonths - 1)
    ) %>% filter(newTimeElapsed < 25) %>%
    dplyr::select("safe non-conveyance", "non-conveyed", "season", "ooh", "call_cat","rural_urban", "imd_decile",  "ltc", "age", "sex", "risk" , "wi", "los", "intervention", "rot_paras", "rp", "rp_table", "newTimeElapsed", "conveyed", "recontact", "recontact_conveyed", conveyed, recontact, recontact_RRV, recontact_Amb, rp_id)

}

# Synthetic data ----------
if(synth_data == TRUE) {
  
  df <- readRDS('SynData/synthetic-dataset-with-wi.rds') %>%
    mutate(
      call_cat = as.character(call_cat),
      age = ordered(age, levels = c("[0,5]", "(5,10]", "(10,15]", "(15,20]", "(20,25]", "(25,30]", "(30,35]", "(35,40]", "(40,45]", "(45,50]", "(50,55]", "(55,60]", "(60,65]","(65,70]","(70,75]", "(75,80]", "(80,85]", "(85,90]", "(90,95]", "(95,100]", "(100,105]", "(105,110]")),
      los = ordered(los, levels=c("<1 year", "1 to 5 years", ">5 years")),
      rp_table = ifelse(rp == 1, "Intervention", "Control")
    )

}

# Economic analysis -----------------
# Calculate the per incident cost for an SP
# 10 weeks 

ten_weeks_salary = (31121/52) * 10

# 10 weeks salary for 10 SPs
ten_for_ten = ten_weeks_salary * 10

# SPs attended 2059 cases (including missing wi) in the post-rotation phase

salary_per_inc = round(ten_for_ten / 2059, 2)

# £29.07 per incident.

# Calculate the total cost for each incident based on the unit costs
df$cost <- mapply(function(conveyed, recontact, recontact_conveyed, rp, intervention)
  {
  
    call_cost <- 7.33
    S_and_T <- 209.38
    S_T_and_C <- 257.34
    A_E <- 135
    
    cost = 0
    
    # Add placement cost if rp
    
    if(rp == "Rotational Paramedics" & intervention == "Post") {
      cost = cost + salary_per_inc
    }
    
    # Add 999 call
    
    cost = cost + call_cost
    
    # If no ambulances and RRV conveyed, then need to ST and C
    
    if(conveyed == 1) {
      cost = cost + S_T_and_C + A_E
    } else {
      cost = cost + S_and_T
    }
    
    # If not conveyed but there is a recontact
    # Then need to add these costs
    
    if(conveyed == 0 & recontact == 1) {
      
      # Add 999 call
      
      cost = cost + call_cost
      
      # If no ambulances and RRV conveyed, then need to ST and C
      
      if(recontact_conveyed == 1) {
        cost = cost + S_T_and_C + A_E
      } else {
        cost = cost + S_and_T
      }
      
    }
    
    return(cost)
    
  },
  conveyed = df$conveyed, recontact = df$recontact, recontact_conveyed = df$recontact_conveyed, rp = df$rot_paras, intervention = df$intervention)

# Table 1 ---------------------

table1_df <- df %>%
  mutate(
    age = fct_collapse(age,
                       "[0,15]" = c("[0,5]", "(5,10]", "(10,15]"),
                       "(15, 65]" = c("(15,20]", "(20,25]", "(25,30]", "(30,35]", "(35,40]", "(40,45]", "(45,50]", "(50,55]", "(55,60]", "(60,65]"),
                       "(65,80]" = c("(65,70]", "(70,75]", "(75,80]"),
                       "(80,110]" = c("(80,85]", "(85,90]", "(90,95]", "(95,100]", "(100,105]", "(105,110]"),
                       NULL = "Unknown"),
    wi = fct_lump(wi, n = 10)
  )
  

matchedTbl_pre_post_control_rp <- CreateTableOne(
  vars = c("safe non-conveyance", "non-conveyed", "season", "ooh", "call_cat","rural_urban", "imd_decile",  "ltc", "age", "sex", "risk" , "wi", "los"),
  strata = c("intervention", "rp_table"),
  data = table1_df,
  test = F,
  factorVars = c("safe non-conveyance", "non-conveyed", "season", "call_cat", "ooh", "risk", "los", "age", "sex", "imd_decile", "rural_urban", "ltc", "wi")
)

# table1_df %>% 
#   #unite(col = "group", c(intervention, rp_table)) %>% 
#   filter(intervention == "Pre") %>%
#   select(`safe non-conveyance`, `non-conveyed`, season, ooh, call_cat, rural_urban, imd_decile, ltc, age, sex, risk, wi, los, rp_table) %>%
#   tbl_summary(by = rp_table) %>%
#   add_p()
# 

matrix_tbl <- print(matchedTbl_pre_post_control_rp)
col1 <- rownames(matrix_tbl)

# Formatting of headings

col1[2] <- "Appropriately not conveyed n (%)"
col1[3] <- "Not conveyed n (%)"
col1[4] <- "Yearly quarter n (%)"
col1[9] <- "Out-of-hours n (%)"
col1[10] <- "Call category"
col1[16] <- "Urban location n (%)"
col1[17] <- "IMD decile n (%)"
col1[28] <- "Prevalence of Long-term conditions n (%)"
col1[33] <- "Patient age in years n (%)"
col1[38] <- "Patient sex n (%)"
col1[42] <- "NEWS category n (%)"
col1[47] <- "Clinical working impression n (%)"
col1[59] <- "Years registered as a paramedic"

# This will come in handy for Table 1 headers
#list_of_cols <- c(4, 10,  17, 28, 33, 38, 42, 47, 59)


df_summary <- bind_cols(data.frame(Measure = col1, stringsAsFactors = F), as_tibble(matrix_tbl)) %>%
  dplyr::select(Measure, `Pre:Control`, `Pre:Intervention`, `Post:Control`, `Post:Intervention`)

colnames(df_summary) <- c("Measure", "Control", "Intervention", "Control", "Intervention")



```


```{r sensitivity-analysis, results = FALSE}

# Need to undertake the sensitivity analysis first to report the results later.
source('Code/prep_no_wi.R')

```

As part of the HEE rotational paramedic pilot, 10 SPs undertook a 10 week placement in a primary care setting in the Leeds area. Five commenced their placement in June 2018, with a further three starting in August 2018 and the final two starting their placement in October 2018.

Between 1st June 2017 and 31st December, 2019 there were 8849 incidents attended by one of the intervention group SPs. Once data was adjusted to remove any cases during the 10 week GP placement, and outside of the 12 months prior to the start of the rotation and 12 months after the end of the rotation, 7349 cases remained (Figure \@ref(fig:figure1)) . A further 6 had no sex recorded, 15 had no age recorded, 8 had no post code and 4 cases were excluded due to either a missing index of multiple deprivation decile (3 cases), rural urban classification (3 cases) and/or prevalence of missing long-term condition data (4 cases). Finally, no working impression was included in 1785 cases, resulting in a final dataset of 5537/7349 (75.3%) cases for inclusion in the final analysis. Due to the high number of missing working impressions, a sensitivity analysis was performed excluding the working impression as a variable (Supplementary 1).


```{r figure1, fig.cap="STROBE flow chart of patient selection" }

# https://rpubs.com/phiggins/461686

data <- tibble(x= 1:100, y= 1:100)

p <- data %>%
  ggplot(aes(x, y)) +
  scale_x_continuous(minor_breaks = seq(10, 100, 10), limits = c(15, 95)) +
  scale_y_continuous(minor_breaks = seq(10, 100, 10), limits = c(20,100)) +
  theme_linedraw()

p <- p +
  # Total cases
  geom_rect(xmin = 36, xmax=64, ymin=94, ymax=100, color='black',
            fill='white', size=0.25) +
  annotate('text', x= 50, y=97,label= 'Incidents attended by intervention SPs (n=8849)', size=2.5) +
  
  # Arrows
  geom_segment(x=50, xend=50, y=94, yend=83.5, 
  size=0.15, linejoin = "mitre", lineend = "butt",
  arrow = arrow(length = unit(2, "mm"), type= "closed")) +
  
  geom_segment(
    x=50, xend=69.5, y=88.5, yend=88.5, 
    size=0.15, linejoin = "mitre", lineend = "butt",
    arrow = arrow(length = unit(2, "mm"), type= "closed")) + 
  
  # Exclude those not in 12 month pre/post
  geom_rect(xmin = 70, xmax=95, ymin=84, ymax=93, color='black',
            fill='white', size=0.25) +
  annotate('text', x= 71, y=89,label= 'Excluded (n=1500)\n  Incident occured more than 12 months before/after\n  or during GP placement', size=2.5, hjust=0) +
  
  # Cases that are potentially eligible
  geom_rect(xmin = 36, xmax=64, ymin=77, ymax=83, color='black',
            fill='white', size=0.25) +
  annotate('text', x= 50, y=80,label= 'Incidents eligible for inclusion (n=7349)', size=2.5) +
  
  # Arrows
  geom_segment(x=50, xend=50, y=77, yend=56.5, 
  size=0.15, linejoin = "mitre", lineend = "butt",
  arrow = arrow(length = unit(2, "mm"), type= "closed")) +
  
  geom_segment(
    x=50, xend=69.5, y=66.5, yend=66.5, 
    size=0.15, linejoin = "mitre", lineend = "butt",
    arrow = arrow(length = unit(2, "mm"), type= "closed")) + 
  
  # Exclude those who could have been eligible but had to be removed
  geom_rect(xmin = 70, xmax=95, ymin=58, ymax=75, color='black',
            fill='white', size=0.25) +
  annotate('text', x= 71, y=67,label= 'Excluded (n=1812)\n  No sex recorded (n=6)\n  No age recorded (n=15)\n  No postcode (n=8)\n  Missing IMD, rural/urban, long-term condition (n=4)\n  No working impression (n=1785)', size=2.5, hjust=0) +
  
  # Final set for analysis
  geom_rect(xmin = 36, xmax=64, ymin=50, ymax=56, color='black',
            fill='white', size=0.25) +
  annotate('text', x= 50, y=53,label= 'Incidents available for matching (n=5537)', size=2.5) +
  
  # Arrows
  geom_segment(x=50, xend=50, y=50, yend=40.5, 
  size=0.15, linejoin = "mitre", lineend = "butt",
  arrow = arrow(length = unit(2, "mm"), type= "closed")) +
  
  geom_segment(
    x=50, xend=69.5, y=44.5, yend=44.5, 
    size=0.15, linejoin = "mitre", lineend = "butt",
    arrow = arrow(length = unit(2, "mm"), type= "closed")) + 
  
  # Exclude unmatched cases
    geom_rect(xmin = 70, xmax=95, ymin=41, ymax=47, color='black',
            fill='white', size=0.25) +
  annotate('text', x=71, y=44,label= 'Excluded (n=339)\n  Incidents not matched', size=2.5, hjust=0) +
  
    # Matched cases
  geom_rect(xmin = 36, xmax=64, ymin=36, ymax=40, color='black',
            fill='white', size=0.25, size=0.25) +
  annotate('text', x=50, y=38,label= 'Matched incidents (n=5198)', size=2.5) +

  # Pre-placement

  geom_rect(xmin = 16, xmax=44, ymin=20, ymax=24, color='black',
            fill='white', size=0.25, size=0.25) +
  annotate('text', x=30, y=22,label= 'Pre-placement incidents (n=3297)', size=2.5) +

  # Post-placement
  
    geom_rect(xmin = 56, xmax=84, ymin=20, ymax=24, color='black',
            fill='white', size=0.25, size=0.25) +
  annotate('text', x=70, y=22,label= 'Post-placement incidents (n=1901)', size=2.5) +
  
  # Final Arrows
  geom_segment(x=50, xend=50, y=36, yend=30, 
  size=0.15, linejoin = "mitre", lineend = "butt") +
  
  geom_segment(
    x=50, xend=30, y=30, yend=30, 
    size=0.15, linejoin = "mitre", lineend = "butt") +
  
    geom_segment(
    x=50, xend=70, y=30, yend=30, 
    size=0.15, linejoin = "mitre", lineend = "butt") +
  
    geom_segment(
    x=30, xend=30, y=30, yend=24.5, 
    size=0.15, linejoin = "mitre", lineend = "butt",
    arrow = arrow(length = unit(2, "mm"), type= "closed")) +
  
    geom_segment(
    x=70, xend=70, y=30, yend=24.5, 
    size=0.15, linejoin = "mitre", lineend = "butt",
    arrow = arrow(length = unit(2, "mm"), type= "closed")) 

p + theme_void()

```

## Matched dataset for analysis {-}

The matching algorithm utilised 5198/5537 (93.9%) cases (Table \@ref(tab:table1)). Overall, the control group was closely matched to the rotational paramedic (intervention group) incidents (defined as less than 10% in standardised mean difference). Only the NEWS risk category and prevalence of long-term conditions were outside this limit.

In addition to the substantial reduction in number of cases attended in the post-placement phase, there were also other differences in pre- and post-placement cases, which could have contributed to the change in rate of non-conveyance, validating the decision to include a matched control (Table \@ref(tab:table1)).

## Pre- and Post-rotation exploratory data analysis {-}

Operational activity was lower post-placement since intervention group SPs had to undertake a range of additional activities in the post-placement phase, including staffing a dedicated SP dispatch desk in EOC and working in GP practices as part of the HEE pilot (Table 2). Post-placement, there were also differences in triage call category and physiological acuity based on the NEWS risk category that the SPs were tasked to attend (Supplementary 2).


```{r table1, cache = F}
  
library(kableExtra)

# This will come in handy for Table 1 headers
#list_of_cols <- c(4, 10, 17, 28, 32, 55, 59, 64, 103)
list_of_cols <- c(4, 10,  17, 28, 33, 38, 42, 47, 59)
df_summary <- df_summary[-list_of_cols, ]
rownames(df_summary) = NULL

# Add asterix for footnote for pain: other
df_summary$Measure[49] = paste0(df_summary$Measure[49], '*')

kableone(df_summary, caption="Comparison of matched control and rotational paramedic groups, stratified by pre and post-placement phases", booktabs = TRUE, longtable = TRUE, format = format) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"), latex_options = c("repeat_header", "striped", "hold_position")) %>%
  add_header_above(c(" ", "Pre-placement" = 2, "Post-placement" = 2)) %>%
  pack_rows(col1[4], 4, 7) %>%
  pack_rows(col1[10], 9, 13) %>%
  pack_rows(col1[17], 15, 24) %>%
  pack_rows(col1[28], 25, 28) %>%
  pack_rows(col1[33], 29, 32) %>%
  pack_rows(col1[38], 33, 35) %>%
  pack_rows(col1[42], 36, 39) %>%
  pack_rows(col1[47], 40, 50) %>%
  pack_rows(col1[59], 51, 53) %>%
  footnote(
    general = "lrti - lower respiratory tract infection",
    symbol = "This working impression denotes pain that has not been classed as abdominal pain, cardiac chest pain or non-traumatic back pain.", threeparttable = T)
```


```{r activity-stats}

# Number of incidents per month
op_act <- df %>%
  filter(rp == 1) %>%
  count(intervention, newTimeElapsed)

op_act_pre = fivenum(op_act$n[op_act$intervention=="Pre"])
op_act_post = fivenum(op_act$n[op_act$intervention=="Post"])

op_act_pre_text = paste0("median ", op_act_pre[3], " incidents per month (IQR ", op_act_pre[2], "--", op_act_pre[4], ")")
op_act_post_text = paste0("median ", op_act_post[3], " incidents per month (IQR ", op_act_post[2], "--", op_act_post[4], ")")

# Cat 1 and 2 calls
cat_df <- df %>% 
  filter(rp == 1) %>%
  count(cat1or2 = call_cat %in% c("cat1", "cat2"), newTimeElapsed) 

cat_act_pre = cat_df %>% filter(newTimeElapsed < 13) %>% pull(n) %>% fivenum
cat_act_post = cat_df %>% filter(newTimeElapsed >= 13) %>% pull(n) %>% fivenum

cat_act_pre_text = paste0("median ", cat_act_pre[3], " incidents per month (IQR ", cat_act_pre[2], "--", cat_act_pre[4], ")")
cat_act_post_text = paste0("median ", cat_act_post[3], " incidents per month (IQR ", cat_act_post[2], "--", cat_act_post[4], ")")

# NEWS risk

new_df <- df %>% 
  filter(rp == 1) %>%
  count(lownews = risk == "Low", newTimeElapsed) 

new_act_pre = new_df %>% filter(newTimeElapsed < 13) %>% pull(n) %>% fivenum
new_act_post = new_df %>% filter(newTimeElapsed >= 13) %>% pull(n) %>% fivenum

new_act_pre_text = paste0("median ", new_act_pre[3], " incidents per month (IQR ", new_act_pre[2], "--", new_act_pre[4], ")")
new_act_post_text = paste0("median ", new_act_post[3], " incidents per month (IQR ", new_act_post[2], "--", new_act_post[4], ")")



```


```{r activity}

if(synth_data == TRUE) {
  
  activity_df <- readRDS('SynData/median_activity_by_month.rds') 
  
} else {
  activity_df <- readRDS('Data/median_activity_by_month.rds') 
}

# kableone(activity_df, caption="SP daliy activity (exluding leave and days off) stratified by pre- and post-placement time periods", booktabs = TRUE, longtable = TRUE, format = format) %>%
#   kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"), latex_options = c("repeat_header", "striped", "hold_position")) %>%
#   footnote(
#     general = "EOC - emergency operations centre, OPS - operational shift responding to 999 calls, STUDY - study leave and other training activities",threeparttable=T
#   )

ops_pre <- glue::glue("(median {activity_df[6,3]} (IQR {activity_df[6,4]}--{activity_df[6,5]}) hours per month)")
ops_post <- glue::glue("(median {activity_df[3,3]} (IQR {activity_df[3,4]}--{activity_df[3,5]}) hours per month)")
  
  

```

Operational activity was higher pre-placement `r ops_pre` than post-placement `r ops_post`, since intervention group SPs had to undertake a range of additional activities in the post-placement phase, including staffing a dedicated SP dispatch desk in EOC and working in GP practices as part of the HEE pilot. In addition, there were also differences in triage call category (a marker of perceived acuity following telephone triage of the call), and physiological acuity based on the NEWS risk category that the SPs were tasked to attend, (Table \@ref(tab:table1) and Supplementary 1).

## Time series {-}

```{r time-series-prep }

ts_df <- df %>%
  group_by(rot_paras, newTimeElapsed) %>%
  summarise(
    n = n(),
    propnonConveyed = sum(conveyed == 0)/n,
    propnonRecontact = sum(`safe non-conveyance` == 1)/n,
    intervention = first(intervention),
    rp = first(rp)
  ) %>% 
  ungroup() %>%
  mutate(
    intervention = ifelse(intervention == "Pre", 0, 1),
     timeSinceIntervention = ifelse(intervention == 0, 0, newTimeElapsed - 12)
  ) %>%
  rename(
    level = intervention,
    trend = timeSinceIntervention,
    time = newTimeElapsed
  ) %>%
  mutate(
    rptime = ifelse(rp == 1, time, 0),
    rplevel = ifelse(rp == 1, level, 0),
    rptrend = ifelse(rp == 1, trend, 0)
  )

ts_df_econ <- df %>%
  mutate(
    intervention = ifelse(intervention == "Pre", 0, 1),
     timeSinceIntervention = ifelse(intervention == 0, 0, newTimeElapsed - 12)
  ) %>%
  rename(
    level = intervention,
    trend = timeSinceIntervention,
    time = newTimeElapsed,
    snc = `safe non-conveyance`
  ) %>%
  mutate(
    rptime = ifelse(rp == 1, time, 0),
    rplevel = ifelse(rp == 1, level, 0),
    rptrend = ifelse(rp == 1, trend, 0)
  )

```


```{r fig5, fig.cap="Plot of data for OLS regression with control group"}

step4its_gg <- ts_df %>%
  mutate(
    outcome = round(propnonRecontact, 2)  )

step4its_gg_econ <- ts_df_econ %>%
  mutate(
    outcome = cost  
    )

cols2 <- c("control"="#0000ff", "intervention"="#ff0000")

fig5_fn <- function(data, flag) {
  a <- ggplot(data = data, aes(x = time, y = outcome)) + 
  # Prepare graph
  theme_bw() +
  scale_x_continuous(name="Months elapsed", breaks = seq(1,24,1), labels = seq(1,24,1), expand = c(0,0)) +
  geom_vline(xintercept = 12.5, color="black", size = 2) +
  annotate("text", label = "Pre-placement", x = 4, y = 0.9, size = 4, colour = "black") +
  annotate("text", label = "Post-placement", x = 16, y = 0.9, size = 4, colour = "black") +
  
  # Prep control/intervention data
  geom_point(data=data %>% filter(rp == 0), aes(color="control")) +
  geom_line(data=data %>% filter(rp == 0), aes(color="control"), linetype="solid") +
  geom_point(data=data %>% filter(rp == 1), aes(color="intervention")) +
  geom_line(data=data %>% filter(rp == 1), aes(color="intervention"), linetype="solid") +

  scale_color_manual(name="Group", values = cols2) +
  theme(legend.position = "bottom")
  
  if(flag == 'cits') {
     a +  scale_y_continuous(name = "Proportion of patients appropriately non-conveyed", expand = c(0,0), breaks=seq(0,1,0.1), limits = c(0,1), labels=scales::percent)
    } else {
     a + scale_y_continuous(name = "Mean cost (£)", expand = c(0,0), breaks=seq(0,400,50), limits = c(0,400)) 
    }

}

fig5 <- fig5_fn(step4its_gg, 'cits')

#fig5_econ <- fig5_fn(step4its_gg_econ, '')

```

```{r cits-workflow }

library(tidymodels)

lm_mod <- linear_reg() %>%
  set_engine('lm') 

lm_fit <- 
  lm_mod %>% 
  fit(propnonRecontact ~ time + rp + rptime + level + trend + rplevel + rptrend, data = ts_df)

mean_pred <- predict(lm_fit, new_data = ts_df)

plot_data <- 
  ts_df %>% 
  bind_cols(mean_pred)

# Intercept is the initial value of the control group
# time is existing trend in control group
# rp is the difference in levels between control and intervention
# rptime is the trend of hte intervention with reference to control
# level is post-pilot control change in level of non-conveyance
# trend is post-pilot control change in trend on non-conveyance
# rplevel shows post-pilot intervention group change in level
# rptrend is the post-pilot intervention group change in trend


dw_test <- tidy(lmtest::dwtest(lm(propnonRecontact ~ time + rp + rptime + level + trend + rplevel + rptrend, data = ts_df),iterations=12,alternative="two.sided"))


```

```{r cits-table-prep }

f <- function(x, places = 1, prop = T) {
  
  y <- sprintf(glue::glue("%.{places}f"), x * 100,1)
  
  if(!prop) {
      y <- sprintf(glue::glue("%.{places}f"), x)
  }
  
  return(y)
}

cits_tidy <- tidy(lm_fit, conf.int = T) %>%
  mutate_at(c("estimate", "conf.low", "conf.high"), f) %>%
  mutate(
    ci = glue::glue("{conf.low}--{conf.high}"),
    p.value = ifelse(p.value < 0.001, "<0.001", sprintf("%.3f", p.value))
  )


ols_table_fn <- function(model, flag = '') {
  tidy(model, conf.int = T) %>%
  mutate_at(c("estimate", "conf.low", "conf.high"), f) %>%
  mutate(
    ` ` = case_when(
      term == "(Intercept)" ~ "Initial control group level",
      term == "time" ~ "Pre-placement control group trend",
      term == "rp" ~ "Difference in level between control and intervention groups",
      term == "rptime" ~ "Intervention group trend relative to control group",
      term == "level" ~ "Post-placement change in control group level",
      term == "trend" ~ "Post-placement change in control group trend",
      term == "rplevel" ~ "Post-placement intervention group change in level relative to control group",
      term == "rptrend" ~ "Post-placement intervention group change in trend relative to control group",
      TRUE ~ 'Safe non-conveyance'
    ),
    `Coefficient (%)` = estimate,
    `95% CI` = glue::glue("{conf.low} to {conf.high}"),
    `P value` = ifelse(p.value < 0.001, "<0.001", sprintf("%.3f", p.value))
  ) %>%
  dplyr::select(` `, `Coefficient (%)`, `95% CI`, `P value`)
}


ols_table <- ols_table_fn(lm_fit)



```

Figure \@ref(fig:fig6) illustrates the change in raw and fitted CITS model data between the pre- and post-placement phase. There was no indication of auto-regression, where future values are based on past values (Durbin-Watson statistic `r round(dw_test$statistic,2)`, p=`r round(dw_test$p.value,2)`). Post-placement, the intervention group significantly increased their appropriate non-conveyance rate by `r cits_tidy$estimate[7]`% (95%CI `r cits_tidy$ci[7]`%, p=`r cits_tidy$p.value[7]`) relative to the control group (Table \@ref(tab:cits-table)). However, there was a non-statistically significant decrease in the trend of appropriate non-conveyance relative to the control group of `r cits_tidy$estimate[8]`% (95%CI `r cits_tidy$ci[8]`%, p=`r cits_tidy$p.value[8]`). The sensitivity analysis (excluding working impression as a matching variable) demonstrated a smaller increase appropriate non-conveyance in the intervention group relative to the control group of  `r cits_tidy_no_wi$estimate[7]`% (95%CI `r cits_tidy_no_wi$ci[7]`%, p`r cits_tidy_no_wi$p.value[7]`), and smaller decrease in the trend of appropriate non-conveyance (`r cits_tidy_no_wi$estimate[8]`%, 95%CI `r cits_tidy_no_wi$ci[8]`%, p=`r cits_tidy_no_wi$p.value[8]`).


```{r fig6, fig.cap="Effect of 10-week primary care placement on appropriate non-conveyance. a) Monthly appropriate non-conveyance rates b) Fitted CITS model. Dashed lines represent the counterfactuals (what would have happened in the absence of the intervention).", fig.height = 10}

# There was an outlier in the intervention group at month 18, but a sensitivity analysis conducted with the data point removed, suggested it had little effect on the post-rotation level and trend of appropriate non-conveyance (`r cits_tidy_no_18$estimate[7]`%, 95%CI `r cits_tidy_no_18$ci[7]`%, p=`r cits_tidy_no_18$p.value[7]` and `r cits_tidy_no_18$estimate[8]`%, 95%CI `r cits_tidy_no_18$ci[8]`%, p=`r cits_tidy_no_18$p.value[8]` respectively).


plot_fig6_fn <- function(data, model, flag) {

  # Alternating control and rp
  new_data_points <- data.frame(
    time = c(1, 1, 12, 12, 13, 13, 24, 24),
    rp = rep(c(0, 1), 4),
    rptime = c(0, 1, 0, 12, 0, 13, 0, 24),
    level = c(0, 0, 0, 0, 1, 1, 1, 1),
    trend = c(0, 0, 0, 0, 1, 1, 12, 12),
    rplevel = c(0, 0, 0, 0, 0, 1, 0, 1),
    rptrend = c(0, 0, 0, 0, 0, 1, 0, 12),
    stringsAsFactors = F
  )

  # Control then rp
  cf_data_points <- data.frame(
    time = c(13, 24, 13, 24),
    rp = c(0, 0, 1, 1),
    rptime = c(0, 0, 13, 24),
    level = c(0, 0, 1, 1),
    trend = c(0, 0, 12, 12),
    rplevel = c(0, 0, 0, 0),
    rptrend = c(0,0, 0, 0),
    stringsAsFactors = F
  )

  # 12 months rp non-conveyance
  
  rp_12_months_data_points <- data.frame(
    time = c(12, 24),
    rp = c(1, 1),
    rptime = c(12, 24),
    level = c(1, 1),
    trend = c(12, 12),
    rplevel = c(1, 1),
    rptrend = c(1, 12),
    stringsAsFactors = F
  )

  rp_12_months_pred <- predict(model, new_data = rp_12_months_data_points)
  rp_12_months_pred_ci <- predict(model, new_data = rp_12_months_data_points, type = "conf_int")

  mean_pred <- predict(model, new_data = new_data_points)
  cf_mean_pred <- predict(model, new_data = cf_data_points)

  plot_data <- new_data_points %>%
    bind_cols(mean_pred)

  cf_plot_data <- cf_data_points %>%
    bind_cols(cf_mean_pred)

  cols2 <- c("control"="#0000ff", "intervention"="#ff0000")

  a <- 'propnonRecontact'
  ypos <- 0.9
  
  if(flag == 'econ') {
    a <- 'cost' 
    ypos <- 250
  }
  
  b <- ggplot(data = data, aes(x = time, y = !!sym(a))) + 
  # Prepare graph
  theme_bw() +
  scale_x_continuous(name="Months elapsed", breaks = seq(1,24,1), labels = seq(1,24,1), expand = c(0,0)) +
  geom_vline(xintercept = 12.5, color="black", size=2) +
  annotate("text", label = "Pre-placement", x = 4, y = ypos, size = 4, colour = "black") +
  annotate("text", label = "Post-placement", x = 16, y = ypos, size = 4, colour = "black") +
  
  # Plot actual data points
  geom_point(data=data %>% filter(rp == 0), aes(color="control"), alpha = 0.2) +
  geom_point(data=data %>% filter(rp == 1), aes(color="intervention"), alpha = 0.2) +
  
  # Plot rp lines
  geom_line(data=plot_data %>% filter(rp == 1, level == 0), aes(y = .pred, color="intervention"), linetype="solid") +
  geom_line(data=plot_data %>% filter(rp == 1, level == 1), aes(y = .pred, color="intervention"), linetype="solid") +
  
  # Plot counterfactual rp lines
  geom_line(data=cf_plot_data %>% filter(rp == 1), aes(y = .pred, color="intervention"), linetype="dashed") +
  geom_line(data=cf_plot_data %>% filter(rp == 1), aes(y = .pred, color="intervention"), linetype="dashed") +
  
  # Plot control lines
  geom_line(data=plot_data %>% filter(rp == 0, level == 0), aes(y = .pred, color="control"), linetype="solid") +
  geom_line(data=plot_data %>% filter(rp == 0, level == 1), aes(y = .pred, color="control"), linetype="solid") +
  
  # Plot counterfactual control lines
  geom_line(data=cf_plot_data %>% filter(rp == 0), aes(y = .pred, color="control"), linetype="dashed") +
  geom_line(data=cf_plot_data %>% filter(rp == 0), aes(y = .pred, color="control"), linetype="dashed") +

  scale_color_manual(name="Group", values = cols2) +
  theme(legend.position = "bottom")
  
  if(flag == 'cits') {
    b + scale_y_continuous(name = "Proportion of patients appropriately non-conveyed", expand = c(0,0), breaks=seq(0,1,0.1), limits = c(0,1), labels=scales::percent) 
  } else {
    b + scale_y_continuous(name = "Cost (£)", expand = c(0,0), breaks=seq(0,400,50), limits = c(0,400)) 
  }
    
}

fig6 <- plot_fig6_fn(ts_df, lm_fit, 'cits')
#fig6_econ <- plot_fig6_fn(ts_df_econ, lm_fit_econ, 'econ')

ggpubr::ggarrange(fig5, fig6, nrow = 2, ncol = 1, labels = "auto", common.legend = T)

#ggpubr::ggarrange(fig5_econ, fig6_econ, nrow = 2, ncol = 1, labels = "auto", common.legend = T)

```

```{r cits-table, cache = F}
knitr::kable(ols_table, caption="Result of segmented regression analysis for appropriate non-conveyance", booktabs = TRUE, longtable = T, format = format) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"), latex_options = c("repeat_header", "striped", "hold_position")) %>%
  column_spec(1, width = "25em")
```

## Economic analysis {-}


```{r econ_1}

#https://www.tidymodels.org/learn/statistics/bootstrap/

fit_lm_bootstrap <- function(split) {
    lm(cost ~ time + rp + rptime + level + trend + rplevel + rptrend + snc, data = split)
}

econ_df <- ts_df_econ %>%
  mutate(
    strata = case_when(
      level == 0 & rot_paras == 'Control' ~ 'P1',
      level == 0 & rot_paras == 'Rotational Paramedics' ~ 'P2',
      level == 1 & rot_paras == 'Control' ~ 'P3',
      level == 1 & rot_paras == 'Rotational Paramedics' ~ 'P4',
    )
  )

set.seed(123)
econ_boots <- bootstraps(econ_df, 1000, strata = strata)

econ_models <- econ_boots %>%
  mutate(
    model = map(splits, fit_lm_bootstrap),
    coef_info = map(model, tidy)
  )

econ_coefs <- econ_models %>% unnest(coef_info)

percentile_intervals <- int_pctl(econ_models, coef_info)
#percentile_intervals


calc_cost <- function(level, rp, rplevel, rptime, rptrend, snc, time, trend, pi, which_coef) {

  est <- pi %>% select(!!which_coef) %>% pull()

  est_costs <- est[1] + (est[2] * level) + (est[3] * rp) + (est[4] * rplevel) + (est[5] * rptime) + (est[6] * rptrend) + (est[7] * snc) + (est[8] * time) + (est[9] * trend)

}

est <- percentile_intervals %>% select(".estimate") %>% pull()
est_upper <- percentile_intervals %>% select(".upper") %>% pull()
est_lower <- percentile_intervals %>% select(".lower") %>% pull()

final_econ_df <- ts_df_econ %>%
  rowwise() %>%
  mutate(
    est_costs = calc_cost(level, rp, rplevel, rptime, rptrend, snc, time, trend, percentile_intervals, ".estimate"),
    est_upper_costs = calc_cost(level, rp, rplevel, rptime, rptrend, snc, time, trend, percentile_intervals, ".upper"),
    est_lower_costs = calc_cost(level, rp, rplevel, rptime, rptrend, snc, time, trend, percentile_intervals, ".lower")
  )

#saveRDS(final_econ_df, 'Data/final_econ_df.rds')
# if(synth_data == FALSE) {
#   final_econ_df <- readRDS('Data/final_econ_df.rds')
# } else {
#   final_econ_df <- readRDS('SynData/final_econ_df.rds')
# }
#
diff_in_safe_conveyance <- (tidy(lm_fit) %>% filter(term == 'rplevel') %>% pull(estimate))

pre_post_econ_df <- final_econ_df %>%
  group_by(level, rot_paras) %>%
  summarise(
    mean_cost = mean(est_costs),
    mean_upper_cost = mean(est_upper_costs),
    mean_lower_cost = mean(est_lower_costs),
    n = n(),
    non_convey = sum(snc == 1),
    cost_per_safe_conveyance = sum(est_costs)/sum(snc == 1),
    cost_upper_per_safe_conveyance = sum(est_upper_costs)/sum(snc == 1),
    cost_lower_per_safe_conveyance = sum(est_lower_costs)/sum(snc == 1),
  )

# saveRDS(pre_post_econ_df, 'Data/pre_post_econ_df.rds')
# if(synth_data == FALSE) {
#     pre_post_econ_df <- readRDS('Data/pre_post_econ_df.rds')
#   } else {
#     pre_post_econ_df <- readRDS('SynData/pre_post_econ_df.rds')
#   }


#CEA = Cost Pre - Cost Post / rplevel

  diff_in_safe_conveyance <- (tidy(lm_fit) %>% filter(term == 'rplevel') %>% pull(estimate))

  cea_df <- bind_rows(
      pre_values <-  pre_post_econ_df %>% filter(level == 0, rot_paras == 'Rotational Paramedics') %>% select(ends_with('safe_conveyance')),
    post_values = pre_post_econ_df %>% filter(level == 1, rot_paras == 'Rotational Paramedics') %>% select(ends_with('safe_conveyance'))
  ) %>%
    pivot_longer(cols = cost_per_safe_conveyance:cost_lower_per_safe_conveyance) %>%
    group_by(name) %>%
    summarise(
      mean_diff = first(value) - last(value),
     cea = (first(value) - last(value))/diff_in_safe_conveyance
    )

  # saveRDS(cea_df, 'Data/cea_df.rds')
  # if(synth_data == FALSE) {
  #   cea_df <- readRDS('Data/cea_df.rds')
  # } else {
  #   cea_df <- readRDS('SynData/cea_df.rds')
  # }
  
 
```

```{r abstract-data, cache = F}

abstract_df <- data.frame(

  # CITS data
  level_val = cits_tidy$estimate[7],
  level_ci = cits_tidy$ci[7],
  level_p = cits_tidy$p.value[7],
  trend_val = cits_tidy$estimate[8],
  trend_ci = cits_tidy$ci[8],
  trend_p = cits_tidy$p.value[8],
  
  # Economic data

  rp_mean_cost_per_nc = round(pre_post_econ_df %>% filter(level == 1, rot_paras == 'Rotational Paramedics') %>% pull(cost_per_safe_conveyance),2),
  rp_ci_per_nc = paste0(round(round(pre_post_econ_df %>% filter(level == 1, rot_paras == 'Rotational Paramedics') %>% pull(cost_lower_per_safe_conveyance),2),2), "--£", round(round(pre_post_econ_df %>% filter(level == 1, rot_paras == 'Rotational Paramedics') %>% pull(cost_upper_per_safe_conveyance),2),2)),
  control_mean_cost_per_nc = round(pre_post_econ_df %>% filter(level == 0, rot_paras == 'Rotational Paramedics') %>% pull(cost_per_safe_conveyance),2),
  control_ci_per_nc = paste0(round(round(pre_post_econ_df %>% filter(level == 0, rot_paras == 'Rotational Paramedics') %>% pull(cost_lower_per_safe_conveyance),2),2), "--£", round(round(pre_post_econ_df %>% filter(level == 0, rot_paras == 'Rotational Paramedics') %>% pull(cost_upper_per_safe_conveyance),2),2)),
  
  diff_mean = round(cea_df$mean_diff[cea_df$name=="cost_per_safe_conveyance"], 2),
  diff_ci = paste0(round(cea_df$mean_diff[cea_df$name=="cost_upper_per_safe_conveyance"],2), "--£", round(cea_df$mean_diff[cea_df$name=="cost_lower_per_safe_conveyance"], 2)),
  
  mean_cea = round(cea_df$cea[cea_df$name=="cost_per_safe_conveyance"], 2),
  ci_cea = paste0(round(cea_df$cea[cea_df$name=="cost_upper_per_safe_conveyance"],2), "--£", round(cea_df$cea[cea_df$name=="cost_lower_per_safe_conveyance"], 2)),
  
  
  # Sensitivty econ
  
    rp_mean_cost_per_nc_no_wi = round(pre_post_econ_df_no_wi %>% filter(level == 1, rot_paras == 'Rotational Paramedics') %>% pull(cost_per_safe_conveyance),2),
  rp_ci_per_nc_no_wi = paste0(round(round(pre_post_econ_df_no_wi %>% filter(level == 1, rot_paras == 'Rotational Paramedics') %>% pull(cost_lower_per_safe_conveyance),2),2), "--£", round(round(pre_post_econ_df_no_wi %>% filter(level == 1, rot_paras == 'Rotational Paramedics') %>% pull(cost_upper_per_safe_conveyance),2),2)),
  control_mean_cost_per_nc_no_wi = round(pre_post_econ_df_no_wi %>% filter(level == 0, rot_paras == 'Rotational Paramedics') %>% pull(cost_per_safe_conveyance),2),
  control_ci_per_nc_no_wi = paste0(round(round(pre_post_econ_df_no_wi %>% filter(level == 0, rot_paras == 'Rotational Paramedics') %>% pull(cost_lower_per_safe_conveyance),2),2), "--£", round(round(pre_post_econ_df_no_wi %>% filter(level == 0, rot_paras == 'Rotational Paramedics') %>% pull(cost_upper_per_safe_conveyance),2),2)),
  
  diff_mean_no_wi = round(cea_df_no_wi$mean_diff[cea_df_no_wi$name=="cost_per_safe_conveyance"], 2),
  diff_ci_no_wi = paste0(round(cea_df_no_wi$mean_diff[cea_df_no_wi$name=="cost_upper_per_safe_conveyance"],2), "--£", round(cea_df_no_wi$mean_diff[cea_df_no_wi$name=="cost_lower_per_safe_conveyance"], 2)),
  
  mean_cea_no_wi = round(cea_df_no_wi$cea[cea_df_no_wi$name=="cost_per_safe_conveyance"], 2),
  ci_cea_no_wi = paste0(round(cea_df_no_wi$cea[cea_df_no_wi$name=="cost_upper_per_safe_conveyance"],2), "--£", round(cea_df_no_wi$cea[cea_df_no_wi$name=="cost_lower_per_safe_conveyance"], 2)),
  
  stringsAsFactors = F
  
)

adf <- abstract_df

if(synth_data == TRUE) {
  saveRDS(abstract_df, 'SynData/abstract-data.rds')
} else {
  saveRDS(abstract_df, 'Data/abstract-data.rds')
}

```


Post-placement, the cost per appropriate non-conveyance for intervention group SPs was a mean of £`r adf$rp_mean_cost_per_nc` (95% bootstrapped CI £`r adf$rp_ci_per_nc`) versus £`r adf$control_mean_cost_per_nc` (95% bootstrapped CI £`r adf$control_ci_per_nc`) for the same group in the pre-placement phase. This represents a mean saving of £`r adf$diff_mean` per appropriate non-conveyance (95% bootstrapped CI £`r adf$diff_ci`) and a cost-effectiveness ratio of £`r adf$mean_cea` per percentage increase in appropriate non-conveyance (95% bootstrapped CI £`r adf$ci_cea`).

The sensitivity analysis (excluding the working impression) calculated the mean post-placement cost per appropriate non-conveyance for intervention group SPs to be £`r adf$rp_mean_cost_per_nc_no_wi` (95% bootstrapped CI £`r adf$rp_ci_per_nc_no_wi`) versus £`r adf$control_mean_cost_per_nc_no_wi` (95% bootstrapped CI £`r adf$control_ci_per_nc_no_wi`) for the same group in the pre-placement phase. This represents a mean saving of £`r adf$diff_mean_no_wi` per appropriate non-conveyance (95% bootstrapped CI £`r adf$diff_ci_no_wi`) and a cost-effectiveness ratio of £`r adf$mean_cea_no_wi` per percentage increase in appropriate non-conveyance (95% bootstrapped CI £`r adf$ci_cea_no_wi`).