---
title: "Slides"
execute:
  cache: true
  freeze: auto
  include: true
  echo: false
  warning: false
number-sections: true
---

```{r}
library(tidyverse)
library(dplyr)
library(ggplot2)
library(survival)
library(emmeans)
library(foreign)
library(gtsummary)
library(gt)
library(ggsurvfit)
library(gridExtra)
library(survminer)
```


```{r}
dat <- read.csv("./unos.txt", sep = "\t")
names(dat) <- c("hla.match", "age.donor", "age.rec", "cold.isc", "death",
                "year", "sex", "tx.type", "follow.up")
dat <- dat |> 
  mutate(
    sex = factor(sex, levels = c(0,1), labels = c("Female","Male")),
    tx.type = factor(tx.type, levels = c(0,1), labels = c("Cadaveric","Living")),
    hla.match = factor(hla.match),
    year = factor(year)
  )
```

```{r}
my.theme <- theme_minimal() +
  theme(
    legend.position = "bottom",
    plot.title = element_text(size = 17, face = "bold"),
    axis.title = element_text(size = 15),
    axis.text = element_text(size = 12),
    legend.text = element_text(size = 12),
    plot.margin = margin(20, 30, 20, 30)
  )
```

::: {.callout-warning}
There are 25 repondents with `follow.up = 0`, 21 of which with `death = 0` and
other 4 with `death = 1`.

```{r, echo=TRUE}
dat[dat$follow.up == 0, ] |>
  group_by(death) |>
  summarise(n = n())
```

Reasons to omit them, that is, have `dat <- dat[dat$follow.up > 0,]` at the 
very beginning:

- If `death = 1`, transplant failed. They shouldn't be included in the research
  question "survival rate of a *successful* tranplant".
- If `death = 0`, transplant was successful, but they were immediately removed
  from populatoin at risk, contributiong nothing to the analysis.
:::

# Title 

# Table of Contents (?)

# Introduction (M)

# Method & Result

## Identify Predictors (M)

- Data source
- Study population
```{r}
nrow(dat)
```
- Covariates
- Outcome
```{r}
names(dat)
```

## Table (L)

```{r}
dat |>
  select(sex, age.rec, age.donor, hla.match, cold.isc, tx.type) |> 
  tbl_summary(
    by = tx.type,
    statistic = list(
      all_continuous() ~ "{median} ({p25}, {p75})"
    ),
    label = list(
      hla.match ~ "HLA matches, n(%)",
      age.donor ~ "Donor age, median (IQR)",
      age.rec ~ "Recipient age, median (IQR)",
      cold.isc ~ "Cold ischemic time (hours), median (IQR), ",
      sex ~ "Sex, n(%)"
    ),
    missing = "ifany"
  ) |>
  add_overall() |>
  modify_footnote(all_stat_cols() ~ NA)
```

# Elementary Analysis: Transplant Type (L)

## Transplant Type vs Sex

`sex` are similar across `tx.type`

```{r, fig.width=7, fig.height=5}
plot.tx.sex <- dat |>
  mutate(Overall = "Overall") |>
  pivot_longer(
    cols = c(tx.type, Overall),
    names_to = "Attribute",
    values_to = "Category"
  ) |>
  mutate(
    Attribute = recode(
      Attribute,
      "tx.type" = "Transplant Type"
    )
  ) |>
  count(Attribute, Category, sex) |>
  group_by(Attribute, Category) |>
  mutate(
    total = sum(n),
    percent = n / total
  ) |>
  ungroup() |>
  ggplot(aes(x = Category, y = percent, fill = sex)) +
  geom_col(position = "dodge") +
  facet_grid(
    ~ Attribute,
    scales = "free_x",
    space = "free_x"
  ) +
  labs(
    title = "Percentage of Sex by Transplant Type",
    x = "Group",
    y = "Percentage",
    fill = NULL
  ) +
  scale_x_discrete(
    labels = c("Cadaveric" = "Deceased")
  ) +
  my.theme
plot.tx.sex
```

## Transplant Type vs Recipient Age

```{r, fig.width=7, fig.height=5}
plot.tx.rec <- ggplot(data = dat) +
  geom_density(aes(x = age.rec, color = tx.type)) +
  geom_density(
    aes(x = age.rec, color = "Overall"),
    linewidth = 0.5,
    linetype = "dashed"
  ) +
  scale_color_manual(
    values = c(
      "Cadaveric" = "darkorange",
      "Living" = "darkgreen",
      "Overall" = "gray50"
    ),
    labels = c(
      "Cadaveric" = "Deceased"
    )
  ) +
  labs(
    title = "Density of Recipient Age by Transplant Type",
    x = "Recipient Age",
    y = "Density",
    color = NULL
  ) +
  my.theme
plot.tx.rec
```


# Elementary Analysis: Transplant Type (Cont.)

## Transplant Type vs HLA Match

Living donors have less `hla.match` then cadaveric donors.

```{r, fig.width=7, fig.height=5}
ggplot(data = dat) +
  geom_bar(aes(x = hla.match)) +
  facet_wrap(tx.type ~ ., ncol = 1) +
  labs(
    title = "Distribution of HLA Match by Transplant Type",
    x = "HLA match",
    y = "Count",
    color = NULL
  ) +
  my.theme

```

## Transplant Type vs Donor Age

```{r, fig.width=7, fig.height=5}
plot.tx.donor <- ggplot(data = dat) +
  geom_density(aes(x = age.donor, color = tx.type)) +
  geom_density(
    aes(x = age.donor, color = "Overall"),
    linewidth = 0.5,
    linetype = "dashed"
  ) +
  scale_color_manual(
    values = c(
      "Cadaveric" = "darkorange",
      "Living" = "darkgreen",
      "Overall" = "gray50"
    ),
    labels = c(
      "Cadaveric" = "Deceased"
    )
  ) +
  labs(
    title = "Density of Donor Age by Transplant Type",
    x = "Recipient Age",
    y = "Density",
    color = NULL
  ) +
  my.theme

plot.tx.donor
```

# Overall Kaplan-Meier Curve

```{r}
km_all <- survfit(Surv(follow.up, death) ~ 1, data = dat)
```

```{r, fig.width=7, fig.height=5}
km_all |>
  ggsurvfit(type = "survival") +
  add_confidence_interval() +
  scale_y_continuous(limits = c(0, 1)) +
  labs(
    title = "Kaplan-Meier Curve for Overall Survival",
    x = "Years of Follow-up",
    y = "Survival Probability",
  ) +
  my.theme
```

```{r}
summary(km_all, times = c(0, 4, 8, 12))
```

# Cox Model (with intervals?)

# Cox Model: Transplant Type

```{r}
cox.tx <- coxph(Surv(follow.up, death) ~ tx.type, data = dat)
summary(cox.tx)
```

```{r}
km.tx <- survfit(Surv(follow.up, death) ~ tx.type, data = dat)
```

```{r, fig.width=7, fig.height=5}
km.tx |>
  ggsurvfit(type = "survival") +
  add_confidence_interval() +
  scale_color_discrete(
    labels = c("Deceased", "Living")
  ) +
  scale_fill_discrete(
    labels = c("Deceased", "Living")
  ) +
  labs(
    title = "Survival by Donor Type",
    x = "Years of Follow-up",
    y = "Survival Probability",
    color = "Donor Type",
    fill = "Donor Type"
  ) +
  my.theme
```

```{r}
summary(km.tx, times = c(0, 4, 8, 12))
```

# Cox Model: Age Recipient (Continuous)

```{r}
cox.age.rec <- coxph(Surv(follow.up, death) ~ age.rec, data = dat)
summary(cox.age.rec)
```

```{r}
km.age.rec <- survfit(Surv(follow.up, death) ~ age.rec, data = dat)
```

```{r, fig.width=7, fig.height=7}
km.age.rec |>
  ggsurvfit(type = "survival") +
  scale_color_discrete(
    labels = seq(1, 18)
  ) +
  labs(
    title = "Survival by Recipient Age",
    x = "Years of Follow-up",
    y = "Survival Probability",
    color = "Recipient Age",
  ) +
  my.theme
```

<details>
<summary>View life table</summary>

```{r}
summary(km.age.rec, times = c(0, 4, 8, 12))
```
</details>


# Cox Model: Age Recipient (Categorical)

```{r}
class.age <- function(age) {
  if (is.na(age)) return(NA)
  if (age < 2) { 
    return("0-1")
  } else if (age < 6) {
    return("2-5")
  } else if (age < 11) {
    return("6-10")
  } else if (age < 19) {
    return("11-18")
  }
}

dat.age.rec.group <- dat
dat.age.rec.group$age.rec.group = sapply(dat$age.rec, class.age) |>
  factor(levels = c(
    "0-1",
    "2-5",
    "6-10",
    "11-18"
  ))
cox.age.rec.group <- coxph(Surv(follow.up, death) ~ age.rec.group,
                           data = dat.age.rec.group)
```


```{r, echo=TRUE}
cox.age.rec.group
```

</details>


```{r, echo=TRUE}
eme.age.rec.group <- emmeans(cox.age.rec.group, pairwise ~ age.rec.group,
                             type = "response")
eme.age.rec.group
```


```{r}
km.age.rec.group <- survfit(Surv(follow.up, death) ~ age.rec.group, 
                            data = dat.age.rec.group)
```

```{r, fig.width=7, fig.height=7}
km.age.rec.group |>
  ggsurvfit(type = "survival") +
  add_confidence_interval() +
  scale_color_discrete(
    labels = c("0-1", "2-5", "6-10", "11-18")
  ) +
  scale_fill_discrete(
    labels = c("0-1", "2-5", "6-10", "11-18")
  ) +
  labs(
    title = "Survival by Recipient Age Group",
    x = "Years of Follow-up",
    y = "Survival Probability",
    color = "Recipient Age Group",
    fill = "Recipient Age Group",
  ) +
  my.theme
```

```{r, fig.width=7, fig.height=7}
eme.age.rec.group$contrast |> 
  as.data.frame() |>
  select(contrast, ratio, SE, p.value) |>
  mutate(
    contrast = factor(contrast),
    log.ratio = log(ratio),
    SE.log = SE / ratio,
    low = exp(log.ratio - 1.96 * SE.log),
    up = exp(log.ratio + 1.96 * SE.log)
  ) |>
  ggplot(aes(y = reorder(contrast, ratio))) +
  geom_errorbarh(aes(xmin = low, xmax = up)) +
  geom_point(aes(x = ratio)) +
  geom_vline(xintercept =  1, linetype = "dashed") +
  scale_y_discrete(
    labels = function(x) {
      gsub("[()]", "", x = x)
    }
  ) +
  labs(
    x = "Hazard Ratio",
    y = "Recipient Age Group Comparison",
    title = "Pairwise Hazard Ratios by Recipient Age Groups"
  ) +
  my.theme
```

# Identifying Predictors

TODO: write a more generic function

```{r}
Waldtest <- function(cox.fit, i.betas){
  q <- length(i.betas)
  coefs <- cox.fit$coefficients
  var <- cox.fit$var[i.betas, i.betas]
  Wald <- coefs[i.betas]%*%solve(var)%*%coefs[i.betas]
  p.value <- 1-pchisq(as.numeric(Wald), df = q)
  print(p.value)
  return(p.value)
}
```

```{r}
vars <- c("hla.match", "age.donor", "age.rec", "cold.isc", "year", "sex", 
          "tx.type")
included <- vars == "tx.type"
included <- c(FALSE, FALSE, TRUE, TRUE, FALSE, FALSE, TRUE)
included <- c(FALSE, FALSE, TRUE, TRUE, FALSE, FALSE, TRUE)

find.best.surv <- function(included) {
  print('---')
  test.vars <- vars[!included]
  p.values <- sapply(test.vars, function(test.var) {
    new.surv <- reformulate(
      termlabels = c(vars[included], test.var),
      response = "Surv(follow.up, death)"
    )
    fit.tx <- coxph(new.surv, data = dat)
    Waldtest(fit.tx, sum(included))
  })
  if (sum(p.values > 0.05) == sum(included)) {
    print(3)
    return(included) 
  }
  if (sum(included == TRUE) == length(included)) {
    print(2)
    return(included)
  }
  print(1)
  print(which.min(p.values))
  print(included)
  print(p.values)
  print(which.min(p.values))
  included[which.min(p.values)] <- TRUE
  print(included)
  # find.best.surv(included)
}


find.best.surv(included)

```

```{r}
# surv <- Surv(follow.up, death) ~ tx.type + age.rec + hla.match
# fit.cox.model(surv, 3)
# surv <- Surv(follow.up, death) ~ tx.type + age.rec + age.donor
# fit.cox.model(surv, 3)
# surv <- Surv(follow.up, death) ~ tx.type + age.rec + cold.isc
# fit.cox.model(surv, 3)
# surv <- Surv(follow.up, death) ~ tx.type + age.rec + year
# fit.cox.model(surv, 3)
# surv <- Surv(follow.up, death) ~ tx.type + age.rec + sex
# fit.cox.model(surv, 3)
```



---


# Old

<details>

## Death & Censored


```{r, echo=TRUE}
dat |>
  group_by(death) |>
  summarise(
    n = n(),
    percentage = n() / nrow(dat) * 100
  )
```

Most of the patients (95.24%) were censored.

```{r}
n.pop <- nrow(dat)
dat.accum <- dat[dat$follow.up > 0,] |>
  select(follow.up, death) |>
  mutate(censored = ifelse(death == 1, 0, 1)) |>
  group_by(follow.up) |>
  summarize(
    death = sum(death),
    censored = sum(censored),
    .groups = "drop"
  ) |>
  arrange(follow.up) |>
  mutate(
    death.accum = cumsum(death),
    censored.accum = cumsum(censored),
    event.accum = death.accum + censored.accum,
    n.at.risk = n.pop - c(0, event.accum[-n()])
  )
dat.accum |>
  pivot_longer(
    cols = c(death.accum, censored.accum, n.at.risk),
    names_to = "type",
    values_to = "accum",
  ) |>
  ggplot(aes(x = follow.up, y = accum, color = type)) +
  geom_step(linewidth = 1, direction = "hv") +
  my.theme
```

```{r}
dat[dat$death == 1,] |>
  ggplot(aes(x = follow.up)) +
  geom_histogram(bins = 50)
```


```{r}
dat[dat$follow.up == 0,]
```

```{r}
head(dat)
```

## Cox Model - Age as a Continuous Variable

```{r, echo=TRUE}
cox.age.rec <- coxph(Surv(follow.up, death) ~ age.rec, data = dat)
cox.age.rec |> summary()
```

## Cox Model - Age as a Categorical Variable


```{r, fig.width=10, fig.height=10}
cox.final <- coxph(Surv(follow.up, death) ~ tx.type + age.rec + hla.match + age.donor + year, data = dat)
cox.zph(cox.final)
plot(cox.zph(cox.final))

ggcoxzph(cox.zph(cox.final),
         ggtheme = theme_minimal() +
         theme(
           legend.position = "bottom",
           plot.title = element_text(size = 17, face = "bold"),
           axis.title = element_text(size = 15),
           axis.text = element_text(size = 12),
           legend.text = element_text(size = 12),
           strip.text = element_blank(),
           plot.margin = margin(20, 30, 20, 30)
         ))
```

## Table 1 (L)


### HLA match `hla.match`

```{r}
dat$hla.match |> table(useNA = "always")
```

```{r}
ggplot(dat, aes(x = hla.match)) +
  geom_bar() +
  labs(x = "HLA match", y = "Count") +
  theme_minimal()

```

```{r}
ggplot(dat, aes(x = hla.match, fill = tx.type)) +
  geom_bar(position = "dodge") +
  labs(x = "HLA match", y = "Count") +
  theme_minimal()
```

::: {.callout-warning}
TODO: change to percentage within each `tx.type`
:::

::: {.callout-note}
Living donors have less `hla.match` then cadaveric donors
:::


### Donor age `age.donor`

```{r}
#| echo: true
mean(dat$age.donor, na.rm = TRUE)
median(dat$age.donor, na.rm = TRUE)
```

```{r}
ggplot(dat, aes(x = age.donor)) +
  geom_bar() +
  labs(x = "Donor Age", y = "Count") +
  theme_minimal()
```

```{r, fig.width = 8, fig.height = 12}
ggplot(dat, aes(x = age.donor)) +
  geom_bar() +
  labs(x = "Donor Age", y = "Count") +
  theme_minimal() +
  facet_grid(hla.match ~ .)
```

```{r, fig.width= 8, fig.height= 12}
ggplot(dat, aes(x = age.donor, color = tx.type)) +
  geom_density() +
  labs(x = "Donor Age", y = "Density") +
  theme_minimal() +
  facet_grid(hla.match ~ .)
```

```{r}
ggplot(dat, aes(x = age.donor, color = hla.match)) +
  geom_density() +
  labs(x = "Donor Age", y = "Count") +
  theme_minimal()
```

```{r}
ggplot(dat, aes(x = as.factor(tx.type), y = age.donor)) +
  geom_boxplot() +
  theme_minimal()
```

::: {.callout-note}
There is age difference between different `tx.type`
:::


### Recipient Age `age.rec`

```{r}
#| echo: true
mean(dat$age.rec, na.rm = TRUE)
median(dat$age.rec, na.rm = TRUE)
```


```{r}
ggplot(dat, aes(x = age.rec)) +
  geom_bar() +
  labs(x = "Recipient Age", y = "Count") +
  theme_minimal()

```

```{r}
ggplot(dat, aes(x = as.factor(age.rec), y = age.donor)) +
  geom_boxplot() +
  theme_minimal()

```

```{r}
ggplot(dat, aes(x = age.rec, fill = tx.type)) +
  geom_bar(position = "dodge") +
  theme_minimal()

```

```{r}
ggplot(dat, aes(x = age.rec, color = hla.match)) +
  geom_density() +
  theme_minimal()
```

```{r}
ggplot(dat, aes(x = as.factor(age.rec), y = cold.isc)) +
  geom_boxplot() +
  theme_minimal()
```


### Cold Ischemia Time `cold.isc`

```{r}
#| echo: true
mean(dat$cold.isc, na.rm = TRUE)
median(dat$cold.isc, na.rm = TRUE)
```

```{r}
ggplot(dat, aes(x = cold.isc)) +
  geom_density() +
  labs(x = "Cold Ischemia Time (hours)", y = "Probability Density") +
  theme_minimal()
```

```{r}
ggplot(dat, aes(x = cold.isc, color = tx.type, group = tx.type)) +
  geom_density() +
  labs(x = "Cold Ischemia Time (hours)", y = "Probability Density") +
  theme_minimal()
```

```{r}
ggplot(dat, aes(x = cold.isc)) +
  geom_density() +
  theme_minimal() +
  facet_grid(tx.type ~ .)
```

### Transplant Type `tx.type`

```{r}
dat$tx.type |> table(useNA = "always")
```

```{r}
#| echo: true
dat$tx.type |> table()
```

```{r}
ggplot(dat, aes(x = tx.type)) +
  geom_bar() +
  labs(x = "Transplant Type", y = "Count") +
  theme_minimal()

```

### Year `year`

```{r}
dat$year |> table()
```

```{r}
ggplot(dat, aes(x = year)) +
  geom_bar() +
  labs(x = "Year", y = "Count") +
  theme_minimal()
```

```{r}
ggplot(dat, aes(x = year, y = follow.up)) +
  geom_boxplot()
```

```{r}
ggplot(dat, aes(x = year, fill = tx.type)) +
  geom_bar(position = "dodge")
```

```{r}
ggplot(dat, aes(x = year, y = age.rec)) +
  geom_boxplot()
```

```{r}
ggplot(dat, aes(x = year, y = age.donor)) +
  geom_boxplot()
```

## Kaplan-Meier 

### Overall (L)

```{r}
km_all <- survfit(Surv(follow.up, death) ~ 1, data = dat)
summary(km_all, times = c(4, 8, 12))
```

```{r}
km_all |>
  ggsurvfit(type = "survival") +
  add_confidence_interval() +
  scale_y_continuous(limits = c(0, 1), labels = scales::label_percent()) +
  labs(
    x = "Years of Follow-up",
    y = "Overall Survival Probability"
  ) +
  theme_minimal()
```

### `tx.type` (M)

```{r, fig.width=7, fig.height=5}
km.tx <- survfit(Surv(follow.up, death) ~ tx.type, data = dat)

km.tx |>
  ggsurvfit(type = "survival") +
  add_confidence_interval() +
  scale_x_continuous(
    breaks = seq(0, 20, by = 4)
  ) +
  scale_y_continuous(
    limits = c(0, 1),
    breaks = seq(0, 1, by = 0.2),
    labels = scales::label_number(accuracy = 0.1)
  ) +
  labs(
    x = "Years of Follow-up",
    y = "Overall Survival Probability"
  ) +
  theme_minimal() +
  theme(
    legend.position = "bottom",
    plot.title = element_text(size = 17, face = "bold"),
    axis.title = element_text(size = 15),
    axis.text = element_text(size = 10),
    legend.text = element_text(size = 12),
    plot.margin = margin(20, 30, 20, 30)
  )
```

## Cox Model

```{r}
get.life.table <- function(dat, time.intervals) {
  n.pop <- nrow(dat)

  dat |>
    recode.dat(time.intervals) |>
    group_by(fu.interval) |>
    summarize(
      n.censored = sum(.data$death == 0),
      n.event = sum(.data$death),
    ) |>
    ungroup() |>
    calculate.hazard(n.pop)
}

get.life.table.by.groups <- function(dat, time.intervals, grps) {
  grps |>
    lapply(function(grp) {
      dat |>
        get.life.table.by.group(time.intervals, grp) |>
        mutate(
          grp.name = grp,
          grp.value = pick(1)[[1]]
        ) |>
        select(-1)
    }) |>
    bind_rows()
}

get.life.table.by.group <- function(dat, time.intervals, grp) {
  dat |>
    recode.dat(time.intervals) |>
    group_by(fu.interval, .data[[grp]]) |>
    summarize(
      n.censored = sum(.data$death == 0),
      n.event = sum(.data$death),
      .groups = "keep"
    ) |>
    ungroup(fu.interval) |>
    group_modify(function(df.sub, grp) {
      grp.name <- names(grp)
      grp.value <- grp[[1]]
      n.pop <- (dat[[grp.name]] == grp.value) |> sum()
      calculate.hazard(df.sub, n.pop)
    }) |>
    ungroup()
}

calculate.hazard <- function(life.table, n.pop) {
  n.removed <- life.table$n.event + life.table$n.censored
  n.removed.accum <- c(0, cumsum(n.removed)[-length(n.removed)])
  life.table |>
    mutate(
      n.at.risk = n.pop - n.removed.accum,
      # TODO: how to account for censored? How do we adjust for uneven interval?
      hazard.rate = n.event / n.at.risk
    )
}

recode.dat <- function(dat, time.intervals) {
  df <- dat[dat$follow.up <= sum(time.intervals), ]
  time.points <- cumsum(time.intervals)
  df$fu.interval <- sapply(df$follow.up, function(time) {
      time.points[time <= time.points][1]
  })

  df
}
```

### `death` Distribution (?)

```{r}
# dat |>
#   mutate(
#     accum.death = cumsum(death),
#     accum.censored = if_else(death == 1, 0, 1) |> cumsum()
#   ) |>
#   ggplot() +
#   geom_pont(aes(x = follow.up, y = accum.death, color = death))
```

```{r}

```

```{r}
plot.death = dat[dat$death == 1,] |>
  ggplot(aes(x = follow.up)) +
  geom_histogram(bins = 50)
plot.death
```


### Overall (L)

::: {.callout-note}
skip overall, jump directly to `tx.type`
:::

```{r}
time.intervals <- c(1/3, 1/3, 1/3, 1, 1, 1, 1)
get.life.table(dat, time.intervals)
```

### `tx.type` (M)


### `age` (continuous) (L)

### `age` (categorical) (M)

### Full model (L)

```{r}
m1 <- coxph(Surv(follow.up, death) ~ hla.match + tx.type, data = dat)
summary(m1)

m2 <- coxph(Surv(follow.up, death) ~ hla.match * tx.type, data = dat)
summary(m2)

anova(m1, m2, test = "LRT")
```

### Discussion: include `year` or not?

## Assumption Testing


  ## Why Survival Analysis (L)

Motivation: study the distribution of time to event $T$.

Example: time of death after kidney transplant. 


```{r}
ex <- data.frame(
  id = c(1, 2, 3, 4, 5),
  transplant = c(2000, 2000, 2001, 2003, 2004),
  death = c(2005, 2009, 2005, 2004, 2016)
)

ex_table_1 <- ex |>
  gt() |>
  cols_label(
    id = "ID",
    transplant = "Transplant",
    death = "Death"
  ) %>%
  cols_align(align = "center", columns = everything())

ex_plot_real_time <- ggplot(ex) +
  geom_segment(aes(x = transplant, xend = death, y = factor(id),
                   yend = factor(id)), color = "grey50", linewidth = 1) +
  geom_point(aes(x = transplant, y = factor(id), color = "trans"), size = 3) +
  geom_point(aes(x = death, y = factor(id), color = "death"), size = 3) +
  scale_color_manual(values = c("trans" = "#00BFC4", "death" = "#F8766D")) +
  scale_y_discrete(limits = rev) +
  labs(x = "Year", y = "Subject ID", color = "Event") +
  theme_minimal()
```

```{r}
ex_table_1
ex_plot_real_time
```

---

We then calculate time to death for each respondents. 

With this, all we need is to fit a linear model `t ~ X` or `log(t) ~ X`

```{r}
ex_t <- ex |>
  mutate(
    t = death - transplant
  )

ex_table_2 <- ex_t |>
  gt() |>
  cols_label(
    id = "ID",
    transplant = "Transplant",
    death = "Death",
    t = "Time to death"
  ) |>
  cols_align(align = "center", columns = everything())

ex_plot_uniform_time <- ggplot(ex_t) +
  geom_segment(aes(x = 0, xend = t, y = factor(id),
                   yend = factor(id)), color = "grey50", linewidth = 1) +
  geom_point(aes(x = 0, y = factor(id), color = "trans"), size = 3) +
  geom_point(aes(x = t, y = factor(id), color = "death"), size = 3) +
  scale_color_manual(values = c("trans" = "#00BFC4", "death" = "#F8766D")) +
  scale_y_discrete(limits = rev) +
  labs(x = "Year", y = "Subject ID", color = "Event") +
  theme_minimal()

```


```{r}
ex_table_2
ex_plot_uniform_time
```

---

What if we do not know when exactly some respondents die?

Scenario 1: the study ends at the year 2008?

```{r}
ex_t_c <- ex_t |>
  mutate(
    death_censored = if_else(death <= 2008, death, 2008),
    death_censored_txt = if_else(death <= 2008, as.character(death), "> 2008"),
    status = if_else(death <= 2008, 1, 0),
    t_1 = death_censored - transplant,
    t_1_txt = if_else(death <= 2008, as.character(t_1),
                      paste(">", as.character(t_1)))
  )
```

```{r}
ex_table_3 <- ex_t_c |>
  select(id, transplant, death_censored_txt, t_1_txt) |>
  gt() |>
  cols_label(
    id = "ID",
    transplant = "Transplant",
    death_censored_txt = "Death",
    t_1_txt = "Time to death"
  ) |>
  cols_align(align = "center", columns = everything())

ex_plot_real_time_1 <- ggplot(ex_t_c) +
  geom_segment(aes(x = transplant, xend = death_censored, y = factor(id),
                   yend = factor(id)), color = "grey50", linewidth = 1) +
  geom_point(aes(x = transplant, y = factor(id), color = "trans"), size = 3) +
  geom_point(aes(x = death_censored, y = factor(id), color =
                   if_else(status == 1, "death", "censored")), size = 3) +
  scale_color_manual(values = c("trans" = "#00BFC4", "death" = "#F8766D",
                                "censored" = "orange")) +
  scale_y_discrete(limits = rev) +
  labs(x = "Year", y = "Subject ID", color = "Event") +
  xlim(2000, 2016) +
  geom_vline(xintercept = 2008, linetype = "dashed", color = "orange",
             linewidth = 0.8) +
  theme_minimal()


ex_plot_uniform_time_1 <- ggplot(ex_t_c) +
  geom_segment(aes(x = 0, xend = t_1, y = factor(id),
                   yend = factor(id)), color = "grey50", linewidth = 1) +
  geom_point(aes(x = 0, y = factor(id), color = "trans"), size = 3) +
  geom_point(aes(x = t_1, y = factor(id), color =
                   if_else(status == 1, "death", "censored")), size = 3) +
  scale_color_manual(values = c("trans" = "#00BFC4", "death" = "#F8766D",
                                "censored" = "orange")) +
  scale_y_discrete(limits = rev) +
  labs(x = "Year", y = "Subject ID", color = "Event") +
  theme_minimal()
```


```{r}
ex_table_3
ex_plot_real_time_1
ex_plot_uniform_time_1
```

**Right Censoring**: only observe the event (death) if it occurs before a 
certain time (2008).

---

Scenario 2: respondent 3 move away; loss follow up

```{r}
ex_alt <- ex_t_c
ex_alt$death_censored_txt[3] <- "> 2005"
ex_alt$status[3] <- 0
ex_alt$t_1_txt[3] <- "> 4"


ex_table_4 <- ex_alt |>
  select(id, transplant, death_censored_txt, t_1_txt) |>
  gt() |>
  cols_label(
    id = "ID",
    transplant = "Transplant",
    death_censored_txt = "Death",
    t_1_txt = "Time to death"
  ) |>
  cols_align(align = "center", columns = everything())

ex_plot_real_time_2 <- ggplot(ex_alt) +
  geom_segment(aes(x = transplant, xend = death_censored, y = factor(id),
                   yend = factor(id)), color = "grey50", linewidth = 1) +
  geom_point(aes(x = transplant, y = factor(id), color = "trans"), size = 3) +
  geom_point(aes(x = death_censored, y = factor(id), color =
                   if_else(status == 1, "death", "censored")), size = 3) +
  scale_color_manual(values = c("trans" = "#00BFC4", "death" = "#F8766D",
                                "censored" = "orange")) +
  scale_y_discrete(limits = rev) +
  labs(x = "Year", y = "Subject ID", color = "Event") +
  xlim(2000, 2016) +
  geom_vline(xintercept = 2008, linetype = "dashed", color = "orange",
             linewidth = 0.8) +
  theme_minimal()


ex_plot_uniform_time_2 <- ggplot(ex_alt) +
  geom_segment(aes(x = 0, xend = t_1, y = factor(id),
                   yend = factor(id)), color = "grey50", linewidth = 1) +
  geom_point(aes(x = 0, y = factor(id), color = "trans"), size = 3) +
  geom_point(aes(x = t_1, y = factor(id), color =
                   if_else(status == 1, "death", "censored")), size = 3) +
  scale_color_manual(values = c("trans" = "#00BFC4", "death" = "#F8766D",
                                "censored" = "orange")) +
  scale_y_discrete(limits = rev) +
  labs(x = "Year", y = "Subject ID", color = "Event") +
  theme_minimal()
```

```{r}
ex_table_4
ex_plot_real_time_2
ex_plot_uniform_time_2
```

---

How many patients are right censored?

```{r}
dat |>
  mutate(Overall = "Overall") |>
  pivot_longer(
    cols = c(Overall, sex, tx.type), 
    names_to = "Attribute", 
    values_to = "Category"
  ) |>
  count(Attribute, Category, death) |>
  ggplot(aes(x = Category, y = n, fill = factor(death))) +
  geom_col(position = "dodge") +
  facet_wrap(~ Attribute, scales = "free_x") +
  labs(x = "Group", y = "Count", fill = "Death Status") +
  theme_minimal()
```

## Challenges in Survival Analysis (L)

- **Right Censoring**: only observe the event if it occurs before a certain 
  time.
- **Left Censoring**: event has occurred prior to the start of a research
  - Follow up every 3 years.
  - Event has occurred -> event happened sometime before follow up.
- **Left Truncation**: delayed entry; respondents are included only if they
  survived long enough.
  - Start follow up with patients 100 days after the transplant
  - Patients dies within 100 day wouldn't be included in the dataset
- **Right Truncation**: respondents are included only if they have already
  experienced the event.
  - Retrospective analysis from deceased patients between 1990 and 2000.
  - Patients not dead before 2000 are not included in the dataset.
</details>