---
title: foo
execute:
  cache: true
  freeze: auto
number-sections: true
---

```{r}
library(tidyverse)
library(survival)
# library(gtsummary)
```

```{r}
dat <- read.csv("./unos.txt", sep = "\t")
head(dat)
```

```{r}
names(dat) <- c("hla.match", "age.donor", "age.rec", "cold.isc", "death",
                "year", "sex", "tx.type", "follow.up")
```



# Exercise

## Exercise 1 

> Illustrate in a table the characteristics of the population (age, sex, race, 
donor, . . . ).

```{r}
g <- ggplot(dat)
```

```{r}
g + geom_point(aes(x = follow.up, y = death))
g +  geom_density(aes(x = follow.up))

g +  geom_density(aes(x = age.donor))
g +  geom_bar(aes(x = age.rec))

g + geom_boxplot(aes(x = age.rec, y = age.donor, group = age.donor))

# dat$age.1 |> table()
```

## Exercise 2

Plot the Kaplan-Meier overall survival curve for pediatric kid-
ney transplant recipients for the first 12 years after transplantation.

```{r}
km <- survfit(Surv(follow.up, death) ~ 1, data = dat[dat$follow.up  <= 12, ])
plot(km)



```

## Exercise 3

We are going to compare mortality rates (hazard functions)
between children whose transplanted kidney was provided by a living donor
(in general a family member) and those whose source was recently deceased
(variable donor type: `txtype`). Use the life table method to calculate the death
rates for the first 5 years for each group (take in the first year intervals of 4
months and then look at each year) and show the results in a table. Estimate
the hazard ratio in each time interval as the ratio between the mortality rates
in the two groups. What do you notice?

```{r}
dat.5 <- dat[dat$follow.up <= 5, ]
head(dat.5)
classify_time_interval = function(fu) {
  if (fu <= 1/3) {
    return(1/3)
  } else if (fu <= 2/3) {
    return(2/3)
  } else if (fu <= 1) {
    return(1)
  }
  ceiling(fu)
}

dat.5$fu.interval <- sapply(dat.5$follow.up, classify_time_interval)
table(dat.5$fu.interval)
head(dat.5)
```

```{r}
dat.5.life <- dat.5 |>
  group_by(fu.interval) |>
  summarize(
    n.censored = sum(death == 0),
    n.event = sum(death),
    n.at.risk = nrow(dat),
  )

for (i in 2:nrow(dat.5.life)) {
  j <- i - 1

  n.censored.pre <- dat.5.life$n.censored[j]
  n.event.pre <- dat.5.life$n.event[j]
  n.at.risk.pre <- dat.5.life$n.at.risk[j]

  n.at.risk <- n.at.risk.pre - n.event.pre - n.censored.pre

  dat.5.life$n.at.risk[i] <- n.at.risk
}

print(nrow(dat))
dat.5.life

```

```{r}
dat.5.life <- dat.5.life |>
  mutate(
     hazard.rate = n.event / n.at.risk
  )

```

---


```{r}
get_life_table = function(dat) {
  dat <- dat |>
    group_by(fu.interval) |>
    summarize(
      n.censored = sum(death == 0),
      n.event = sum(death),
      n.at.risk = nrow(dat),
    )

  for (i in 2:nrow(dat)) {
    j <- i - 1

    n.censored.pre <- dat$n.censored[j]
    n.event.pre <- dat$n.event[j]
    n.at.risk.pre <- dat$n.at.risk[j]

    n.at.risk <- n.at.risk.pre - n.event.pre - n.censored.pre

    dat$n.at.risk[i] <- n.at.risk
  }

  dat <- dat |>
    mutate(
       hazard.rate = n.event / n.at.risk
    )

  return(dat)
}
```

```{r}
dat.5.tx0 = dat.5[dat.5$tx.type == 0, ]
dat.5.tx1 = dat.5[dat.5$tx.type == 1, ]
```

```{r}
tx0.life <- get_life_table(dat.5.tx0)
tx0.life
```

```{r}
tx1.life <- get_life_table(dat.5.tx1)
tx1.life
```


```{r}
tx1.life$hazard.rate / tx0.life$hazard.rate
```

```{r}
hazard.df <- data.frame(
  fu.interval = tx1.life$fu.interval,
  hazard.rate.0 = tx0.life$hazard.rate,
  hazard.rate.1 = tx1.life$hazard.rate,
  hazard.ratio = tx1.life$hazard.rate / tx0.life$hazard.rate
) 

ggplot(hazard.df, aes(x = fu.interval)) +
  geom_line(aes(y = hazard.rate.0), color = "blue") + 
  geom_line(aes(y = hazard.rate.1), color = "orange")

ggplot(hazard.df, aes(x = fu.interval)) +
  geom_line(aes(y = hazard.ratio))

```



## Exercise 4

Show a plot with Kaplan-Meier survival curves for the two donor types.

```{r}
km.tx <- survfit(Surv(follow.up, death) ~ tx.type, data = dat[dat$follow.up  <= 12, ])

plot(km.tx, col = c("blue", "orange"))
legend(legend = c("cadaveric", "living"), "bottomleft", lwd = 2, col = c("blue", "orange"))
```

## Exercise 5

Fit a univariate Cox model with predictor donor type. Report
the hazard ratio and 95% confidence interval and interpret the result obtained.

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

```{r}
1.90539
```

```{r}
1.90539 + 1.96 * exp(0.09558)
(2.298 - 1.58) / 2 |> exp() / 2
```

Exercise 6 — Research shows that an important determinant of mortality
after kidney transplant is the age of the recipient. Fit a Cox model with age
as predictor and estimate the hazard ratio and its confidence interval. Consider
age first as continuous variable and then divide into categories.

Exercise 7 — Fit a multivariate Cox model by using other predictors and
describe your results.

Exercise 8 — Estimate the survival function for specific covariate patterns.
Based on the previous results choose the best predictors.

Exercise 9 — Check the proportional hazards assumption. You may use the
function cox.zph. Discuss the result and possible implications.
Exercise 10 — Plot the Schoenfeld residuals and comment.