pem_vs_pam.Rmd

---
title: "PEM vs. PAM split point sensitivity"
site: workflowr::wflow_site
output:
  workflowr::wflow_html:
    toc: false
---

```{r setup}
library(ggplot2)
theme_set(theme_bw())
library(batchtools)
```


Function for data simulation (using `pammtools::sim_pexp`):

```{r}
## simulation function
sim_wrapper <- function(data, job, n = 250, time_grid = seq(0, 10, by = 0.05)) {

  # create data set with covariates
  df <- tibble::tibble(x1 = runif(n, -3, 3), x2 = runif(n, 0, 6))
  # baseline hazard
  f0 <- function(t) {dgamma(t, 8, 2) * 6}
  # define function that generates nz exposures z(t_{z,1}), ..., z(t_{z,Q})

  sim_pexp(formula = ~ -3.5 + f0(t), data = df, cut = time_grid)

}
```

Function to estimate hazard from simulated data, either by a PEM or PAM

```{r}
## estimation function
pam_wrapper <- function(data, job, instance,
  cut      = NA,
  bs       = "ps",
  mod_type = c("pem", "pam") ,
  max_time = 10) {

  if(is.na(cut)) {
    cut <- NULL
  } else {
    if(cut == "rough") {
      cut <- seq(0, max_time, by = 0.5)
    } else {
      if(cut == "fine") {
        cut <- seq(0, max_time, by = 0.2)
      }
    }
  }

  ped <- as_ped(data = instance, formula = Surv(time, status) ~ ., cut = cut, id="id")

  form <- "ped_status ~ s(tend) + s(x1) + s(x2)"
  if(mod_type == "pem") {
    form     <- ped_status ~ interval
    time_var <- "interval"
  } else {
    form     <- ped_status ~ s(tend, bs = bs,k = k)
    time_var <- "tend"
  }

  mod <- gam(formula = form, data = ped, family = poisson(), offset = offset, method = "REML")
  # summary(mod)

  make_newdata(ped, tend=unique(tend)) %>%
    add_hazard(mod, type="link", se_mult = qnorm(0.975), time_var = time_var) %>%
    mutate(truth = -3.5 + dgamma(tend, 8, 2) * 6)

}
```


Setup simulation using `batchtools`:

```{r, cache = TRUE, message = FALSE}
if(!checkmate::test_directory_exists("output/sim-pem-vs-pam-registry")) {
  reg <- makeExperimentRegistry("output/sim-pem-vs-pam-registry",
    packages = c("mgcv", "dplyr", "tidyr", "pammtools"),
    seed     = 20052018)
  reg$cluster.functions = makeClusterFunctionsMulticore(ncpus = 2)
  addProblem(name   = "pem-vs-pam", fun = sim_wrapper)
  addAlgorithm(name = "pem-vs-pam", fun = pam_wrapper)

  algo_df <- tidyr::crossing(
    cut = c(NA, "fine", "rough"),
    mod_type = c("pem", "pam"))

  addExperiments(algo.design  = list("pem-vs-pam" = algo_df), repls = 20)
  submitJobs()
  waitForJobs()
}
```

Evaluate Simulation:
```{r}
reg     <- loadRegistry("output/sim-pem-vs-pam-registry", writeable = TRUE)
ids_pam <- findExperiments(prob.name="pem-vs-pam", algo.name="pem-vs-pam")
pars    <- unwrap(getJobPars()) %>% as_tibble()
res     <- reduceResultsDataTable(ids=findDone(ids_pam)) %>%
  as_tibble() %>%
  tidyr::unnest() %>%
  left_join(pars) %>%
  mutate(cut = case_when(is.na(cut) ~ "default", TRUE ~ cut))

res %>%
  mutate(
    sq_error = (truth - hazard)^2,
    covered = (truth >= ci_lower) & (truth <= ci_upper)) %>%
  group_by(job.id, mod_type, cut) %>%
  summarize(
    RMSE = sqrt(mean(sq_error)),
    coverage = mean(covered)) %>%
  group_by(mod_type, cut) %>%
  summarize(
    RMSE     = mean(RMSE),
    coverage = mean(coverage))


```

```{r}
ggplot(res, aes(x=tend, y = hazard)) +
  geom_step(aes(group = job.id), alpha = 0.3) +
  geom_line(aes(y = truth, col = "truth"), lwd = 2) +
  facet_grid(cut ~ mod_type) +
  coord_cartesian(ylim=c(-5, 0)) +
  geom_smooth(aes(col="average estimate"), method="gam", formula = y ~ s(x),
    se=FALSE) +
  scale_color_brewer("Method", palette = "Dark2") +
  xlab("time")
```