# Comparison with other models

This vignette shows a brief comparison of the survival_ln_mixture with other survival models, available through `censored`.

We begin by loading the packages and preparing the data.

    library(lnmixsurv)
    library(readr)
    require(censored)
    require(purrr)
    require(dplyr)
    require(ggplot2)

    set.seed(4)

    # Gerando dados
    data <- simulate_data(n = 6000, k = 3, mixture_components = 2,
                          percentage_censored = 0.3)$data |>
      filter(t < 500) |>
      rename(x = cat, y = t)

    new_data <- data |>
      distinct(x)

    formula <- Surv(y, delta) ~ x

For comparison, lets also estimate the Kaplan-Meier survival function.

    library(ggsurvfit)

    km <- survfit2(formula, data)

    surv_km <- tidy_survfit(km, type = "surv") |>
      select(.eval_time = time, .pred_survival = estimate, id = strata) |>
      tidyr::nest(.pred = c(.eval_time, .pred_survival))

The we build our `parsnip` specifications and store them in a list.

    ln_survival <- survival_reg(dist = "lognormal") |>
      set_engine("survival")

    ph_survival <- proportional_hazards() |>
      set_engine("survival")

    decision_tree <- decision_tree(cost_complexity = 0) |>
      set_engine("rpart") |>
      set_mode("censored regression")

    ln_mixture <- survival_reg() |>
      set_engine("survival_ln_mixture",
                 iter = 4000, warmup = 2000, starting_seed = 10,
                 em_iter = 450, mixture_components = 3)

    ln_mixture_em <- survival_reg() |>
      set_engine("survival_ln_mixture_em",
                 iter = 250, starting_seed = 15,
                 mixture_components = 3)

    specs <- list(
      ln_survival = ln_survival, ph_survival = ph_survival, ln_mixture = ln_mixture, decision_tree = decision_tree, ln_mixture_em = ln_mixture_em
    )

Finally, thanks to the great parsnip API, we can fit and predict all models at once.

    set.seed(1)

    models <- map(specs, ~ fit(.x, formula, data))

    pred_sob <- map(models, ~ predict(.x, new_data,
                                      type = "survival",
                                      eval_time = seq(500)))

The following plot compares each model with the Kaplan-Meier estimates of the survival function.

    all_preds <- bind_rows(pred_sob, .id = "modelo") |>
      group_by(modelo) |>
      dplyr::mutate(id = new_data$x) |>
      ungroup() |>
      tidyr::unnest(cols = .pred)

    km_fit <- surv_km |>
      tidyr::unnest(cols = .pred) |>
      filter(.eval_time < 500)

    ggplot(aes(x = .eval_time, y = .pred_survival, col = id), data = all_preds) +
      theme_bw() +
      geom_line() +
      facet_wrap(~modelo) +
      geom_line(data = km_fit, linetype = "dashed")