---
title: "Paper: PBSC application"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Paper: PBSC application}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 6,
  fig.height = 5
)
```

```{r setup}
library(simplexgof)
```

## The PBSC application

This article reproduces the peripheral blood stem cell (PBSC)
transplantation application from the companion methodological paper
(Ospina, Espinheira, Silva and Barros, 2026), using the `pbsc` dataset
(Edmonton Hematopoietic Institute - Alberta Health Services).

The response `recovery` is the CD34+ cell recovery rate, a continuous
proportion in $(0, 1)$. The constant-dispersion model used in
`paper_pbsc()` is

$$
\mathrm{logit}(\mu_t) = \beta_1 + \beta_2\,\mathrm{adj\_age}_t +
  \beta_3\,\mathrm{chemo}_t
$$

$$
\log(\sigma^2_t) = \gamma_1
$$

where `adj_age` is the adjusted patient-age variable and `chemo` is the
chemotherapy protocol indicator (0 = one-day, 1 = three-day protocol).

## The data

```{r}
data(pbsc)
head(pbsc)
summary(pbsc)
```

## One-call reproduction

The function `paper_pbsc()` fits the model, runs the bootstrap GoF test,
and produces the diagnostic plots from the paper in a single call. We use
`B = 50` bootstrap replicates here for speed; the paper uses `B = 1000`.

```{r, fig.alt = "Diagnostic plots for the PBSC application"}
res <- paper_pbsc(B = 50, seed = 456, plot = TRUE, verbose = FALSE)
```

### Parameter estimates

```{r}
print(res$table_params, row.names = FALSE)
```

### Goodness-of-fit results

```{r}
print(res$table_gof, row.names = FALSE)
```

## Step by step

```{r}
X <- cbind(1, pbsc$adj_age, pbsc$chemo)
colnames(X) <- c("(Intercept)", "adj_age", "chemo")
Z <- matrix(1, nrow(pbsc), 1)
colnames(Z) <- "(Intercept)"

fit <- simplex_fit(pbsc$recovery, X, Z)
fit

dg <- simplex_diag(fit)
dg$Tn
dg$Un
```

```{r, fig.alt = "Influence index plot for the PBSC model"}
plot_influence(dg)
```

```{r}
set.seed(456)
gof <- simplex_gof(pbsc$recovery, X, Z, B = 50, verbose = FALSE)
gof
```

```{r, fig.alt = "Bootstrap distribution of Un for the PBSC application"}
plot_gof_boot(gof)
```

With $n = 242$, this larger sample illustrates the bootstrap calibration
in a setting where the asymptotic approximation is already reasonably
well behaved, and serves as a useful contrast with the small-sample
ammonia application.

## References

Ospina, R., Espinheira, P. L., Silva, F. C., Barros, M. (2026). A
Bootstrap-Calibrated Local Influence Goodness-of-Fit Procedure for
Simplex Regression Models.