---
title: "Analyzing Clinical Significance: The Statistical Approach"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{4. Statistical Approach}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  chunk_output_type: console
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 5,
  fig.align = "center"
)
```

## Introduction

The statistical approach to clinical significance evaluates whether a patient has **moved from a dysfunctional ("clinical") population to a functional ("non-clinical") population** as a result of an intervention. This method is based on the idea that a meaningful change involves not just a reduction in symptoms, but a transition to a state of healthy functioning.

To apply this method, we must first define the score distributions of both the clinical and functional populations. From these, we calculate a **cutoff score** that optimally separates the two groups. A patient is then considered to have made a clinically significant change if they were in the clinical range before treatment and in the functional range after treatment.

This vignette demonstrates how to use the `cs_statistical()` function to perform this analysis. It's important to note that this method is a key component of the powerful **Combined Approach**, which is often the most informative way to assess clinical significance.

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

## Defining Populations and Calculating a Cutoff

The most crucial step in this approach is defining the functional population. This requires obtaining summary statistics (mean and standard deviation) for the outcome measure from a relevant non-clinical or healthy sample.

For our example using the BDI-II from the `claus_2020` dataset, we will use normative data from Kühner et al. (2007), who reported a mean of 7.69 and a standard deviation of 7.52 for a German non-clinical sample.

The `clinicalsignificance` package provides three methods for calculating the cutoff, specified by the `cutoff_type` argument:
- **`"a"`**: Based only on the clinical sample's distribution.
- **`"b"`**: Based on the functional sample's mean and the clinical sample's standard deviation.
- **`"c"`**: **(Recommended)** Incorporates the mean and standard deviation from *both* the clinical and functional populations to find an optimal midway point. This is generally the most robust and objective choice.

### Example Analysis

Let's perform the analysis using the recommended cutoff type "c". The function will automatically calculate the mean and standard deviation for the clinical sample from the `claus_2020` pre-treatment data.

```{r stat-basic}
# Perform the statistical analysis
stat_results <- claus_2020 |>
  cs_statistical(
    id = id,
    time = time,
    outcome = bdi,
    pre = 1,
    post = 4,
    m_functional = 7.69,
    sd_functional = 7.52,
    cutoff_type = "c"
  )

summary(stat_results)
```
The summary tells us that the calculated cutoff score is 21.6. Based on this, 32.5% of patients were classified as "Improved," meaning they started above this cutoff (in the clinical range) and ended below it (in the functional range).

### Visualizing the Results

The plot for the statistical approach is unique. It features two dashed lines representing the cutoff score on both the pre-treatment (x-axis) and post-treatment (y-axis). These lines divide the plot into four quadrants:

* **Top-Right**: Clinical before and after (Unchanged).
* **Bottom-Left**: Functional before and after (Unchanged).
* **Bottom-Right**: Clinical before, functional after (Improved).
* **Top-Left**: Functional before, clinical after (Deteriorated).

```{r stat-basic-plot}
plot(stat_results)
```

## Grouped Analysis

We can also investigate if the proportion of patients who transitioned to the functional population differs between the treatment groups (TAU vs. PA).

```{r stat-grouped}
# Grouped statistical analysis
stat_grouped <- claus_2020 |>
  cs_statistical(
    id = id,
    time = time,
    outcome = bdi,
    pre = 1,
    post = 4,
    m_functional = 7.69,
    sd_functional = 7.52,
    cutoff_type = "c",
    group = treatment
  )

summary(stat_grouped)
```
The analysis reveals a substantial difference: 47.6% of patients in the Placebo Amplification (PA) group moved into the functional range, compared to only 15.8% in the Treatment as Usual (TAU) group.

The plot makes this difference visually apparent:
```{r stat-grouped-plot}
plot(stat_grouped)
```

## Summary and Next Steps

The statistical approach provides a powerful criterion for clinical significance by focusing on a patient's **end-state functioning**.

* **Strength**: It defines recovery in an absolute sense (return to normality) rather than just relative change.
* **Limitation**: It requires reliable normative data for a functional population, which may not always be available. Also, it doesn't consider the *magnitude* of change for patients who do not cross the cutoff.

This is why the statistical approach is most powerful when used as part of a **Combined Approach**, where it is paired with a measure of reliable or meaningful change. We highly recommend reviewing the vignette on the **Combined Approach** to see how to integrate these concepts for the most comprehensive assessment of patient outcomes.