Date: 2025-11-26

# Analyzing Clinical Significance: The Percentage-Change Approach

#### 2025-11-26

## Introduction

The percentage-change approach defines clinical significance based on the relative change in a patient’s score from baseline. This method is common in clinical trials where a specific reduction in symptoms, such as “a 50% improvement,” is a primary endpoint for defining treatment response.

A change is considered clinically significant if it meets or exceeds a predefined Percentage-Change Cutoff (PCC). For example, if the PCC is 50% (or 0.5), any patient who shows at least a 50% reduction in symptoms would be classified as “Improved”.

A key consideration for this method is that it is highly dependent on the patient’s baseline score. A 10-point drop is a 50% improvement for a patient starting at 20 points, but only a 25% improvement for a patient starting at 40 points. This characteristic should be kept in mind when interpreting the results.

This vignette demonstrates how to use the `cs_percentage()` function to apply this approach.

    library(clinicalsignificance)

## Basic Analysis

Let’s analyze the `claus_2020` dataset. A common benchmark for depression treatment trials is a 50% reduction in symptom scores. We will set this as our `pct_improvement` cutoff.

    # Analyze change using a 50% improvement cutoff
    pct_results <- claus_2020 |>
      cs_percentage(
        id = id,
        time = time,
        outcome = bdi,
        pre = 1,
        post = 4,
        pct_improvement = 0.5
      )

    summary(pct_results)
    #>
    #> ---- Clinical Significance Results ----
    #>
    #> Approach:                 Percentage-based
    #> Percentage Improvement:   50.00%
    #> Percentage Deterioration: 50.00%
    #> Better is:                Lower
    #> N (original):             43
    #> N (used):                 40
    #> Percent used:             93.02%
    #> Outcome:                  bdi
    #>
    #> Category     |  N | Percent
    #> ---------------------------
    #> Improved     | 11 |  27.50%
    #> Unchanged    | 29 |  72.50%
    #> Deteriorated |  0 |   0.00%

The summary shows that based on this 50% criterion, about 28% of patients are classified as having improved.

### Visualizing the Results

The plot for the percentage-change approach looks similar to those for the anchor- and distribution-based methods. However, the shaded area is now determined by the percentage-change cutoff relative to each individual’s starting score. This means the boundaries of the “unchanged” area are not parallel lines.

    plot(pct_results)
    #> Ignoring unknown labels:
    #> • colour : "Group"

## Grouped Analysis

We can also explore if the proportion of “responders” differs between the treatment groups (TAU vs. PA).

    # Grouped analysis with a 50% improvement cutoff
    pct_grouped <- claus_2020 |>
      cs_percentage(
        id = id,
        time = time,
        outcome = bdi,
        pre = 1,
        post = 4,
        pct_improvement = 0.5,
        group = treatment
      )

    summary(pct_grouped)
    #>
    #> ---- Clinical Significance Results ----
    #>
    #> Approach:                 Percentage-based
    #> Percentage Improvement:   50.00%
    #> Percentage Deterioration: 50.00%
    #> Better is:                Lower
    #> N (original):             43
    #> N (used):                 40
    #> Percent used:             93.02%
    #> Outcome:                  bdi
    #>
    #> Group |     Category |  N | Percent | Percent by Group
    #> ------------------------------------------------------
    #> TAU   |     Improved |  2 |   5.00% |           10.53%
    #> TAU   |    Unchanged | 17 |  42.50% |           89.47%
    #> TAU   | Deteriorated |  0 |   0.00% |            0.00%
    #> PA    |     Improved |  9 |  22.50% |           42.86%
    #> PA    |    Unchanged | 12 |  30.00% |           57.14%
    #> PA    | Deteriorated |  0 |   0.00% |            0.00%

The results suggest that a much higher proportion of patients in the Placebo Amplification (PA) group (42.9%) achieved a 50% symptom reduction compared to the Treatment as Usual (TAU) group (10.5%).

The plot clearly visualizes this difference:

    plot(pct_grouped)

## Using Different Cutoffs for Improvement and Deterioration

A useful feature of `cs_percentage()` is the ability to set different cutoffs for improvement and deterioration via the `pct_deterioration` argument. For instance, in some contexts, a small worsening of symptoms (e.g., 20%) might already be considered a significant deterioration, while a larger change (e.g., 50%) is required for improvement.

    pct_asymmetric <- claus_2020 |>
      cs_percentage(
        id = id,
        time = time,
        outcome = bdi,
        pre = 1,
        post = 4,
        pct_improvement = 0.5,
        pct_deterioration = 0.2 # A smaller threshold for worsening
      )

    summary(pct_asymmetric)
    #>
    #> ---- Clinical Significance Results ----
    #>
    #> Approach:                 Percentage-based
    #> Percentage Improvement:   50.00%
    #> Percentage Deterioration: 20.00%
    #> Better is:                Lower
    #> N (original):             43
    #> N (used):                 40
    #> Percent used:             93.02%
    #> Outcome:                  bdi
    #>
    #> Category     |  N | Percent
    #> ---------------------------
    #> Improved     | 11 |  27.50%
    #> Unchanged    | 26 |  65.00%
    #> Deteriorated |  3 |   7.50%