Waterfall Plots for Oncology Trials

Introduction

Oncology clinical trials frequently generate a large amount of tumor-response data. A statistical table can summarize response categories, while a longitudinal plot can show how individual tumors change over time.

A waterfall plot provides a different perspective. It displays the magnitude of tumor change for individual patients, usually using each patient's best percentage change from baseline in a target-lesion measure.

Each patient is represented by a vertical bar. Patients are commonly ordered from the greatest tumor reduction to the greatest tumor increase.

What Does a Waterfall Plot Show?

For a typical oncology waterfall plot, the vertical axis represents the percentage change from baseline in tumor burden.

Negative values indicate tumor shrinkage, while positive values indicate tumor growth.

For example:

The resulting bars provide an immediate visual summary of the distribution of tumor responses across patients.

The Percentage Change From Baseline

Let:

• \(B_i\) = baseline tumor measurement for patient \(i\)
• \(Y_i\) = tumor measurement at a particular post-baseline assessment

The percentage change from baseline is:

Suppose a patient's baseline sum of target-lesion diameters is 80 mm and a subsequent assessment is 60 mm.

The percentage change is:

Thus, the patient's tumor burden has decreased by 25% relative to baseline.

What Is Usually Plotted?

In many solid-tumor analyses, the quantity displayed is the best percentage change from baseline in the sum of target-lesion measurements.

If patient \(i\) has post-baseline percentage changes:

then the best tumor reduction is:

The patient would therefore be represented by a bar at:

This is why the term best percentage change is important. The waterfall plot is generally not displaying the patient's final tumor measurement.

Why Use the Best Change?

Cancer treatment response is dynamic. A patient may initially experience substantial tumor shrinkage and later progress.

If the objective is to visualize the maximum observed tumor reduction, using the best post-baseline change captures the strongest response observed during the relevant assessment period.

For example:

The best percentage change is:

The waterfall plot therefore displays −42% for this patient.

RECIST 1.1 and Waterfall Plots

Waterfall plots are frequently used in oncology trials involving RECIST 1.1 tumor-response assessments.

Under RECIST 1.1, tumor response is not determined solely by looking at the best percentage change in target lesions. The overall response assessment incorporates target lesions, non-target lesions, and new lesions.

Common RECIST Thresholds on a Waterfall Plot

For target-lesion measurements, two familiar reference thresholds are:

• −30%: the magnitude of target-lesion shrinkage associated with the partial-response threshold under RECIST 1.1, subject to the complete RECIST assessment.
• +20%: the magnitude of target-lesion increase associated with the progressive-disease threshold, together with the required absolute increase and other RECIST conditions.

These thresholds are often drawn as horizontal reference lines.

Constructing the Waterfall Plot

The basic workflow is:

A Worked Example

Suppose an oncology study includes eight patients with the following baseline and best post-baseline target-lesion measurements.

For patient 001:

For patient 007:

The waterfall plot would order the patients from −62.5% through +37.5%.

Why Patients Are Ordered

The ordering is one of the defining characteristics of a waterfall plot.

Patients are generally sorted by their best percentage change from baseline:

Because shrinkage is represented by increasingly negative values, the sorting is usually ascending.

df <- df[order(df$best_change), ]

After sorting, the bars form the characteristic descending-to-ascending waterfall pattern.

Why Sorting Matters

Without sorting, the plot becomes primarily a collection of individual bars.

Sorting creates a visual distribution of tumor response.

It immediately allows the reader to see:

• The largest observed tumor reductions
• The proportion of patients with any tumor shrinkage
• The number crossing a clinically relevant shrinkage threshold
• The distribution of tumor growth
• Potentially unusual or extreme observations

Reference Lines

A conventional waterfall plot often includes horizontal reference lines.

For a RECIST-oriented visualization, investigators may display:

and:

These lines provide visual landmarks for the reader.

A patient below the −30% line has experienced at least 30% target-lesion shrinkage from baseline at the selected best assessment.

A patient above +20% has experienced at least 20% target-lesion growth relative to baseline, although formal RECIST progressive disease requires the complete set of RECIST criteria.

Waterfall Plot Versus RECIST Response Rate

The waterfall plot and objective response rate answer related but different questions.

A waterfall plot therefore provides a useful individual-patient visualization, but it should be interpreted alongside the formal efficacy analyses.

Best Percentage Change Is Not the Same as Best Overall Response

This distinction is especially important in clinical study reports.

Suppose a patient has a 45% reduction in target-lesion measurements but develops a new lesion.

The target lesions may show substantial shrinkage, yet the overall RECIST response may be progressive disease because of the new lesion.

Therefore:

Handling Patients With Tumor Growth

Patients with positive percentage changes should generally remain in the plot when the purpose is to display the distribution of tumor change.

For example:

Removing patients simply because their tumors grew can make the treatment appear more effective than it actually was.

Handling Missing Tumor Assessments

Missing assessments require particular attention.

A patient with no evaluable post-baseline tumor assessment does not necessarily have a best change of 0%.

The appropriate handling of such patients depends on the estimand, analysis population, endpoint definition, and prespecified statistical analysis plan.

Patients With No Post-Baseline Assessment

Consider a patient who has a valid baseline scan but withdraws before the first post-baseline tumor assessment.

There is no observed post-baseline tumor change from which to calculate a best percentage change.

The analyst should therefore follow the prespecified rules for the relevant analysis rather than assigning an arbitrary value.

Patients With Only One Post-Baseline Assessment

If a patient has only one evaluable post-baseline assessment, that assessment may be the best observed change for the purpose of a descriptive waterfall plot.

For example:

However, whether that patient is considered evaluable for a formal response endpoint depends on the prespecified endpoint definition and assessment requirements.

Progression Before a Documented Best Response

Some patients progress rapidly.

For example, a patient might have:

The best tumor change in the mathematical sense is:

This illustrates why the exact definition of the waterfall variable matters.

A formal analysis may use rules involving progression, censoring, assessment windows, or other analysis conventions that are not captured by simply taking the numerical minimum of every available measurement.

Target Lesions and Non-Target Lesions

A common waterfall plot is based on the sum of target-lesion diameters.

Non-target lesions are generally not combined into this continuous percentage change calculation in the same way.

However, non-target disease can influence the overall RECIST response.

Therefore, the waterfall plot should not be presented as though it completely summarizes every component of disease response.

New Lesions

New lesions are another important distinction.

A patient can show substantial shrinkage of measured target lesions and still have progressive disease if a new lesion is detected.

For example:

does not guarantee a partial response if other RECIST components indicate progressive disease.

Waterfall Plots in Randomized Trials

Waterfall plots can be useful in randomized oncology trials, particularly when comparing the distribution of tumor changes between treatment groups.

However, a single combined waterfall plot can become difficult to interpret when multiple treatment arms are present.

A common approach is to create:

• One waterfall plot per treatment arm
• Consistent vertical scales across treatment arms
• Consistent definitions of best change
• Consistent reference lines

Maintaining the same y-axis scale is particularly important when the plots are intended for direct visual comparison.

Example With Two Treatment Arms

The analyst could create separate plots for Drug A and Drug B while using the same vertical range.

Color-Coding the Bars

Color can be used to communicate additional information.

For example, bars may be categorized according to a prespecified response classification or treatment group.

However, color should not replace the numerical y-axis.

Should Bars Be Colored by RECIST Response?

This can be useful, but it requires careful data integration.

For example, a plot could distinguish:

• Complete response
• Partial response
• Stable disease
• Progressive disease
• Not evaluable

But the response category should come from the formal RECIST assessment, not simply from whether the bar crosses a visual threshold.

Annotating the Plot

A publication-quality waterfall plot may include:

• Patient identifier or an anonymized sequential patient number
• Treatment arm
• Best percentage change from baseline
• Reference line at −30%
• Reference line at +20%
• A legend explaining bar categories
• A clearly labeled y-axis
• A footnote describing the analysis population

Patient Identifiers

Patient identifiers should generally be anonymized in external presentations and publications.

Instead of displaying an internal subject identifier such as:

SUBJ-001-002-ABC

a sequential identifier may be preferable:

001  002  003  004  005 ...

The exact presentation should follow the study's data privacy and reporting requirements.

Ordering Within Ties

Two or more patients may have exactly the same best percentage change.

For example:

The patients may be ordered using a secondary variable such as patient identifier or treatment assignment.

The secondary ordering should be deterministic so that repeated executions produce the same plot.

Best Change and Assessment Windows

The phrase "best change" sounds simple but can hide important analysis decisions.

Suppose tumor assessments occur at:

• Week 6
• Week 12
• Week 18
• Week 24
• Week 36

If the analysis defines a particular assessment window, measurements outside that window may not be eligible for inclusion in the best-change calculation.

Therefore, the waterfall dataset should generally be derived from the same prespecified assessment rules used by the clinical analysis.

Waterfall Plots Are Descriptive

One of the most important statistical limitations is that a waterfall plot is primarily descriptive.

It can show the observed distribution of tumor changes, but it does not by itself establish:

• Statistical significance
• Causal treatment effect
• Improvement in overall survival
• Improvement in progression-free survival
• Improvement in objective response rate

Those conclusions require the appropriate prespecified statistical analyses.

The Problem With Small Samples

Waterfall plots can be visually impressive even when the sample size is small.

Suppose only 12 patients are shown and four have large tumor reductions.

That pattern may look highly encouraging.

But four responses among 12 patients is still an estimate with substantial uncertainty.

The waterfall plot should therefore be considered alongside confidence intervals, response-rate analyses, time-to-event endpoints, and other relevant evidence.

The Problem With Selective Inclusion

A particularly serious issue occurs when only patients with measurable tumor assessments are shown without clearly identifying who was excluded.

If patients with early treatment discontinuation or missing scans are omitted, the displayed distribution can be more favorable than the experience of the entire enrolled population.

Waterfall Plot Versus Spider Plot

Waterfall and spider plots are complementary.

A waterfall plot answers: "How much did each patient's tumor shrink or grow at its best observed point?"

A spider plot answers: "How did each patient's tumor burden change over time?"

Waterfall Plot Versus Swimmer Plot

A swimmer plot focuses on patient-level timelines rather than tumor percentage change.

It can display:

• Treatment duration
• Response duration
• Progression
• Death
• Follow-up
• Other clinically relevant events

Thus, the three plots provide different perspectives on the same trial.

Preparing the Analysis Dataset

A clean waterfall plot usually requires a patient-level dataset containing at least:

• Patient identifier
• Treatment arm
• Baseline tumor measurement
• Post-baseline tumor measurements
• Assessment dates or visits
• Percentage change from baseline
• Best percentage change
• Relevant response category
• Analysis-population flags
• Evaluability indicators

For example:

Deriving Percentage Change in R

Suppose the analysis dataset contains baseline and post-baseline target-lesion sums.

df$change_pct <-
  (df$target_sum - df$baseline_sum) /
  df$baseline_sum * 100

For example, if:

baseline_sum = 80
target_sum   = 60

then:

change_pct
# -25

Deriving Best Change

If each row represents a valid tumor assessment, the best observed percentage change can be obtained by taking the minimum percentage change for each patient.

library(dplyr)

best_change <- df %>%
  group_by(USUBJID) %>%
  summarise(
    best_change = min(
      change_pct,
      na.rm = TRUE
    )
  )

However, this simple calculation is appropriate only when the input data have already been filtered according to the study's analysis rules.

Ordering Patients in R

plot_df <- best_change %>%
  arrange(best_change) %>%
  mutate(
    patient_order = row_number()
  )

This creates an ordering from the largest tumor reduction to the largest tumor increase.

Creating a Basic Waterfall Plot in R

library(ggplot2)

ggplot(
  plot_df,
  aes(
    x = patient_order,
    y = best_change
  )
) +
  geom_col() +
  geom_hline(
    yintercept = 0
  ) +
  geom_hline(
    yintercept = -30,
    linetype = "dashed"
  ) +
  geom_hline(
    yintercept = 20,
    linetype = "dashed"
  ) +
  labs(
    x = "Patients",
    y = "Best Percentage Change From Baseline (%)"
  ) +
  theme_classic()

The key graphical element is:

geom_col()

which creates one bar for each patient.

Adding Patient Labels

Patient labels can be added when the sample size is sufficiently small and the identifiers remain readable.

ggplot(
  plot_df,
  aes(
    x = patient_order,
    y = best_change
  )
) +
  geom_col() +
  scale_x_continuous(
    breaks = plot_df$patient_order,
    labels = plot_df$USUBJID
  ) +
  theme_classic()

For larger trials, labeling every patient can create severe visual clutter.

Coloring by Response Category

Suppose the dataset contains the formal RECIST overall response category.

ggplot(
  plot_df,
  aes(
    x = patient_order,
    y = best_change,
    fill = RESPONSE
  )
) +
  geom_col() +
  geom_hline(
    yintercept = 0
  ) +
  geom_hline(
    yintercept = -30,
    linetype = "dashed"
  ) +
  geom_hline(
    yintercept = 20,
    linetype = "dashed"
  ) +
  labs(
    x = "Patients",
    y = "Best Percentage Change From Baseline (%)",
    fill = "RECIST Response"
  ) +
  theme_classic()

The exact colors should be selected according to the reporting environment, accessibility requirements, and corporate or publication standards.

Adding Response Labels

For a small study, response labels can be added above or below the bars.

ggplot(
  plot_df,
  aes(
    x = patient_order,
    y = best_change,
    fill = RESPONSE
  )
) +
  geom_col() +
  geom_text(
    aes(
      label = RESPONSE
    ),
    vjust = -0.4,
    size = 3
  ) +
  geom_hline(
    yintercept = -30,
    linetype = "dashed"
  ) +
  geom_hline(
    yintercept = 20,
    linetype = "dashed"
  )

In practice, labels should be positioned carefully so that they do not overlap the bars or each other.

Displaying the Percentage Above Each Bar

Another useful option is to display the numerical value itself.

ggplot(
  plot_df,
  aes(
    x = patient_order,
    y = best_change
  )
) +
  geom_col() +
  geom_text(
    aes(
      label = sprintf(
        "%.1f%%",
        best_change
      )
    ),
    vjust = ifelse(
      plot_df$best_change < 0,
      1.2,
      -0.3
    )
  )

This is usually practical only for relatively small datasets.

Handling Very Large Responses

Some patients may have very large increases in tumor burden.

For example:

A single +350% value can compress the visual differences among the shrinking tumors.

Several approaches are possible, but they should be chosen carefully.

• Retain the full scale and accept the compression.
• Use an axis break only when clearly indicated.
• Annotate extreme observations.
• Use a separate supplementary visualization.

Negative Values and Axis Interpretation

A common mistake is to interpret a bar at −60% as "60% worse" because the number is negative.

The correct interpretation is:

Similarly:

The sign communicates direction.

Why the Zero Line Matters

The horizontal zero line represents no change from baseline.

Bars below zero represent shrinkage. Bars above zero represent growth.

The zero line should normally remain visually clear because it is the primary reference point for interpreting the direction of tumor change.

Interpreting a Typical Waterfall Plot

Imagine that a trial produces the following distribution:

• Several patients have reductions greater than 50%.
• Several additional patients have reductions between 10% and 30%.
• A group of patients has little change.
• Several patients have tumor growth.

The plot immediately communicates that tumor shrinkage occurred across a substantial portion of the population.

However, the plot alone does not tell us:

• How durable those responses were.
• Whether the response rate is statistically persuasive.
• Whether survival improved.
• Whether patients with shrinkage were more likely to remain progression-free.
• Whether the observed distribution differs from a control group.

Waterfall Plots in Early-Phase Oncology

Waterfall plots are particularly common in early-phase oncology studies.

They can be useful when investigators want to visualize heterogeneous individual responses to a treatment.

For example, an early-phase study may show:

These observations can help characterize the treatment's activity profile, particularly when combined with longitudinal and time-to-event endpoints.

Waterfall Plots in Dose-Escalation Studies

In a dose-escalation study, a waterfall plot can sometimes be annotated by dose level.

This may help illustrate whether tumor reductions appear across multiple dose levels.

However, dose-response conclusions should not be drawn solely from the visual distribution of bars.

Waterfall Plots in Expansion Cohorts

Expansion cohorts can produce substantially larger samples than the original dose-escalation cohort.

In such settings, separate waterfall plots may be useful for:

• Disease cohorts
• Treatment arms
• Biomarker-defined populations
• Dose levels
• Prior-treatment subgroups

Subgroup waterfall plots should be accompanied by the number of patients represented in each subgroup.

Waterfall Plots and Biomarker Subgroups

Suppose an oncology study evaluates treatment activity according to biomarker status.

Separate plots might be created for:

• Biomarker-positive patients
• Biomarker-negative patients

The plots can reveal visually different response distributions.

However, apparent differences should be evaluated with the prespecified statistical analysis rather than judged solely from the plot.

Waterfall Plot Limitations

Waterfall plots have several important limitations.

1. They emphasize the best observed response. This can make treatment activity look stronger than a longitudinal assessment would suggest.
2. They can hide duration. A patient who briefly shrinks by 60% and then progresses can appear similar to a patient who remains at −60% for a prolonged period.
3. They do not automatically incorporate all RECIST components. Non-target lesions and new lesions can affect overall response.
4. They can exclude patients with missing assessments. If exclusions are not transparent, the visualization may be misleading.
5. They are descriptive. A visual pattern is not a substitute for inferential analysis.
6. Small samples can be unstable. A few patients can dominate the visual impression.

The "Best Response" Bias in Visualization

Suppose every patient is followed for a long period and the analyst selects the most favorable tumor measurement observed during that period.

The resulting distribution will naturally emphasize the most favorable point for each patient.

This is not necessarily wrong—the best percentage change may be exactly the quantity the plot is intended to display.

But it means that a waterfall plot should not be interpreted as a longitudinal summary.

A More Complete Oncology Visualization Set

For many oncology trials, a useful set of efficacy graphics includes:

Creating a Reproducible Waterfall Dataset

A strong workflow separates data derivation from visualization.

The general structure is:

This is preferable to performing complicated derivations directly inside the plotting code.

Recommended Patient-Level Variables

Quality Control Checks

Before producing the final plot, perform explicit data checks.

• Confirm every included patient has a valid baseline measurement.
• Verify that the baseline measurement is correctly identified.
• Check that percentage changes are mathematically correct.
• Verify the best-change derivation.
• Confirm that assessment windows are correctly applied.
• Review missing assessments.
• Review extreme values.
• Confirm treatment-arm assignment.
• Confirm response-category derivation.
• Verify the number of patients represented.

Numerical QC Example

Suppose a patient has:

and a best post-baseline target-lesion sum of:

Then:

The programming output should therefore contain approximately:

BEST_CHANGE = -40.0

not:

BEST_CHANGE = 40.0

A sign error can completely reverse the interpretation of the plot.

Check for Impossible Values

For a conventional percentage change calculated from a nonnegative tumor measurement, values below −100% should generally trigger investigation.

For example:

would generally indicate a derivation, denominator, or source-data problem rather than a plausible tumor reduction.

Common Programming Mistakes

1. Using the final assessment instead of the best assessment. This changes the meaning of the plot.
2. Sorting in the wrong direction. Patients should normally progress visually from greatest shrinkage to greatest growth.
3. Converting missing values to zero. Missing does not mean unchanged.
4. Ignoring baseline errors. An incorrect baseline can distort every subsequent percentage change.
5. Using all tumor records without applying analysis rules. Not every raw assessment necessarily belongs in the waterfall derivation.
6. Assigning RECIST response solely from the waterfall bar. Formal RECIST response uses more information than target-lesion percentage change alone.
7. Using inconsistent y-axis scales between treatment arms. This can make visual comparisons misleading.
8. Truncating extreme growth without disclosure. This can materially alter the interpretation of treatment activity.

Common Interpretation Mistakes

1. "Everyone below −30% is a responder." Not necessarily. The formal response category depends on the complete response-assessment algorithm.
2. "The tallest negative bars prove efficacy." No. They demonstrate observed tumor shrinkage, not statistical evidence of efficacy.
3. "The waterfall plot shows response durability." No. Durability requires longitudinal information.
4. "A patient above +20% automatically has progressive disease." Not necessarily. The full RECIST progression criteria must be considered.
5. "Patients without evaluable scans can simply be omitted." Only if that is consistent with the prespecified analysis and the omission is transparent.
6. "A waterfall plot is enough to summarize oncology efficacy." No. It should generally be considered one component of a broader efficacy presentation.

Waterfall Plots in Clinical Study Reports

In a Clinical Study Report, the waterfall plot should normally be accompanied by sufficient text to define the plotted quantity.

A useful figure title is:

The figure footnote can specify:

• The analysis population
• The tumor-assessment criteria
• The definition of baseline
• The definition of best percentage change
• The meaning of reference lines
• The treatment arm
• The handling of patients without post-baseline assessments

Example CSR Footnote

A concise footnote might state:

Waterfall Plots and Objective Response Rate

Suppose 40 patients are included in the response analysis and 12 achieve a formal complete or partial response.

The objective response rate is:

or:

The waterfall plot provides individual-level context for those aggregate results.

The ORR answers: "How many patients met the formal response definition?"

The waterfall plot answers: "What was the distribution of observed tumor change across patients?"

Confidence Intervals Still Matter

If ORR is a key efficacy endpoint, the estimated response rate should generally be accompanied by an appropriate confidence interval.

For example:

The waterfall plot and confidence interval answer different questions and should not be substituted for one another.

Waterfall Plots and Statistical Inference

A waterfall plot can support interpretation of a treatment's activity profile, but inferential conclusions require the appropriate statistical framework.

Depending on the trial, this may involve:

• Exact binomial confidence intervals
• Hypothesis tests for response rate
• Risk differences
• Risk ratios
• Odds ratios
• Time-to-event methods
• Regression models
• Randomized treatment comparisons

The appropriate method depends on the study design and estimand.

When a Waterfall Plot Is Especially Useful

Waterfall plots are particularly useful when:

• Individual tumor response is scientifically important.
• The trial has a measurable tumor-burden endpoint.
• Heterogeneity of response is of interest.
• There is interest in visualizing tumor shrinkage and growth simultaneously.
• The sample size is small enough that individual bars remain interpretable.
• The plot can be presented alongside formal efficacy analyses.

When a Waterfall Plot May Be Less Useful

A waterfall plot may be less informative when:

• There are very few evaluable patients.
• Most patients have no post-baseline assessment.
• Tumor burden is not an appropriate measure of treatment effect.
• The endpoint is primarily time-to-event.
• Longitudinal tumor dynamics are more important than best response.
• The plot becomes too dense to interpret.

A Practical Waterfall Plot Workflow

Final QC Checklist

The Most Important Concept

The most important concept is that a waterfall plot is a patient-level visualization of tumor change, not a standalone efficacy analysis.

The typical calculation begins with:

and the patient's best observed change is then derived according to the prespecified tumor-assessment and analysis rules.

Patients are subsequently ordered from the greatest reduction to the greatest increase.

The result provides a compact visual representation of the heterogeneity of tumor response.

References

Eisenhauer, E.A., Therasse, P., Bogaerts, J., Schwartz, L.H., Sargent, D., Ford, R., Dancey, J., Arbuck, S., Gwyther, S., Mooney, M., Rubinstein, L., Shankar, L., Dodd, L., Kaplan, R., Lacombe, D. & Verweij, J. (2009). New response evaluation criteria in solid tumours: Revised RECIST guideline (version 1.1). European Journal of Cancer, 45(2), 228–247.

Therasse, P., Arbuck, S.G., Eisenhauer, E.A., Wanders, J., Kaplan, R.S., Rubinstein, L., Verweij, J., Van Glabbeke, M., van Oosterom, A.T., Christian, M.C. & Gwyther, S.G. (2000). New guidelines to evaluate the response to treatment in solid tumors. European Organization for Research and Treatment of Cancer, National Cancer Institute of the United States, National Cancer Institute of Canada. Journal of the National Cancer Institute, 92(3), 205–216.

Schwartz, L.H., Litière, S., de Vries, E., Ford, R., Gwyther, S., Mandrekar, S., Shankar, L., Bogaerts, J., Chen, A., Dancey, J. & Sargent, D. (2016). RECIST 1.1 — Update and clarification: From the RECIST Committee. European Journal of Cancer, 62, 132–137.

National Cancer Institute. RECIST 1.1 Guidelines. Clinical trial response evaluation guidance for solid tumors.

FDA. (2018). Clinical Trial Endpoints for the Approval of Cancer Drugs and Biologics. U.S. Food and Drug Administration.