Rethinking Continuous Endpoints in Clinical Decision Analysis Through Decision Curves

In their seminal work, Steyerberg and colleagues established that prediction models must undergo a three-step assessment encompassing discrimination, calibration, and clinical utility. Over recent years, decision curve analysis has become the predominant methodology for evaluating clinical utility, earning widespread endorsement in journal editorials, reporting guidelines, and machine learning benchmarks. Originally developed for models with binary endpoints—such as disease presence or cancer recurrence—and later adapted to survival time outcomes, decision curve analysis quantifies net benefit by weighing true positives against false positives through a decision threshold probability. However, many clinical models forecast continuous outcomes, such as life expectancy or symptom reduction. Writing in Diagnostic and Prognostic Research, Lasai Barreñada and Andrew Vickers investigate how decision curve analysis can be extended to continuous endpoints, while evaluating the theoretical limitations and clinical dilemmas that arise from continuous outcome metrics.

To clarify how continuous models operate, the authors develop a typology categorizing medical prediction tools into three structural groups. The first group comprises models that do not forecast direct clinical events, but instead estimate continuous physiological parameters that are difficult or expensive to measure directly. A classic example is estimated Glomerular Filtration Rate, which quantifies renal function using equations based on age, sex, and serum biomarkers. While direct measurement requires administering clearance agents like iohexol and tracking plasma or urine concentration over time, estimated Glomerular Filtration Rate provides an efficient alternative used to establish contraindications for chemotherapy or predict kidney injury following cardiac surgery. A related application involves radiation therapy planning, where mathematical models predict radiation doses delivered to healthy tissues and tumors. Because these first-type models serve as inputs to downstream algorithms rather than direct medical endpoints, Barreñada and Vickers conclude that they are inappropriate for direct decision analytic evaluation.

In contrast, the researchers focus their analysis on models of the second and third types, which directly inform treatment decisions. The second model type directly predicts a continuous clinical endpoint of immediate medical relevance, such as life expectancy calculated from actuarial tables or comorbidity indices. For localized prostate cancer, where progression is typically slow, life expectancy estimates guide whether patients should undergo aggressive surgery or radiotherapy, sparing men with shorter life expectancy from unneeded intervention. The third model type predicts treatment-related change in a continuous clinical measure. For example, published models predict kidney function following partial versus radical nephrectomy, helping surgeons determine whether kidney preservation justifies higher operative complication risks. Another application predicts headache pain reduction following a course of acupuncture. For these direct decision models, the authors formulate continuous net benefit by placing treatment harms and disease disutilities onto a unified continuous scale defined by an explicit treatment threshold.

The mathematical foundation of continuous net benefit indexes patient-level disutility under treated and untreated states. The therapeutic treatment effect is defined as the difference between disease disutility without treatment and disease disutility with treatment. Decision-makers reach indifference when the treatment benefit exactly equals the disutility of the treatment itself, defining the continuous decision threshold T. Setting the disutility of no treatment to zero ensures that continuous net benefit is zero if a patient is untreated or if the treatment effect equals treatment disutility. In single-arm cohort studies of absolute predictions, where untreated patients are assumed to experience zero change, continuous net benefit averages the difference between observed improvement and threshold T across all patients whose model-predicted benefit meets or exceeds T. If the clinical outcome represents a beneficial gain, such as pain reduction, the formula shifts from disutility to utility, subtracting threshold burden from observed individual gains whenever predicted gains warrant intervention.

To illustrate this calculation, the authors analyze a hypothetical cohort of six patients evaluated for treatment to reduce pain on a 0–10 scale. Assuming therapy requires at least a 3-point pain reduction to justify its inconvenience and costs, threshold T is set to 3. For patients whose predicted pain reduction falls below 3, continuous net benefit is 0 because treatment is withheld. For a patient predicted to exceed 3 who achieves an observed pain reduction of 5, net utility equals 2 after subtracting the treatment disutility of 3. Averaged across the six patients, continuous net benefit is 0.5 for the model-driven strategy, compared to 0.333 for treat-all and 0 for treat-none. Using the model is clinically equivalent to achieving a pain reduction of 0.167 points across the entire cohort without treating any patient, or matching the pain reduction of treating all patients while avoiding 5.6 percent of treatments.

To validate this methodology, the authors executed a simulation study of one million virtual patients receiving pain medication to estimate continuous net benefit on a 0–100 pain scale. The simulation incorporated four independent predictors: age, sampled from a truncated normal distribution between 18 and 90 years with a mean of 50 and standard deviation of 15; quality of life, sampled from a truncated normal distribution between 1 and 30 with a mean of 15 and standard deviation of 5; and comorbidity status and sex, each drawn from Bernoulli distributions with 50 percent probabilities. Baseline pain was generated via linear regression using coefficients of 1.25 for age, negative 0.5 for quality of life, 25 for comorbidities, and negative 15 for sex. Post-treatment pain after one year incorporated a 10 percent reduction from baseline plus random error, resulting in a mean baseline pain score of 60, a mean follow-up score of 54, and an average pain reduction of 6 points.

The authors compared four prediction models: a full model with all four predictors; a limited model containing only age and comorbidities; and two miscalibrated models that decreased or increased baseline pain by 1.5 points. The full model yielded the highest continuous net benefit, followed closely by the limited model. In the model that underestimated pain reduction, net benefit fell below the treat-all strategy at low thresholds of 3.5 or less, reflecting clinical harm when patients forgo beneficial treatment. Conversely, the model that overestimated pain reduction performed worse than treat-none at high thresholds of 9 and above, inappropriately recommending treatment to non-responders. Although these miscalibration patterns matched binary decision curve behavior, the performance losses were attenuated in continuous net benefit. Because continuous net benefit assumes linear utility, small prediction errors do not cause the drastic utility shifts seen when binary probabilities cross decision thresholds.

To evaluate continuous net benefit under skewed conditions violating linear assumptions, the authors conducted a secondary simulation of one million patients with log-normally distributed survival months, defining an intervention threshold of six months survival. A logistic regression model predicting six-month survival achieved higher net benefit across threshold probabilities from 0.35 to 0.85 than a linear regression model whose continuous predictions were converted via the cumulative distribution function. In parallel, the researchers examined real trial data evaluating acupuncture for chronic headache pain, measuring weekly diary headache scores. Using a 5-point pain reduction threshold, continuous net benefit for the full model was 2.86 versus 1.48 for treat-all, equivalent to an added 1.38-point pain reduction across all patients or sparing 28 percent of patients from treatment. At a 50 percent binary probability threshold, binary net benefit was 0.163 versus 0.076 for treat-all, sparing 8.7 percent of patients from unnecessary treatment.

Despite showing that continuous net benefit correctly ranks models, the authors highlight significant theoretical concerns regarding the assumption of linear utility. In prostate cancer, guidelines recommend that curative treatment be reserved for men with at least a 10-year life expectancy, yet living 20 years does not mean a patient benefits twice as much. Even on a single pain scale, a 3-point reduction from 9 to 6 restores substantial daily functioning, whereas a 3-point reduction from 3 to 0 yields much smaller utility gains.

Furthermore, the authors note that continuous decision rules introduce conceptual confusion regarding probability thresholds. Requiring a 10-year life expectancy or a 5-point pain reduction statistically implies that a patient has an approximately 50 percent probability of exceeding that threshold. However, clinicians and hospice benefit programs—such as Medicare or Medicaid requiring a six-month prognosis—use “expectancy” in the colloquial sense of certainty or nearly all of the time, not as an even 50:50 chance. Because continuous and binary decision curves yield identical model rankings, Barreñada and Vickers recommend converting continuous predictions into threshold probabilities. When outcomes are symmetric and thresholds vary, researchers should convert continuous estimates into probabilities using the cumulative distribution function of linear models. When continuous outcomes are heavily skewed or decision thresholds are universally defined, researchers should dichotomize the outcome at the clinical threshold and fit a logistic regression model directly.

Subject of Research: Decision curve analysis for continuous clinical prediction endpoints

Article Title: The problem of continuous endpoints for clinical decision making: a decision curve analysis approach

Article References: Barreñada, L., & Vickers, A. (2026). The problem of continuous endpoints for clinical decision making: a decision curve analysis approach. Diagnostic and Prognostic Research, 10(1), Article 30. https://doi.org/10.1186/s41512-026-00243-w

Image Credits: AI Generated

DOI: 10.1186/s41512-026-00243-w

Keywords: decision curve analysis, net benefit, prediction models, continuous endpoints, clinical utility, logistic regression, probability thresholds, calibration, problem, continuous, endpoints, clinical