⚡ electrical engineering

ConRad: Efficient Conformal Prediction for Radiomics

ConRad is an efficient conformal prediction framework that leverages image appearance, mask geometry, and segmentation uncertainty to construct adaptive, distribution-free prediction intervals for radiomic features, significantly improving interval efficiency while maintaining near-nominal coverage across diverse medical imaging datasets.

Original authors: Matt Y. Cheung, Ashok Veeraraghavan, Guha Balakrishnan

Published 2026-07-10

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Matt Y. Cheung, Ashok Veeraraghavan, Guha Balakrishnan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a detective trying to solve a mystery using clues from a blurry photo. You have a robot assistant that draws a rough outline (a "mask") around the suspect in the photo. Based on that outline, the robot calculates a "radiomic" number—maybe the size of the suspect's hat or the texture of their coat. This number helps doctors make big decisions.

But here's the catch: the robot isn't perfect. Sometimes it's overconfident, drawing a shaky outline that looks solid. If you just take the robot's number and say, "The hat size is 10 inches," you might be wrong, and you won't know how wrong you could be. You need a safety net, a range of possible values like "The hat is between 8 and 12 inches."

For a long time, scientists tried to build these safety nets using a "black box" approach. They'd look at the final number and guess a range, ignoring how the robot drew the outline. It was like guessing the weather based only on the temperature, ignoring the wind, humidity, and cloud shapes. This made the safety nets too wide and clumsy.

Enter ConRad, a new method proposed by Matt Cheung and his team at Rice University. Think of ConRad as a super-smart detective who doesn't just look at the final number. Instead, ConRad checks the robot's sketchbook while it's working. It asks: "How wiggly is the outline? Is the robot unsure about the edges? How big is the shape?"

By using these extra clues—specifically the uncertainty near the boundaries of the robot's drawing—ConRad can shrink those clumsy safety nets. It makes the range of possible answers much tighter and more useful, without losing its promise to be right most of the time.

The Big Test Drive

To see if this really works, the team didn't just guess; they ran a massive test drive. They used five different medical imaging datasets (like photos of skin, the inside of the stomach, chest X-rays, and thyroid ultrasounds) and tracked 171 different radiomic targets (all those hat sizes, textures, and shapes).

They compared ConRad against the old "black box" methods and some slightly smarter versions that looked at the image but ignored the shaky edges. The results were promising:

On four out of five datasets, ConRad made the safety nets significantly tighter. For example, on the thyroid ultrasound data (TN3K), the intervals got about 2.03% narrower on average. On the skin image data (HAM10000), they improved by 5.47%.
It won the most often: In 82.5% of the skin image cases and 91.3% of the chest X-ray cases, ConRad provided a better (narrower) range than the best competing method.
It stayed honest: Even though the ranges got smaller, ConRad kept its promise. It still covered the true answer about 90% of the time (the target was set at 1 −α = 0.9). In fact, 170 out of 171 targets hit that 90% mark.

The Secret Sauce: The Edge Matters

One of the most fun discoveries was figuring out why ConRad worked so well. The team played a game of "what if we remove this clue?" They took away the clues about the shape, the brightness, and the predicted numbers, one by one.

They found that the boundary uncertainty—the clues about how shaky the robot's outline was near the edges—was the MVP. It was responsible for about 40.5% of the improvement. It turns out that knowing exactly where the robot is confused (usually right at the edge of the object) is the most powerful way to tighten the safety net. The other clues, like the overall brightness or the shape, helped, but not nearly as much.

What This Doesn't Do (Yet)

It's important to know what ConRad isn't doing. The paper explicitly rules out a few things:

It's not a magic bullet for 3D: The tests were only on 2D images (flat pictures). The authors suggest that 3D radiomics might behave differently, but they haven't tested that yet.
It's not a guarantee for every single case: The method guarantees that it's right 90% of the time across a whole group of patients (marginal coverage). It does not promise that it will be right for every single individual patient or specific subgroup. If the data shifts (like using a different type of scanner), the method might need a tune-up.
It doesn't solve everything at once: Currently, ConRad treats each radiomic target (like "hat size" or "coat texture") separately. It doesn't yet handle complex, multi-part predictions all at once.

The Bottom Line

ConRad suggests that by paying attention to the robot's "shaky hands" at the edges of a drawing, we can make medical predictions much sharper and more reliable. It's a step forward in making sure that when doctors use these fancy computer measurements, they know exactly how much they can trust them. The authors found that this approach works well across many different types of medical images, but they admit there's still work to do before it handles 3D scans or complex, multi-target scenarios.

Technical Summary: ConRad: Efficient Conformal Prediction for Radiomics

Problem Statement

Radiomic features derived from medical images and segmentation masks are critical for clinical decision-making. However, in practice, these features are often computed from predicted segmentation masks generated by automated models. These segmentation models can be overconfident or poorly calibrated, causing derived radiomic measurements to appear more reliable than they actually are.

While Uncertainty Quantification (UQ) is essential in high-stakes scenarios, standard approaches often treat radiomic measurements as arbitrary scalar outputs, ignoring the specific process of their generation. Existing Conformal Prediction (CP) methods for segmentation typically focus on pixel-level uncertainty or volume-based metrics. They fail to provide efficient, calibrated intervals for non-volumetric radiomic targets (e.g., texture, shape, intensity distribution) because they do not leverage test-time information regarding image appearance, mask geometry, and segmentation uncertainty. Consequently, direct UQ methods may miss significant efficiency gains by failing to utilize information contained in the predicted mask.

Methodology: ConRad Framework

The authors propose ConRad, a conformal framework designed to construct adaptive, efficient prediction intervals for scalar radiomic targets derived from predicted segmentation masks. The method utilizes Conformalized Quantile Regression (CQR) to learn conditional quantile models that adapt interval widths based on case difficulty.

Workflow

Input Definition: For a case $i$ $i$ , let $A_i$ $A_{i}$ be the input image, $\hat{M}_i$ $\hat{M}_{i}$ be the predicted segmentation mask (available at inference), and $M_i$ $M_{i}$ be the reference mask (used only for training/calibration). A radiomics extractor $\rho$ $ρ$ maps an image-mask pair to a scalar target.
- Predicted target: $\hat{Y}_i = \rho(A_i, \hat{M}_i)$
- Reference target: $Y_i = \rho(A_i, M_i)$
Feature Construction ( $X_i$ ): ConRad constructs a feature vector $X_i = (\hat{Y}_i, \hat{Z}_i)$ $X_{i} = (\hat{Y}_{i}, \hat{Z}_{i})$ using only test-time information. $\hat{Z}_i$ $\hat{Z}_{i}$ comprises four families of covariates:
- Geometry and Topology: Pixel count, image fraction occupied, and number of connected components in the predicted mask.
- Intensity Distribution: Statistics (mean, std, min, max, percentiles) of the image intensity within the predicted region.
- Predicted Radiomics: The predicted radiomic value itself and other predicted features from shape, first-order intensity, and texture families.
- Boundary Uncertainty: Probability statistics and entropy derived from the predicted probability map, specifically within a boundary band (created by dilating/eroding the mask by 1 pixel) and globally.
Training and Calibration:
- Training: CQR trains lower ( $\hat{Q}_{\alpha/2}$ ) and upper ( $\hat{Q}_{1-\alpha/2}$ ) conditional quantile models on a training set.
- Calibration: On a disjoint calibration set, nonconformity scores $R_i = \max\{\hat{Q}_{\alpha/2}(X_i) - Y_i, Y_i - \hat{Q}_{1-\alpha/2}(X_i)\}$ are computed. A conformal quantile $\hat{q}$ is determined as the $\lceil(1-\alpha)(n+1)\rceil$ -th order statistic of these scores.
- Prediction: For a new test case, the interval is $S(X_{test}) = [\hat{Q}_{\alpha/2}(X_{test}) - \hat{q}, \hat{Q}_{1-\alpha/2}(X_{test}) + \hat{q}]$ .
Theoretical Guarantee: Under the assumption of exchangeability between calibration and test examples, ConRad guarantees finite-sample marginal coverage: $\Pr\{Y_{test} \in S(X_{test})\} \geq 1 - \alpha$ .

Target Filtering

To ensure meaningful evaluation, the authors implement a filtering procedure to remove degenerate radiomic targets (e.g., those with missing values, near-constant values, or zero variance) across three families: shape, first-order intensity, and texture/heterogeneity features.

Key Contributions

ConRad Framework: The formulation of a feature-adaptive conformal prediction framework specifically for scalar radiomic targets derived from predicted segmentation masks. It explicitly uses segmentation output information (geometry, intensity, and boundary uncertainty) to improve interval efficiency.
Evaluation Protocol: The introduction of a scale-normalized, target-level evaluation protocol. Since radiomic features vary in scale and units, the authors evaluate efficiency using target-level win rates and symmetric relative width improvement against the strongest baseline, rather than pooling raw interval widths.

Experimental Results

The method was evaluated on five 2D medical imaging datasets (HAM10000, Kvasir, COVID-QU-EX, TG3K, TN3K) covering dermatology, endoscopy, chest X-rays, and thyroid ultrasound. A total of 171 radiomic targets were retained after filtering.

Performance

Efficiency: ConRad improved feature-level interval efficiency compared to baselines (Split Conformal Prediction, CQR using only predicted values, and CQR using generic features) while maintaining near-nominal empirical coverage.
- Mean Relative Improvement: Positive gains were observed across most datasets, ranging from 2.03% (TN3K) to 5.83% (TG3K).
- Win Rates: ConRad outperformed the strongest baseline in the majority of cases, with win rates ranging from 55.3% (Kvasir) to 91.3% (COVID-QU-EX).
Coverage: Empirical coverage remained close to the nominal 90% level ( $1-\alpha$ ). The minimum mean target-wise coverage was 89.9%, and 170 out of 171 targets achieved at least 90% mean coverage.
Ablation Study: A grouped feature ablation analysis revealed that Boundary Uncertainty features were the largest contributors to efficiency gains, accounting for 40.5% of the normalized ablation importance on average. This suggests that segmentation uncertainty near object boundaries provides complementary information beyond generic image and mask summaries.

Significance and Claims

The paper claims that ConRad extends metric-level conformal uncertainty quantification beyond simple volume-based segmentation measurements to broader radiomic measurements. By leveraging test-time information about the segmentation output and its uncertainty, ConRad constructs narrower uncertainty intervals without sacrificing formal coverage guarantees.

The authors note that while the method improves efficiency, it provides marginal coverage over exchangeable test examples rather than conditional coverage for specific subgroups. They acknowledge limitations, including the focus on 2D datasets (3D radiomics may behave differently) and the reliance on useful probability maps for boundary uncertainty. The work positions itself as a step toward more reliable, uncertainty-aware radiomic pipelines in clinical imaging.