EORTC Risk Tables in Bladder Cancer

• EORTC risk tables are clinical tools that quantify NMIBC recurrence and progression risk based on variables like tumour count, size, grade, and CIS.
• They convert simple clinicopathological metrics into point scores that classify patients into low, intermediate, or high-risk groups to guide cystoscopy and therapy.
• Modern analyses critique the tables for misclassifying intermediate-risk patients and show they underperform compared to contemporary machine-learning models.

Searching arXiv for the specified papers and closely related work on EORTC risk tables. EORTC risk tables are clinical risk stratification tools used in non–muscle-invasive bladder cancer (NMIBC) to estimate an individual patient’s risk of recurrence after transurethral resection of bladder tumour (TURBT) and progression to muscle-invasive disease. In routine practice, clinicians use these tables or related online calculators to assign a point score based on clinicopathological variables and then place patients into low, intermediate, or high-risk groups, which in turn inform surveillance cystoscopy intervals and the intensity of adjuvant intravesical therapy. Recent work frames these tables both as established reference instruments in uro-oncology and as objects of methodological scrutiny, particularly regarding calibration, discrimination, and adaptation to contemporary care pathways (Abbas et al., 26 Jul 2025). Separately, sequential statistical methodology for Bernoulli two-sample problems provides a formal framework for constructing exact anytime-valid confidence intervals for risk difference, relative risk, and odds ratio in $2\times 2$ tables, and this framework can be mapped onto EORTC-defined risk strata or treatment comparisons at fixed follow-up horizons (Turner et al., 2022).

1. Historical role and clinical construction

The EORTC (European Organisation for Research and Treatment of Cancer) risk tables are described as long-standing clinical tools designed to estimate an individual NMIBC patient’s risk of recurrence after TURBT and progression to muscle-invasive disease. Their standard inputs are simple clinicopathological variables: number of tumours, tumour size, prior recurrence rate, T category (Ta/T1), presence of carcinoma in situ (CIS), and tumour grade. In day-to-day practice, these variables are converted into a point score and then into low, intermediate, or high-risk groups (Abbas et al., 26 Jul 2025).

Within the reported NMIBC workflow, those groups are not merely descriptive. They inform surveillance cystoscopy intervals and the intensity of adjuvant intravesical therapy. The tables therefore function as a bridge between baseline pathological features and downstream management decisions, especially where recurrence risk is used to determine follow-up intensity (Abbas et al., 26 Jul 2025).

The paper on AI-based clinical rule discovery states that the EORTC risk tables were implemented as a rule-based model using published scoring logic. This indicates reconstruction of EORTC point scores from the standard published algorithm, with each patient assigned a cumulative recurrence risk score and that score translated into risk categories or into predicted recurrence/non-recurrence for the 3-year horizon used in the PHOTO trial evaluation (Abbas et al., 26 Jul 2025).

A plausible implication is that the EORTC tables persist as a clinically recognizable reference standard partly because they are operationally simple: they use a small fixed variable set, fixed point assignments, and categorical risk outputs. The same simplicity, however, constrains their ability to incorporate additional perioperative, patient-reported, or evolving treatment-context variables.

2. Statistical interpretation as risk contrasts in contingency tables

A separate line of work provides a formal statistical language for interpreting EORTC-style risk comparisons through Bernoulli outcomes and $2\times 2$ tables. In that formulation, two “streams” can represent two EORTC-defined risk strata, “old vs new” treatment, or “predicted low vs predicted high risk” groups, while the binary outcome is “event within a fixed time horizon (yes/no)” (Turner et al., 2022).

For group $g \in \{a,b\}$, observations are modeled as i.i.d. Bernoulli$(\theta_g)$, where $\theta_g$ is the event probability in that group. In an EORTC setting, the event can be defined as recurrence by a fixed horizon such as 1 year, and the resulting block counts form the standard $2\times 2$ contingency table with event and non-event counts in each group (Turner et al., 2022).

The principal effect sizes are expressed directly in terms of $\theta_a$ and $\theta_b$:

• Risk difference: $\text{RD} = \theta_b - \theta_a$
• Relative risk: $\text{RR} = \frac{\theta_b}{\theta_a}$, for $2\times 2$0
• Odds ratio: $2\times 2$1

These quantities correspond to contrasts of risk or odds between EORTC-defined strata or treatments (Turner et al., 2022).

This formulation is especially useful when EORTC outputs are treated as clinically meaningful strata rather than as immutable predictions. For example, low-risk and high-risk EORTC categories can be viewed as two Bernoulli populations whose observed recurrence probabilities are estimated and compared over time. The same framework can also be used for historical-versus-current cohort comparisons, where one asks whether a risk table’s implied event rates remain stable in contemporary practice (Turner et al., 2022).

3. Sequential inference and anytime-valid confidence sequences

The paper “Exact Anytime-valid Confidence Intervals for Contingency Tables and Beyond” develops E-variables and E-processes for sequential inference under optional stopping. For a null hypothesis $2\times 2$2, an E-variable is a nonnegative measurable function $2\times 2$3 such that

$2\times 2$4

If data are collected in blocks and each block yields an E-variable $2\times 2$5, then the product

$2\times 2$6

is a test martingale or E-process, and under the null it is a nonnegative supermartingale (Turner et al., 2022).

The operational consequence is the optional stopping guarantee: $2\times 2$7 for any stopping time $2\times 2$8. Thus the test that rejects $2\times 2$9 as soon as $g \in \{a,b\}$0 remains valid under arbitrary optional stopping and continuation, via Ville’s inequality (Turner et al., 2022).

The same construction yields anytime-valid confidence sequences for an effect size $g \in \{a,b\}$1. For each candidate $g \in \{a,b\}$2, one defines the null set

$g \in \{a,b\}$3

builds the corresponding E-process, and inverts the family of tests to obtain

$g \in \{a,b\}$4

The smallest interval containing this set gives an anytime-valid confidence interval, and a running intersection can be used to tighten bands over time (Turner et al., 2022).

In relation to EORTC risk tables, this means that a comparison between two EORTC strata, between historical and current cohorts, or between two treatments can be monitored continuously without fixing a final sample size in advance. This is explicitly contrasted with classical fixed-sample intervals such as Wald, Wilson, and Clopper–Pearson intervals, which assume a fixed, non-adaptive final sample size and are not automatically valid under repeated looks unless adjusted (Turner et al., 2022).

4. Null geometry, assumptions, and implementation

The sequential framework hinges on how null hypotheses are represented in the $g \in \{a,b\}$5-plane. For risk difference, the equality set

$g \in \{a,b\}$6

is a straight line, and the one-sided sets $g \in \{a,b\}$7 and $g \in \{a,b\}$8 are convex. For relative risk,

$g \in \{a,b\}$9

again a straight line through the origin and therefore convex. For log odds ratio,

$(\theta_g)$0

the equality curve is not convex, but the one-sided sets $(\theta_g)$1 and $(\theta_g)$2 are convex for suitable sign of $(\theta_g)$3, allowing one-sided anytime-valid bounds (Turner et al., 2022).

For Bernoulli $(\theta_g)$4 tables, the single-block E-variable uses a likelihood ratio between a fixed alternative $(\theta_g)$5 and its Kullback–Leibler projection $(\theta_g)$6 onto the null set: $(\theta_g)$7 This construction is growth-rate optimal for convex nulls (Turner et al., 2022).

In practice, the alternative is learned sequentially. Posterior means $(\theta_g)$8 based on previous blocks are used, with a Beta–Beta prior; the paper recommends a beta prior with hyperparameter $(\theta_g)$9 for default use. The KL projection onto $\theta_g$0 is then computed blockwise, and the cumulative E-process is updated multiplicatively (Turner et al., 2022).

The validity of the resulting E-variables and confidence sequences relies on four assumptions stated explicitly in the source: independence of observations within and across groups, i.i.d. Bernoulli outcomes within group $\theta_g$1, block sizes $\theta_g$2 fixed in advance for each block though allowed to depend on past data across blocks, and correct specification of the Bernoulli model. No assumptions are made about a fixed total sample size or a prescribed stopping rule (Turner et al., 2022).

For software, the authors provide the R package safestats, which implements E-variables and safe tests for contingency tables and anytime-valid confidence sequences for RD, RR, and OR. The proposed EORTC adaptation is to input two groups, specify the desired effect size, stream data by patient or in small blocks, and update E-values and confidence sequences at each interim (Turner et al., 2022).

5. Contemporary critiques in NMIBC and benchmarking against newer models

The 2025 Tsetlin Machine study presents EORTC risk tables as important but “decades-old tools” whose clinical reliability is questioned in modern NMIBC management. The stated reasons include changes in intravesical therapy use, TURBT quality and re-resection practices, and pathology grading systems and reporting since the original derivation cohorts. The paper therefore argues that risk estimates derived from the original cohorts may be miscalibrated in today’s patients (Abbas et al., 26 Jul 2025).

A recurring criticism in that study is misclassification of intermediate-risk NMIBC. The authors state that clinicians rely on EORTC and CUETO risk tables to predict recurrence, but that these often misclassify intermediate-risk patients, leading to inappropriate treatment decisions. The paper also states that the cited Fernández-Gómez et al. work is noted as evidence that EORTC tables overestimate risk in some contemporary cohorts, though the paper does not reproduce detailed calibration plots or numerical calibration statistics (Abbas et al., 26 Jul 2025).

The study evaluates EORTC as a rule-based comparator on the PHOTO trial dataset. The dataset is described as a multicentre UK trial from 22 NHS centres, with an initial cohort of 539 NMIBC patients and a final analytic cohort of 330 after exclusions for prior cystectomy before diagnosis confirmation, missing three-year follow-up, and incomplete peri-operative data. The primary endpoint is tumour recurrence within three years of TURBT, treated as binary rather than time-to-event (Abbas et al., 26 Jul 2025).

The benchmarking setup uses an 80:20 stratified train-test split with recurrence approximately 40%, a unified preprocessing pipeline via ColumnTransformer, and Optuna hyperparameter optimisation with 50 TPE trials for the Tsetlin Machine. Comparator models are the Tsetlin Machine, L2-regularised logistic regression with class weighting, XGBoost, and EORTC risk tables applied as originally designed rather than retrained (Abbas et al., 26 Jul 2025).

The reported macro-averaged F1-scores are:

Model	Macro F1-score
Tsetlin Machine	0.80
XGBoost	0.78
Logistic Regression	0.60
EORTC risk tables	0.42

The same source reports TM precision of 0.83 and recall of 0.78, but does not provide AUC, C-index, PPV, NPV, Brier score, calibration slope, or decision-curve analysis. Confidence intervals and p-values for performance comparison are also not reported (Abbas et al., 26 Jul 2025).

The paper’s interpretation is that EORTC shows substantially lower discriminatory performance than modern machine-learning methods in this cohort. It further emphasizes that EORTC’s coarse stratification is especially problematic in the heterogeneous intermediate-risk group, where overtreatment and undertreatment are both common (Abbas et al., 26 Jul 2025).

6. Relation to interpretable AI and possible future positioning

The Tsetlin Machine study contrasts EORTC’s fixed additive point system with a symbolic learner operating on binary features and their negations, where each clause is a conjunction of literals and classification is based on positive and negative clause votes: $\theta_g$3 The final prediction is typically $\theta_g$4 if $\theta_g$5, and $\theta_g$6 otherwise (Abbas et al., 26 Jul 2025).

The paper’s explicit examples show how the learned clauses go beyond EORTC’s variable set:

• “HospitalStay > 3 days AND TumourNumber > 3 $\theta_g$7 Recurrence”
• “EQ5DScore between 0.41–0.49 AND SurgeonGrade $\theta_g$8 Consultant $\theta_g$9 Recurrence”
• “SurgeonGrade = Consultant $2\times 2$0 No Recurrence” (Abbas et al., 26 Jul 2025)

The source interprets these clauses as evidence that the model recovers known clinical logic, such as multiple tumours increasing recurrence risk, while also incorporating factors absent from EORTC, including surgeon experience, hospital length of stay, and EQ-5D quality-of-life scores. It further states that the protective surgeon-grade clause aligns with PHOTO trial findings of hazard ratio $2\times 2$1, $2\times 2$2 for senior versus junior surgeons (Abbas et al., 26 Jul 2025).

This comparison is central to the current debate about EORTC risk tables. EORTC is described as simple and hand-crafted but static, non-adaptive, and unable to naturally incorporate variables such as surgeon experience, perioperative complications, patient-reported outcome measures, or molecular markers. By contrast, the Tsetlin Machine can be retrained on contemporary cohorts and can learn non-linear interactions between such variables (Abbas et al., 26 Jul 2025).

The same paper nonetheless states clear limitations: the evidence comes from a single dataset, external validation is absent, the endpoint is binary three-year recurrence rather than time-to-event, and calibration plots and Decision Curve Analysis are planned future work. It also notes plans for prospective evaluation in a larger UK NMIBC registry and for inclusion of molecular markers such as FGFR3 (Abbas et al., 26 Jul 2025).

A plausible implication is that EORTC risk tables may increasingly function as baseline comparators, scaffolds for clinician familiarity, or components within hybrid decision-support systems rather than as the sole risk-stratification mechanism. That implication is suggested by the paper’s statement that TM could replace or complement EORTC, initially refining risk within EORTC categories and potentially supplanting it after further validation (Abbas et al., 26 Jul 2025).

7. Methodological implications for ongoing EORTC-based research

The sequential inference framework in (Turner et al., 2022) and the NMIBC benchmarking study in (Abbas et al., 26 Jul 2025) address different problems, but together they define a technically coherent research agenda for EORTC risk tables. The first provides exact anytime-valid confidence intervals for risk differences, relative risks, and odds ratios in $2\times 2$3 settings with optional stopping; the second provides a modern empirical setting in which EORTC-defined or EORTC-compared groups are clinically important and contested.

For EORTC-based analyses, the statistical mapping is straightforward when the outcome is fixed-horizon recurrence. One can define group $2\times 2$4 and group $2\times 2$5 as low-versus-high EORTC strata, historical-versus-current cohorts, or old-versus-new management strategies. The event indicator is recurrence by a fixed time horizon, such as one year or three years, yielding Bernoulli observations and enabling RD, RR, or OR monitoring with anytime-valid confidence sequences (Turner et al., 2022).

The source explicitly lists several conceptual use cases in the EORTC setting: sequential validation of EORTC risk predictions, updating risk parameters as new data accumulate, anytime-valid confidence bands around risk estimates, and comparison of different EORTC-like models. It also notes that for full survival outcomes, a Bernoulli reduction requires fixing a time horizon, and that multiple horizons would require multiple tests with multiplicity management if formal guarantees across endpoints are desired (Turner et al., 2022).

Traditional EORTC validation workflows are described as relying on logistic regression for binary outcomes, Cox proportional hazards for time-to-event, fixed-sample 95% confidence intervals, and static validation at prespecified sample sizes. The E-variable approach differs in providing legitimate continuous monitoring, exact non-asymptotic guarantees, robustness to early stopping or adaptive continuation, and coverage that is valid for all times simultaneously (Turner et al., 2022).

At the same time, the limitations of this mapping are stated directly. The exact anytime-valid methods focus on simple Bernoulli outcomes and two-group comparisons, whereas EORTC tables often arise in time-to-event and multivariable settings. The paper does not explicitly treat adaptive covariate-based designs or full multivariable logistic/Cox models, though it states that the E-variable framework is compatible with such extensions when outcome models and null sets are appropriately formulated (Turner et al., 2022).

Taken together, these strands suggest a bifurcated contemporary view of EORTC risk tables. Clinically, they remain canonical stratification tools in NMIBC. Methodologically, they are increasingly treated as baseline models whose discrimination, calibration, and transportability must be re-evaluated in modern cohorts, and whose updates can be monitored sequentially with exact anytime-valid inference when outcomes are cast as fixed-horizon binary events (Turner et al., 2022, Abbas et al., 26 Jul 2025).