Utility-Based Dose Selection for Stereotactic Body Radiation Therapy in Hepatocellular Carcinoma

Abstract

Purpose:

Stereotactic body radiation therapy (SBRT) planning for hepatocellular carcinoma (HCC) typically prescribes the maximum dose associated with an acceptable risk of toxicity, relying on implicit trade-offs between efficacy and toxicity. To make this trade-off quantitative, we developed a utility-based approach to dose selection for SBRT in HCC and studied the expected effects on clinical outcomes.

Methods and Materials:

Using a multi-institutional cohort of SBRT-treated patients, we developed predictive models for local progression, competing mortality, and liver toxicity, defined as an increase of 0.5 or more points in albumin-bilirubin score within 6 months. Individualized risks of local progression and toxicity were integrated using a utility framework with a quantitative efficacy/toxicity trade-off. We then performed a simulation comparing predicted clinical outcomes and overall utility between 2 scenarios: if patients in our cohort had been prescribed SBRT according to Radiation Therapy Oncology Group 1112 (“standard dosing”), versus with our proposed utility-based dose selection.

Results:

Our cohort included 309 patients (75% Child−Pugh A pretreatment liver function and 24% Child−Pugh B). The median tumor prescription dose in BED₁₀ was 79 Gy₁₀ and the total number of fractions ranged from 2 to 6. The estimated optimal prescription dose under utility-based dose selection varied widely with baseline liver function, with an optimal tumor BED₁₀ of 112 Gy for a patient with Child−Pugh A cirrhosis to 26 Gy for a patient with Child−Pugh C cirrhosis. In the simulation study, the magnitude of utility gains with our approach compared with standard dosing depended on the relative weighting of toxicity and tumor control utilities.

Conclusions:

We describe a novel approach to SBRT radiation treatment planning and dose selection for HCC that combines individualized prediction of efficacy, toxicity, and competing mortality with explicit calculation of the efficacy-toxicity trade-off using an expected utility framework. This approach holds promise to personalize SBRT treatment planning. Published by Elsevier Inc.

Introduction

Radiation treatment planning and dose selection involve trade-offs between treatment efficacy and toxicity risk. Higher biologically effective doses (BEDs) tend to produce higher rates of tumor control but may increase the risk of liver injury, depending on conformality, baseline liver function, and tumor size. In practice, this efficacy-toxicity trade-off is made by clinicians based on the urgency of tumor control, clinical consequences of tumor progression, estimated organ at risk (OAR) toxicity risk, and competing mortality risk, among other factors. These considerations affect both the decision to recommend treatment, radiation technique, arrangement of beams, prescription dose, and the choice of acceptable dose limits for individual OARs.

These efficacy-toxicity trade-offs are currently implicit, largely based on the judgment of the managing physician, and rarely quantitative. However, these trade-offs can be made explicit and quantitative using the tools of decision analysis. Explicitly defining efficacy-toxicity trade-offs in terms of relative utility allows the integration of disparate risks—tumor progression, competing mortality, and toxicity—into a single utility scale. Different treatment plans and prescription doses can then be directly compared in terms of their expected utility, incorporating individualized predictions of toxicity and tumor control. This concept has been explored statistically and in the treatment of hepatocellular carcinoma (HCC), although with limited numbers of patients, fixed 1:1 weighting of toxicity versus efficacy, and without accounting for competing mortality risks.^1,2

In this proof-of-concept study, we use a multi-institutional database of patients with HCC undergoing liver stereotactic body radiation therapy (SBRT) to build predictive models of tumor progression, competing mortality, and liver toxicity. We then integrate these models into a unified utility framework, allowing us to calculate the expected utility of various prescription doses based on individual predictions of efficacy and toxicity. We then perform a simulation study, comparing the predicted risks of toxicity, local progression, and overall utility between 2 scenarios: standard dosing according to Radiation Therapy Oncology Group (RTOG) 1112, versus individualizing dosing according to our utility-maximization framework. We hypothesized that this utility-based treatment planning approach would produce a higher predicted tumor control probability for the same toxicity as standard treatment using the RTOG 1112 approach.

Methods and Materials

Data source

This study included patients with HCC treated with SBRT at the University of Michigan and Princess Margaret Cancer Centre from 2004 to 2016. For patients in the Princess Margaret cohort, we performed a retrospective review and

included patients with T1-T3a (American Joint Committee on Cancer [AJCC] 7th edition) HCC receiving a biologically effective dose of at least 45 Gy₁₀ prescribed to the planning target volume (PTV). Patients with extrahepatic spread, ruptured HCC, 5 or more HCC lesions, vascular invasion, or no planned imaging follow-up were excluded. Patients with HCC in the University of Michigan cohort were prospectively collected and included a subset of patients treated on trials of individualized adaptive radiation therapy (NCT01519219, NCT01522937, NCT02460835).³ In this individualized adaptive approach, patients had both pretreatment and mid-treatment liver function assessed using indocyanine green or albumin-bilirubin (ALBI) score (an empiric calculation based on albumin and bilirubin)⁴ to improve prediction of liver toxicity.⁵ This joint data set has been characterized previously.⁶ This study was approved by the local institutional review boards.

Overview of the utility-based treatment planning approach

A common current practice for prescribing liver-directed SBRT for HCC is to prescribe the highest dose to the tumor that is associated with an acceptable risk of toxicity (isotoxic dose prescription).^7,8 This is the approach taken in RTOG 1112, a recently completed randomized trial testing the addition of liver SBRT to sorafenib in HCC.⁹ In that study, the SBRT dose prescription is chosen by an algorithm based on maximum allowable mean liver dose (MLD; Table E1). The prescription starts at a maximum of 50 Gy in 5 fractions and is reduced in 5 Gy increments until an acceptable MLD is achieved while respecting OAR tolerances. Although this approach is intended to maintain a constant toxicity risk across patients, it does not allow for differential weighting of the consequences of tumor progression and liver toxicity and is unlikely to be optimal in terms of the efficacy-toxicity trade-off. Physicians and patients may vary in their tolerance for toxicity risk, and the consequences of local tumor progression may also vary; for example, local progression may be more consequential in patients without feasible salvage therapies or who are ineligible for systemic therapy.

Our utility-based approach seeks to make these efficacy/toxicity trade-offs explicit by modeling individual probabilities of major clinical events (local progression, liver toxicity, and competing mortality), assigning utility values to local progression and liver toxicity, and identifying the prescription dose that maximizes total utility for each patient. This approach enables personalized dosing based on the individual predicted risk of each clinical event. To accomplish this, we first develop models to predict each clinical event. We then create a utility matrix that defines the quantitative trade-off between local tumor progression and liver toxicity and apply the utilities to the individual-level predicted probabilities of each event. Finally, we identify the SBRT prescription dose that maximizes utility for each patient. We compare the “optimized” utility (based on our approach) to the utility associated with the RTOG 1112 prescription algorithm and compare the patient-level risks of local progression and liver toxicity associated with each approach. We also assess the sensitivity of our approach to variation in the quantitative efficacy/toxicity trade-off. Figure 1 and Figure E1 shows an overview of our study design and modeling approach.

Fig. 1.

Overview of the study design. We used a multi-institutional cohort of patients with hepatocellular carcinoma treated with liver SBRT to build prediction models for local progression, liver toxicity, and competing mortality. We then performed a simulation study comparing the predicted clinical outcomes for 2 scenarios: first, if patients in our cohort had received SBRT prescriptions as per the RTOG 1112 dose-selection algorithm, and second, if patients had received SBRT prescriptions based on our proposed utility-maximization framework. For each patient in our cohort, we then compared the predicted risks of each clinical outcome (and overall utility) under each counterfactual dosing strategy to assess how our utility-based approach might differ from standard dosing according to RTOG 1112. Abbreviations: CM = competing mortality; HCC = hepatocellular carcinoma; LP = local progression; SBRT = stereotactic body radiation therapy; tox = liver toxicity; PTV = planning target volume; RTOG = Radiation Therapy Oncology Group

Local progression and competing mortality models

We modeled the risk of local progression after SBRT using a competing risk framework, as mortality because of causes other than cancer (competing mortality) is a common event in patients with HCC.¹⁰ To enable personalized risk estimates, we developed submodels for competing mortality and local progression. The first model was a Weibull model for time to local progression. Local progression was assessed by serial surveillance imaging (multiphasic computed tomography or liver magnetic resonance imaging) using the modified Response Evaluation Criteria in Solid Tumors (RECIST) criteria¹¹ every 3 months during the first 6 to 12 months after SBRT and every 3 to 6 months thereafter. Total tumor BED was used as the sole predictor in this model due to its strong relationship with local control.² Other variables were assessed for inclusion but were not statistically significant in our cohort, including prior treatment, number of active lesions at the time of treatment, lesion location, tumor size, and use of fiducial markers. The model (Table E2) was specified as

$$\log \left(T_{\text{LP}}\right)={\beta }_0+{\beta }_1{\text{BED}}_{10},$$

where $T_{\text{LP}}$ = mean time to local progression and BED₁₀ = total BED in Gy₁₀.

The second model was a Weibull regression model for mean time to death. We considered baseline Child−Pugh (CP) score and age as candidate predictors. In our cohort, age was found to have negligible impact on the risk of death (coefficient estimate [SD] = 0.0002 [0.006]; P = .97) and was excluded from the model. Thus, we specified the cause-specific model for mortality (Table E3) as

$$\log \left(T_D\right)={\beta }_0+{\beta }_{1}C{P}_0,$$

where $T_D$ = mean time to death without local progression and CP₀= baseline CP score.

Let ${\lambda }_1\left(t\mid {\text{BED}}_{10}\right)$ denote the cause-specific hazard of local progression at time t conditional on BED₁₀, and ${\lambda }_2\left(t\mid \left.{\text{CP}}_0\right)\right.$ denote the cause-specific hazard of dying without prior local progression estimated from the Weibull regression models. Then the absolute risk of local progression within 1 year can be calculated as

$$\begin{array}{l}{r}_1\left(1\mid {\text{BED}}_{10},{\text{CP}}_0\right)\\ ={\int }_0^1{\lambda }_1\left(u\mid {\text{BED}}_{10}\right)\\ \exp \left(-{\int }_0^u{\lambda }_1\left(s\mid {\text{BED}}_{10}\right)+{\lambda }_2\left(s\mid {\text{CP}}_0\right)ds\right)du.\end{array}$$

Liver toxicity model

We next developed a logistic regression model to predict liver toxicity risk, defined as a ≥0.5-point increase in ALBI score at 6 months (3 months if 6 months was missing) after SBRT completion. To fit our toxicity model, we utilized only the Princess Margaret patients as their dose was prespecified at baseline and not adapted mid-treatment as was done for the University of Michigan patients. A logistic regression model was fit for the binary toxicity outcome with predictors including MLD (in EQD2_2.5) and baseline ALBI (ALBI₀). We assessed other variables for inclusion, but these were not statistically significant, including baseline CP score, age, sex (male vs. female), race, portal venous thrombosis, and number and type of prior liver-directed therapies. The final model was specified as

$$\mathrm{logit}\left({\pi }_{\text{tox}}\right)={\beta }_0+{\beta }_1{\text{ALBI}}_0+{\beta }_2\text{MLD},$$

where ${\pi }_{\text{Tox}}$ denotes the probability of toxicity (Table E4). Although baseline ALBI was not statistically significant in the final model, we chose to include it as it has been previously shown to be robustly associated with liver toxicity in other cohorts.^5,12–14 In predicting the risk of toxicity for a patient, we restricted the odds ratio of MLD, given a specific ALBI₀ to be ≥1.01, such that a higher dose always leads to higher risk of toxicity.

Calculation of expected utility curves

Using the models predicting local progression and liver toxicity, we quantified the expected utility of varying tumor BED₁₀ prescriptions using a 2 × 2 utility matrix specifying the relative undesirability of local progression and liver toxicity. In our base case, liver toxicity with local progression was assigned a utility of 0, whereas tumor control without liver toxicity was assigned a utility of 100. Liver toxicity with tumor control was assigned a utility of 40, and no liver toxicity with tumor progression was assigned a utility of 60. This explicitly defines liver toxicity as worse than tumor progression, which is consistent with our clinical experience. In a sensitivity analysis, we reverse these values (tumor progression with utility of 40 and liver toxicity with utility of 60) to assess the predicted effects on clinical outcomes and overall utility. Expected utility was then calculated as a weighted average of the probability of 4 combinations of toxicity and efficacy outcomes

$$U=\sum _{k=1}^K{w}_k{\pi }_k,$$

where ${\pi }_k$ denotes the estimated probability of the $k$th outcome and $w_k$ denotes the assigned utility score of outcome $k$, for $k=1,\dots ,4$.We calculated ${\pi }_k$ as the product of the corresponding probabilities from the toxicity and local progression models under the assumption that, conditional on the covariates, the 2 outcomes would be independent.

We then selected the prescription dose that maximized expected utility. Radiation treatment planning for SBRT typically focuses on producing the highest ratio of tumor dose to MLD. Therefore, we first determined the maximum desired tumor BED₁₀ (BED_max; we use 120 Gy for illustration, a dose that leads to nearly 100% tumor control)¹² and the MLD of the radiation plan delivering BED_max. We then varied tumor BED from zero to BED_max and calculated the corresponding MLDs by assuming the ratio of tumor BED₁₀ to MLD was constant. For each combination of tumor BED and MLD, we generated model-predicted probabilities of tumor progression and liver toxicity and calculated the expected utility for each point along the tumor BED₁₀/MLD range. This resulted in an expected utility curve, corresponding to a range of predicted probabilities of liver toxicity (varying with MLD) and local progression (varying with tumor BED₁₀). The optimal prescription dose was defined as the tumor BED₁₀ that maximized expected utility. For each patient, we also determined the tumor dose and MLD that would have been delivered using the RTOG 1112 algorithm, the associated utility, and the predicted local progression and liver toxicity probabilities. Statistical analyses were conducted with SAS v9.4 and R v4.0.4 (R Core Team).

Results

Patient characteristics

Our patient cohort included a total of 309 patients (462 treated HCC tumors), with 103 patients (159 tumors) from Princess Margaret Cancer Centre and 206 patients (303 tumors) from University of Michigan (Table 1). Overall, the median age was 69 years (IQR, 62–77), 75% of the sample was male, 69% was White, and 72% was treated from 2012 to 2016. Before treatment, 75% of the sample had CP A5-A6 liver function and 24% had CP B7-B9. The median pretreatment ALBI score was −2.26 (IQR, −2.64 to −1.84) The median tumor size (maximum dimension) was 2.40 cm (IQR, 1.60–3.60). The median total BED₁₀ delivered was 79 Gy₁₀ (IQR, 60–100) and the median MLD (in BED_2.5) was 13 Gy_2.5. Most patients were treated with either 3 fractions (33%), 5 fractions (39%), or 6 fractions (27%). We observed 67 local progression events, 65 competing mortality events, and 57 liver toxicity events.

Table 1.

Characteristics of the sample

Characteristic
Patient-level characteristics (N = 309)*
Age (y)	69 (62–77)
Race
Asian	50 (16.1)
Black	21 (6.8)
Other	26 (8.4)
White	212 (68.6)
Sex
Female	78 (25.2)
Male	231 (74.8)
Year
2004–2007	23 (7.4)
2008–2011	64 (20.7)
2012–2016	222 (71.8)
Pretreatment ALBI score	−2.26 (−2.64 to −1.84)
Pretreatment Child−Pugh score
A5	146 (47.2)
A6	84 (27.2)
B7	31 (10.0)
B8	21 (6.8)
B9	15 (4.9)
C10+	6 (1.9)
Tumor-level characteristics (N = 462)*
Tumor maximum dimension (cm)	2.40 (1.60–3.60)
Fiducials	37 (8)
Respiratory motion management
Free breathing	126 (27.2)
Breath hold	188 (40.7)
Abdominal compression	106 (22.9)
Unknown	42 (9.1)
Total tumor dose (BED10)	79 (60–100)
Mean liver dose (BED2.5)	13 (8–18)
Number of fractions
2	2 (0.4)
3	154 (33.3)
4	2 (0.4)
5	179 (38.7)
6	125 (27.1)

Abbreviations: ALBI = albumin-bilirubin score; BED = biologically equivalent dose.

^*N (IQR) or N (%).

Integrated utility model

Our first step was to develop models for local tumor control, competing risk of death, and local progression as described above (Fig. 1; Tables E2-E4). As expected, the probability of tumor control increased with higher prescription dose (P < .001). The competing risk of death was higher with worse CP score (P < .001), and liver toxicity risk increased with higher MLD (P = .01).

We then calculated the utility of treatment as it varied with predicted probability of liver toxicity and tumor progression (Fig. 2). The increase in local control and toxicity occurs at different rates over the range of doses, leading in this example to an optimal tumor dose of ~40 Gy in 5 fractions. This would be associated with a risk of toxicity of 14% and provide a 91% probability of 1 year tumor control. In our approach, the relationship of tumor dose and local control probability is affected by individual competing mortality risk, with higher competing mortality risk leading to a lower absolute risk (cumulative incidence) of tumor progression for the same tumor dose. Similarly, patient baseline liver function affects the steepness of the toxicity/MLD curve, with worse baseline liver function leading to a higher risk of toxicity for a given MLD.

Fig. 2.

Dose-toxicity trade-off curves and utility calculation for a hypothetical patient. patient in our cohort, a plan was developed that maximizes the ratio of the tumor dose to the MLD. In our simulations, we then varied the tumor dose and MLD according to this fixed ratio, resulting in a curve describing predicted probability of local progression (varying with tumor dose; upper x axis; black line) and liver toxicity (varying with MLD; lower x axis; gray line). These probabilities are then weighted by their respective utilities and summed. Baseline patient information determines the probability of toxicity and local progression according to the models described in the text, as well as the corresponding expected utility as a function of dose. Abbreviations: Gy = Gray; LP = local progression; MLD = mean liver dose.

Comparison with RTOG 1112 dose selection

We compared the “optimal” tumor dose under our utility-based approach and associated probabilities of local progression and liver toxicity with those that would result from the RTOG 1112 dose selection paradigm. We then varied our assumption of the relative utilities of local progression and liver toxicity. Figure 3 shows the effect of utility-based planning on predicted liver toxicity risk, local progression risk, and total utility under our base-case utility assumptions. Under this utility assumption, which assigns liver toxicity a lower utility (0.40) than local progression (0.60), the utility-based approach recommended radiation plans with lower and more homogeneous MLDs on average, resulting in substantially lower liver toxicity risk for most patients compared to RTOG 1112 doses (Fig. 3A). We found analogous results with respect to tumor BED₁₀ and probability of local progression. The utility-based approach tended to recommend lower tumor doses on average, achieving lower toxicity risk at the expense of higher local progression risk (Fig. 3B). Overall, as expected, utility-based treatment planning led to higher overall expected utility compared with RTOG 1112 (Fig. 3C).

Fig. 3.

Predicted clinical outcomes and utilities under the base-case utility scenario. Each point represents the predicted risk of liver toxicity (A) or the risk of local progression (B) associated with the radiation treatment plan for an individual HCC tumor. For each treatment plan, gray lines connect the predicted risks under the RTOG 1112 algorithm (red) versus our utility-based algorithm (blue). (C) The overall utility of the 2 approaches. In the base-case utility assumption, the utility of toxicity is lower (worse) than the utility of local progression. Abbreviations: HCC = hepatocellular carcinoma; U(LP) = utility of local progression; U(tox) = utility of liver toxicity; RTOG = Radiation Therapy Oncology Group.

We next performed a sensitivity analysis with reversed utilities, assuming instead that local progression has a lower utility (0.40) than liver toxicity (0.60; Fig. 4). In this analysis, our utility-based approach led to fewer changes in MLD and liver toxicity risks (Fig. 4A), local progression risks (Fig. 4B), and overall utility (Fig. 4C) compared with RTOG 1112 doses. Finally, we performed a sensitivity analysis excluding patients with Child-Pugh score of 9 or higher. This showed similar results to the primary analysis (Figure E2)

Fig. 4.

Predicted clinical outcomes and utilities under the alternative utility scenario. Each point represents the predicted risk of liver toxicity (A) or the risk of local progression (B) associated with the radiation treatment plan for an individual HCC tumor. For each treatment plan, gray lines connect the predicted risks under the RTOG 1112 algorithm (red) versus our utility-based algorithm (blue). (C) The overall utility of the 2 approaches. In the alternative utility assumption, the utility of local progression is lower (worse) than the utility of liver toxicity. Abbreviations: HCC = hepatocellular carcinoma; U(LP) = utility of local progression; U(tox) = utility of liver toxicity.

Discussion

In this study, we describe a novel framework for radiation treatment planning based on explicit utility trade-offs between efficacy and toxicity, where risk estimates of tumor progression and toxicity are individualized and based on statistical modeling. Using a multi-institutional liver SBRT database as an illustration, we demonstrate that this approach produces plans that have a higher expected overall utility compared with standard treatment (such as the rules for RTOG 1112), although the magnitude of this benefit depended on the relative utilities of liver toxicity and tumor progression. This general approach to radiation treatment planning can also integrate disparate risk prediction models into a single utility scale. Although our work is preliminary and intended as a proof-of-concept, we believe it holds promise for quantitating efficacy-toxicity trade-offs, enabling future clinical trials of utility-based treatment planning, and eventually improving the personalization of liver SBRT dosing.

Clinical decisions that carefully balance efficacy-toxicity trade-offs are ubiquitous in clinical oncology, but they are rarely made quantitatively.¹⁵ Radiation oncologists routinely escalate or de-escalate prescription doses based on the anticipated consequences of tumor progression, curability, risk of distant progression, administration of concurrent chemotherapy, competing mortality risk, and severity of normal tissue toxicity, among many other considerations—each of which is informed by the clinician’s knowledge of medical literature, their clinical judgment and experience, and the priorities of the patient. These trade-offs are also routine in radiation treatment planning, where historical OAR dose limits may be reasonably violated if the benefit of increased tumor control is judged to outweigh a higher risk of toxicity. Although many statistical models have been developed to predict tumor control and toxicity, these are simply quantitative inputs that inform a clinical decision-making process that is still fundamentally qualitative.

Utility-based selection of optimal dose has been previously described in the context of phase I trials.^16–18 In this setting, the goal is to identify a single optimal dose for all patients. We extend this concept, proposing the use of models with patient-level covariates so that the optimal dose will vary between patients. An additional important distinction is that in the cited references, dose is a univariate scalar quantity. In this paper, we considered a more complex bivariate dose term (tumor dose and MLD) in a setting where dose is subject to pre-existing variability due to both patient factors and site or provider-level preferences. Our goal was to identify the optimal dose for individual patients among doses already in common use.

Utility-based treatment planning can improve the precision of treatment decisions by estimating individual probabilities of efficacy and toxicity and explicitly weighing the trade-offs between them. In this study, the optimal tumor prescription dose varied widely depending on baseline patient characteristics and the individualized predicted relationship between dose and progression/toxicity risk. When we assumed that liver toxicity was worse (lower utility) than tumor progression, the utility-based approach recommended markedly lower prescription doses compared with RTOG 1112, resulting in significantly lower toxicity risk at the expense of a broader range of local progression risk. Notably, when we assumed tumor progression was worse than liver toxicity, the average expected utility with our approach was quite similar to that expected under RTOG 1112, suggesting this particular efficacy/toxicity trade-off may be implicit in the RTOG 1112 dose-selection algorithm.

Although implementing our approach does require physicians to assign utilities to each potential outcome, this is merely making explicit a calculation that has already been performed implicitly by the clinician. Explicitly stating utilities could encourage greater transparency in clinical decision-making and encourage clinicians to consider the risks and potential benefits of treatment more deeply. Our approach could also incorporate the patient perspective by incorporating patients’ individual risk tolerance and perceptions of toxicity. This approach also allows the dynamic updating of predictive models for local progression, competing mortality, and liver toxicity as new data accrue. With the wealth of electronic medical record data, digitization of radiation plans, and the maturation of machine-learning methods for clinical prediction, we anticipate that predictive models will only improve and lead to more refined estimates of expected utility.

Our study is subject to several potential limitations. First, our predictive models are based on a heterogeneous cohort of patients from 2 institutions between 2004 and 2016, some of whom were treated on prospective trials of adaptive radiation therapy. Although this does limit the generalizability of our results, we emphasize that our work is intended as a proof-of-concept that should be adapted, extended, and refined as prediction models mature and new technologies emerge. Second, ALBI score deterioration in patients with HCC treated with SBRT reflects a direct toxic effect of SBRT of liver function as well as a natural decline and/or fluctuation of liver function in cirrhosis. We are currently evaluating more accurate methods of disentangling the toxic effects of SBRT from cirrhosis-related liver function decline, potentially resulting in improved estimates of SBRT toxicity. Third, in this preliminary proof-of-concept study, we chose to use simplified prediction models with a limited set of covariates. In the future, we hope to expand these models with additional variables, such as magnetic resonance imaging-derived liver function parameters that could improve toxicity prediction. We also hope to include other relevant considerations for clinical decision-making, including doses to other OARs (like colon or stomach for peripheral lesions), risks of distant progression, and others. Finally, we have not yet quantified model uncertainty in our clinical predictions or expected utility curves. Although this reflects a long-standing convention in decision analysis, basing clinical practice on highly uncertain predictions could result in erroneous treatment decisions. This is especially true when models suggest treatment decisions that are far from the norm, based on sparse data, or greatly exceed established safety limits. This can be ameliorated by bounding the decision space within prespecified safety limits, such as limiting the maximum possible prescribed dose or placing hard limits on doses to particular OARs. It can also be approached with alternative definitions of optimal dose beyond maximizing the expected utility.¹⁹ These issues are fertile grounds for future research.

In conclusion, we propose a novel approach to radiation treatment planning based on utility-based trade-offs of predicted efficacy and toxicity. We use multi-institutional data from patients with HCC treated with liver SBRT to illustrate this approach, deriving predictive models for local progression, liver toxicity, and competing mortality, and integrating individual predictions into a unified utility framework. This allows selection of a prescription dose that optimally balances efficacy and toxicity on a per-patient basis and on average superior potential outcomes compared with a standard approach such as used in RTOG 1112. We hope to refine this approach and ultimately test it against standard dose selection in a randomized controlled trial.

Supplementary Material

Supplementary material associated with this article can be found in the online version at doi:10.1016/j.ijrobp.2025.07.1408.