1. Utility and Biomarker Based Dose Selection in Radiation Therapy
Matthew Schipper

2. Outline Background Biomarkers Utility Approach to Selecting Dose
Virtual Clinical Trial
Conclusions and Next Steps

3. Setting
Goal: Based on all that we know about a individual patient, develop an ‘optimal’ radiation plan
At baseline using baseline information
Mid-treatment using mid-treatment information
Knowledge was very limited (e.g. stage II/III NSCLC) but increasingly includes biomarkers

4. Outcomes Following RT
Outcomes more complex than single binary indicator (e.g. Response)
Multiple toxicities that are qualitatively different and of varying severity
Pneumonitis, Esophagitis and Cardiac Toxicity for Lung Cancer
Efficacy typically a ‘time-to-event’
May be multiple efficacy endpoints (local control and distant control)

5. Dose in Radiation Oncology
PTVs
Spinal Cord
Brainstem
Constrictors
Mandible
Parotids

6. Dose in Radiation Oncology
After accounting for time/fractionation effect and spatial variation, the dose data is
D = Dose to the tumor
dj = dose to normal tissue/organ j;
j =1,2,... J
In Lung Cancer, concerned about dose to normal lung, esophagus, heart…

7. Current Approach
Give fixed dose to tumor while meeting certain constraints on normal tissue dose
Little individualization
Everyone gets same tumor dose but not same normal tissue dose

8. Treatment Planning Directive

9. Summary of Planning Goals
Priority
Structure
Metric
Goal 1
Cord
Max
45 Gy
Esophagus
63 Gy
Mean
34 Gy
Heart
30 Gy
Lungs-GTV
66 Gy
15 Gy 2
PTV
Min
60 Gy 3
Minimize Mean doses to all organs above and the unspecified normal tissue
Minimize Hotspots in normal tissues
Maximize conformity of the plan (sometimes by making dummy optimization structures)
Notice 1) no biomarkers or clinical factors 2) no prob() just dose

10. Outline Background Biomarkers Utility Approach to Selecting Dose
Virtual Clinical Trial
Conclusions and Next Steps

11. Bradley et al, Lancet Oncology, 2015
Results from RTOG 0617
Bradley et al, Lancet Oncology, 2015

12. High vs Standard Dose Clearly, high dose does not improve OS overall
Some patients may benefit from high dose
Significant number of patients have minimal toxicity AND progress soon after treatment => potentially underdosed
Even standard dose may be too high for some patients
Patients who experience severe toxicity AND long term tumor control
How can we identify these patients at time of treatment?

13. Cytokines and Lung Toxicity

14. miRNA and Overall Survival

15. Don’t forget about clinical factors…
Dess et al, JCO, 2017

16. Subgroup Identification
Using covariates to identify heterogeneity in treatment effectiveness is an active area of statistical research
Xu et al, Biometrics, 2015
Foster et al, Stat Med, 2011
Our setting differs
Treatment: Not A vs B, but RT Plan (can be simplified to continuous dose)
Multiple outcomes with distinct covariates

17. Combining Efficacy and Toxicity
Treatment planning must be based on toxicity and efficacy considerations
Several proposed metrics that combine efficacy and toxicity into single outcome (e.g. QTWiST= Quality-Adjusted Time WIthout Symptoms or Toxicity or QALYs = Quality Adjusted Life Years)
Jang et al, JCO, and Black et al, NEJM 2015
Biomarkers are typically associated with single toxicity OR efficacy outcome, not composite endpoint
Model outcomes separately and then combine predictions when evaluating a particular dose/plan

18. Outline Background Biomarkers Utility Approach to Selecting Dose
Virtual Clinical Trial
Conclusions and Next Steps

19. Utility Approach 𝑃(𝑬=𝟏|𝑹𝑻 𝑷𝒍𝒂𝒏)−𝜃∗𝑃(T=1|RT Plan) Outcomes:
E = binary indicator for Efficacy
T= binary indicator for Toxicity
Define optimal plan as the plan that maximizes
𝑃(𝑬=𝟏|𝑹𝑻 𝑷𝒍𝒂𝒏)−𝜃∗𝑃(T=1|RT Plan)

20. Utility Approach
Incorporate covariates G for E and M for T 𝑃 𝑬 𝑹𝑻 𝑷𝒍𝒂𝒏, 𝑮)−𝜃∗𝑃(T | RT Plan, M) Generalize to multiple toxicity types/grades 𝑃 𝑬 𝑹𝑻 𝑷𝒍𝒂𝒏, 𝑮) − 𝑗 𝜃 𝑗 ∗𝑃 𝑇 𝑗 𝑹𝑻 𝑷𝒍𝒂𝒏, 𝑴

21. Example Schematic

22. Choice of θ
Elicit from clinician or individual patient based on undesirability of toxicity relative to local tumor progression Or
As tuning parameter to control average rate of toxicity
𝑃 𝑇=1 =1/𝑛 𝑖 𝑃( 𝑇 𝑖 =1| 𝑫 𝑖 𝜃, 𝑟 𝑖 , 𝑀 𝑖 )
where 𝐷 𝑖 maximizes (1) and is thus a function of θ, ri and Mi.
Lagrangian multiplier approach

23. Outline Background Biomarkers Utility Approach to Selecting Dose
Virtual Clinical Trial
Conclusions and Next Steps

24. Use of Utility Function in Clinical Trials
Biomarker based dose finding trial
See Ch 7.2 of ‘Bayesian Designs for Phase I-II Clinical Trials’ by Yuan Y, Nguyen H and Thall P.
In RadOnc, data/models already available over a range of dose values
Conduct randomized ph II trial comparing Utility based dosing to standard dosing
Goal: Improve efficacy at same toxicity

25. Virtual Clinical Trial
For each person
calculate recommended doses under Utility approach and Standard approach
calculate expected outcomes for each plan from the models
Calculate average outcomes (across patients) for Utility approach and Standard approach

26. Virtual Clinical Trial: Results
Local Control at 2 Years (%)
Model
Toxicity Model
(on logit scale)
AUC
Toxicity Model Only
Utility: Toxicity and Efficacy Models 1 *d
0.72
40.0
48.4 2
*d-.85*log(IL8)
0.78
42.2
50.2 3
*d-.79*log(IL8)+.03*TGFβ*d
0.83
44.8
51.0 4
*d+0.07*d*I(TGFα>3)
0.76
44.2
52.1 5*
*d+0.16*d*I(TGFα>3) NA
54.0
57.6
Toxicity rate is equal to 15% in every case.
*Hypothetical model.

27. Virtual Clinical Trial: Results
How can Utility based treatment planning increase efficacy without increasing toxicity?
Intuition: by ‘spending’ its toxicity wisely, i.e. Patients exposed to risk (P(Tox)) in proportion to reward (P(Eff))

28. Outline Background Biomarkers Utility Approach to Selecting Dose
Virtual Clinical Trial
Conclusions and Next Steps

29. Conclusions
Better models/markers can be coupled with the proposed utility approach to improve efficacy without increasing toxicity
Standard metrics (such as AUC) do not directly address the question of whether a new marker would be useful in selection of a patient’s dose.

30. Open Areas Expanded virtual clinical trial
Adaptation in addition to individualization
Use mid-treatment imaging to spatially redistributes dose to tumor and normal tissue
Joint modeling of E,T to calculate E(U)
Involving the patient in treatment decisions (e.g. how aggressive of treatment…)

31. Acknowledgements Shuti Jolly and Ted Lawrence
Randy TenHaken and Martha Matuzak
Jeremy Taylor

32. Reference
Schipper MJ, Taylor JMG, TenHaken R, Matuzak M, Kong FM and Lawrence T. Personalized dose selection in Radiation Therapy using statistical models for toxicity and efficacy with dose and biomarkers as covariates. Stat Med 33(30): , PMC

33. Questions?

34. Extra Slides

35. Prognostic and Predictive Biomarkers

36. Prognostic and Predictive Biomarkers

37. Relation to Other Approaches
𝜋 𝐸 (P(E=1)) and 𝜋 𝑇 (P(T=1)), as 1-x where x is given by
1− 𝜋 𝐸 1− 𝜋 𝐸 ∗ 𝑝 + 𝜋 𝑇 𝜋 𝑇 ∗ 𝑝 = 𝑥 𝑝
When p=1, 𝑐∗(1−𝑥)= 𝜋 𝐸 −𝜃∗ 𝜋 𝑇
where c is a constant not depending on dose, and 𝜃= 𝜋 𝐸 ∗ −1 𝜋 𝑇 ∗ .
selecting dose to maximize (1-x) is equivalent to maximizing U().

38. Virtual Clinical Trial
Using previously treated patients, we fit a series of models
Patients: ~100 with stage III NSCLC treated with RT over the past 9 years
Outcomes
Toxicity: Radiation Pneumonitis G2 or higher
Local Control (LC) = Freedom from local progression

39. Marker for Toxicity
Cross Validation used to make group assignments. Main effect or interaction? Difficult to judge w/ limited data. Biologically, marker value is change from baseline, following some dose.

40. Efficacy Model

41. Virtual Clinical Trial
For each person in our dataset, calculate recommended doses under Utility approach and Standard approach
Constraints: D in (55,95Gy) and d < 30Gy
From the efficacy and toxicity models, calculate expected outcomes for selected dose
𝑆 𝐷 𝑖
𝑝 𝑡𝑜𝑥 ( 𝑑 𝑖 )
Calculate average (across patients) of 𝑝 𝑡𝑜𝑥 ( 𝑑 𝑖 ) and 𝑆 𝐷 𝑖
𝑖 𝑆 𝑖 𝐷 𝑖 /n and 𝑖 𝑝 𝑡𝑜𝑥 𝑑𝑖 /n
Based on scaling up/down plan a patient actually received. Similar results if limit dose to <90 or mld < 25

42. Virtual Clinical Trial: Results
Local Control at 2 Years (%)
Model
Toxicity Equation
(on logit scale)
AUC
Isotoxic
Utility Without Efficacy Markers
Utility With Efficacy Markers 1 *d
0.72
40.0
44.1
48.4 2
*d-.85*log(IL8)
0.78
42.2
45.8
50.2 3
*d-.79*log(IL8)+.03*TGFβ*d
0.83
44.8
47.0
51.0 4
*d+0.07*d*I(TGFα>3)
0.76
44.2
45.1
52.1 5*
*d+0.16*d*I(TGFα>3) NA
54.0
54.5
57.6
Toxicity rate is equal to 15% in every case.
*Hypothetical model.

43. Tumor Dose & MLD vs Lung Toxicity

44. Correlation
Tumor Sensitive? No
Yes
Normal Tissue Sensitive? A B C D

45. Optimization Variables = MLC positions & segment weights (MUs)
VMAT
Optimization Variables
= MLC positions & segment weights (MUs)
Delivery is fully dynamic, moving linearly between MLC positions while the beam is on with variable dose rate and gantry speed

46. How to Incorporate Biomarkers?
Clinicians: If particular patient is at increased risk of toxicity, give lower dose
Clinicians: If particular patient is at increased risk of progression, give higher dose
Statisticians want more info
X = x
Expected Efficacy
Expected Toxicity
Low Dose
Standard Dose
High Dose

47. Dose in Radiation Oncology
The dose distribution within any organ or volume can be (accurately) calculated
Dose can vary spatially within an organ
The duration of treatment can also vary
Spatial variation captured via ‘Equivalent Uniform Dose’
Time (fractionation) variation captured via ‘Biologically Equivalent Dose’ or ‘EQD2’