# Integrative kinetics and machine learning modeling for prediction of outcome following immunotherapy in lung cancer

Sébastien Benzekry

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Sébastien Benzekry. Integrative kinetics and machine learning modeling for prediction of outcome following immunotherapy in lung cancer. KSMB-SMB 2024 - Joint annual meeting of the Korean Society for Mathematical Biology and the Society for Mathematical Biology, Jun 2024, Seoul, South Korea. hal-04990485

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Distributed under a Creative Commons Attribution 4.0 International License
# Integrative kinetics and machine learning modeling for prediction of outcome following immunotherapy in lung cancer

S. Benzekry

SMB annual meeting, Seoul, July 2024
# Clinical challenge

* Lung cancer is the leading cause of cancer-related death (25.3 % of all cancer deaths, 13.6 % of new cancer cases)

* 57 % are metastatic at diagnosis (stage IV), 5-year overall survival rate is poor (18.6 %)

* Introduction of new immunotherapies (immune checkpoint inhibitors) in the 2010's has revolutionized treatment of advanced lung cancer

* 20–30 % of patients have long term response (> 10 years)

* Prediction of overall survival from baseline or early data could help

* guide treatment decision during clinical drug development (e.g., combo trials, predict OS from tumor phase I/II data)

* inform personalized health care

* Current state of the art

* Only predictive biomarker used in the clinic: PDL1 expression from immunohistochemistry<fnref n="1" /> (AUC = 0.601)

* Predictive model from baseline clinical and biological data: ROPRO score<fnref n="2" />

* 27 variables

* Developed on 120k+ patients over multiple cancer types

* C-index = 0.69 on OAK as independent test set

* Predictive value of transcriptomic and mutation data is unclear

* Tumor kinetics model parameter growth rate (KG) has important predictive power of hazard ratio (HR)<fnref n="3" />

* Predictive value of kinetics of blood markers (lab tests) is unclear

<figure><img src="image_2.png" /></figure>

Brahmer et al., NEJM 2015

<footnote n="1">¹ Rizvi, H. et al., J Clin Oncol Molecular Determinants of Response to Anti-Programmed Cell Death (PD)-1 and Anti-Programmed Death-Ligand 1 (PD-L1) Blockade in Patients with Non-Small-Cell Lung Cancer Profiled with Targeted Next-Generation Sequencing. J. Clin. Oncol. 2018, 36, 633–641.</footnote>

<footnote n="2">² Becker, T. et al. An enhanced prognostic score for overall survival of patients with cancer derived from a large real-world cohort. Ann Oncol 31, 1561–1568 (2020).</footnote>

<footnote n="3">³ Claret, L. et al. A Model of Overall Survival Predicts Treatment Outcomes with Atezolizumab versus Chemotherapy in Non-Small Cell Lung Cancer Based on Early Tumor Kinetics. Clin Cancer Res 24, 3292–3298 (2018).</footnote>
# kinetics – Machine learning (kML) for prediction of OS

## Raw baseline data

Clinical characteristics
p = 73

Genomic and Transcriptomic
p = 395 and 58,311

Feature
selection

## Minimal signature

Clinical
characteristics

Genomic and
Transcriptomic

## Raw longitudinal data

Tumor Kinetics (TK)
k = 8,635

Blood markers Kinetics (BK)
k = 108,551
Albumin, CRP, Neutrophils, LDH

Mixed-
effects

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

## Model-based
individual parameters

TK

BK

<figure><img src="image_5.png" /></figure>

## Survival
outputs

### Individual prognosis

* C-index

* Survival

### Clinical trial

* Survival curve

* Hazard ratio

Machine
Learning
## Outline

1. Data

2. Modeling the kinetics of longitudinal data using nonlinear mixed-effects modeling (NLME)

1. Tumor size kinetics (TK)

2. Blood markers kinetics (BK)

3. Machine learning (kML)

1. Model development

2. Individual predictions

3. Trial-level predictions

4. Mechanistic modeling

5. Beyond classical biomarkers

1. cfDNA fragmentomics

2. PIONeeR biomarkers (1000+)
# Data for model development and external validation

## Baseline data

* Patients' and disease characteristics
  **p = 73 parameters**

* Transcriptomic and mutational data
  **p = 58,311 and 395**

## Longitudinal data

* Tumor kinetics (TK, SLD)
  **5,570/3,065 observations**

* 4 BK markers (Albumin, CRP, LDH and Neutrophils)
  **61,296/47,255 observations**

<table><thead><tr><th>Study</th><th>Description</th><th>N</th></tr></thead><tbody><tr><td>FIR<br>GO28625</td><td>Phase 2 study for the efficacy and safety of ATZ in advanced NSCLC</td><td>133</td></tr><tr><td>POPLAR<br>GO28753</td><td>Phase 2 randomised controlled trial of ATZ versus docetaxel in NSCLC</td><td>134</td></tr><tr><td>BIRCH<br>GO28754</td><td>Phase 2 study of ATZ in advanced or metastatic NSCLC</td><td>595</td></tr><tr><td>Train</td><td></td><td>862</td></tr><tr><td>Test - OAK<br>GO28915</td><td>Phase 3 RCT of ATZ versus docetaxel (DTX) in patients with previously treated NSCLC</td><td>553 (ATZ)<br>521 (DTX)</td></tr><tr><td>Train + Test</td><td></td><td>1936</td></tr></tbody></table>

Train

Test

NSCLC: Non-Small Cell Lung Cancer; p = number of parameters, N: number of patients treated with atezolizumab (patients from French centers were excluded for legal reasons (N=118)); In total, data from 1074 patients from OAK were used as Test set (553 from the ATZ arm, 521 from the DTX arm); PD: Pharmacodynamic; SLD: Sum of the Largest Diameters. CRP: C Reactive Protein; LDH: Lactate Dehydrogenase.

1. Fehrenbacher L et al. Atezolizumab versus docetaxel for patients with previously treated non-small-cell lung cancer (POPLAR): a multicentre, open-label, phase 2 randomised controlled trial. Lancet (2016)

2. Fehrenbacher L et al. Updated Efficacy Analysis Including Secondary Population Results for OAK: A Randomized Phase III Study of Atezolizumab versus Docetaxel in Patients with Previously Treated Advanced Non-Small Cell Lung Cancer. Journal of Thoracic Oncology (2018)

3. Solange Peters et al. Phase II Trial of Atezolizumab As First-Line or Subsequent Therapy for Patients With Programmed Death-Ligand 1-Selected Advanced Non-Small-Cell Lung Cancer (BIRCH). JCO (2017)

4. Spigel D.R et al. FIR: Efficacy, Safety, and Biomarker Analysis of a Phase II Open-Label Study of Atezolizumab in PD-L1-Selected Patients With NSCLC. Journal of Thoracic Oncology (2018)
# Tumor kinetics

100 random patients

<figure><img src="image_6.png" /></figure>

## Individual kinetics

Double (sum of two) exponential model

<figure><img src="image_7.png" /></figure>

$$S^i(t) = S0^i (e^{-KS^i t} + e^{KG^i t} - 1)$$
# Mixed-effects modeling for population longitudinal data

* **Observation model**

$$y_j^i = M(t_j^i; \theta^i) + \varepsilon_j^i, \varepsilon_j^i \sim \mathcal{N}(0, \sigma_j^i)$$

* **Inter-individual variability model**

$$\ln(\theta^i) = \ln(\theta_{\text{pop}}) + \eta^i, \eta^i \sim \mathcal{N}(0, \omega^2)$$

$M$ = structural model

$y_j^i$ = observation at time $t_j^i$ in patient $i$

$\varepsilon_j^i$ = error model (constant (TK) or proportional (BK))

<figure><img src="image_8.png" /></figure>

* Estimation of the population parameters using the SAEM algorithm for likelihood maximization

* Estimation of the individual empirical Bayes estimates (EBEs) from the maximum a posteriori estimator

* Fits performed using Monolix 2020R1 and scripted using the R Monolix API
# The double exponential model was able to describe individual TK

2 best fits in each response group

*Individual goodness-of-fit*
*(GOF) plots*

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

20 randomly selected individual fits

<figure><img src="image_11.png" /></figure>
# Blood markers kinetics (BK)

## Spaghetti plot

<figure><img src="image_12.png" /></figure>

## Early cycles (normalized)

<figure><img src="image_13.png" /></figure>

Is there any kinetic pattern ?

Does it carry predictive value ?

Can we describe dynamics with a mechanistic model ?
# Empirical structural models to test for BK

$H_0 = \text{Constant}$

<figure><img src="image_14.png" /></figure>

$$y^i = \alpha\rho\alpha^i$$

Equivalent of no significant kinetics
Used as a benchmark

Linear

<figure><img src="image_15.png" /></figure>

$$y^i = \alpha\rho\alpha^i + \beta\alpha^i t$$

q
p
p
q

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

$$y^i = p^i + e^{l^i} \frac{q^i - p^i}{t + e^{l^i}}$$

dexp

<figure><img src="image_18.png" /></figure>

$$y^i = \begin{cases} S0^i e^{KG^i t}, & t \le 0 \\ S0^i (e^{-KS^i t} + e^{KG^i t} - 1), & t > 0 \end{cases}$$

Allows change of
monotonicity
# Is there any kinetic pattern? Yes !

Corrected Bayesian Information Criterion (BICc x 10³) for four empirical kinetic models of BK. b : standard deviation of the proportional error model

<table><thead><tr><th rowspan="2">Model</th><th colspan="2">Albumin</th><th colspan="2">CRP</th><th colspan="2">LDH</th><th colspan="2">Neutrophils</th></tr><tr><th>BICc</th><th>b</th><th>BICc</th><th>b</th><th>BICc</th><th>b</th><th>BICc</th><th>b</th></tr></thead><tbody><tr><td>Double-exponential</td><td>48.4</td><td>0.058</td><td>28.8</td><td>0.21</td><td>39.9</td><td>0.56</td><td>102</td><td>0.14</td></tr><tr><td>Hyperbolic</td><td>48.0</td><td>0.056</td><td>29.7</td><td>0.22</td><td>40.9</td><td>0.62</td><td>103</td><td>0.14</td></tr><tr><td>Linear</td><td>49.4</td><td>0.063</td><td>30.0</td><td>0.23</td><td>42.4</td><td>0.70</td><td>105</td><td>0.17</td></tr><tr><td>Constant</td><td>49.7</td><td>0.065</td><td>31</td><td>0.25</td><td>43.0</td><td>0.74</td><td>106</td><td>0.18</td></tr></tbody></table>

<figure><img src="image_19.png" /></figure>
Does it carry predictive value? Yes !

<figure><img src="image_20.png" /></figure>

⇒ Individual TK and BK model parameters (without baseline) = ML inputs
# Model development and validation

## Model development

### Phase 2 trials

* FIR

* BIRCH

* POPLAR

#### Atezolizumab

ML

Feature selection

NLME

Population prior

Bayesian Estimation

$$ \begin{gathered} N = 533 \\ p = 26 \end{gathered} $$

ML

Train

Trained model

ML

Predict

Individual predictions

$\hat{S}^i(t)$

## Model validation

### Phase 3 trial OAK

#### Atezolizumab arm

Bayesian Estimation

$$ \begin{gathered} N = 377 \\ p = 26 \end{gathered} $$

ML

Predict

Individual predictions

Trial prediction

#### Docetaxel arm

$$ \begin{gathered} N = 354 \\ p = 26 \end{gathered} $$

Individual predictions
# Methodology - Machine learning model development

* Preprocess

Drop zero-variance or >25% NA columns, dummification, NA imputation, scaling

* Dimensionality reduction for RNAseq data (bootstrap LASSO)

* Features selection:

* 5 methods: **LASSO**, random survival forest (RSF) importance, Cox-based and stepwise forward/backward

* 3 strategies: i) all variables, ii) per feature set and iii) pooled selected sets

* 4 survival algorithms tested:

Cox, Cox and accelerated failure time with gradient boosting and **random survival forest (RSF)**

* Evaluation of machine learning models

* Model development: 10-fold cross-validation, C-index, calibration curves and 12-months survival classification metrics

* Study-level predictions: survival curves, **hazard ratios**

Working principle: need for a **minimal signature** model with limited number of easily measurable variables
# kML individual predictions

mBSL = minimal baseline

## Cross-val on train

<figure><img src="image_21.png" /></figure>

6 months

<figure><img src="image_22.png" /></figure>

12 months

<figure><img src="image_23.png" /></figure>

c-index = 0.79

AUC-12 months = 0.86

## Test set

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

24 months

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>

PDL1 : AUC = 0.65

RoPro: c-index = 0.69 AUC-3 months = 0.817

<figure><img src="image_28.png" /></figure>
# kML predicts phase 3 trial results from early data

Arm

+ Atezolizumab

+ Docetaxel

- Model prediction mean

- Data

95% PI Atezolizumab

95% PI Docetaxel

10 weeks
(2.5 months)

<figure><img src="image_29.png" /></figure>

25 weeks
(6.25 months)

<figure><img src="image_30.png" /></figure>

60 weeks
(15 months)

<figure><img src="image_31.png" /></figure>

Full kinetics
(end of study)

<figure><img src="image_32.png" /></figure>

Hazard ratio

<figure><img src="image_33.png" /></figure>

Data

kML Predicted

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>
Mechanistic model

Data: clinical trials for
atezolizumab (ATZ):

* 3 phase 2 **monotherapy**
  **862 patients**
  44,911 data points

* 1 phase 3 **combotherapy**
  ATZ, Bevacizumab and
  Carboplatin + Paclitaxel
  **1115 patients**
  67,507 data points

<figure><img src="image_38.png" /></figure>
Individual fits (Combotherapy)

<figure><img src="image_39.png" /></figure>

* Fits heterogenous BK profiles

• Albumin early drops

• LDH early peaks

* Late sharp increase of LDH
(death shortly after)

• Identifiability

• All RSEs < 35%

* despite the large number of
parameters (14)

- Very large variability of some
parameters

• Small η - shrinkage < 11%
Post-cycle 4 prediction of individual survival

<figure><img src="image_40.png" /></figure>

Longitudinal
data
considered

10 fold Cross-validation, AUC = accuracy at 12 months

<figure><img src="image_41.png" /></figure>

COMBO
# Summary

* Kinetic models based on simple, routinely available blood markers have prognostic value

* Could be used as non-invasive surrogate markers of response

* Modeling >> data only

* The combination of NLME and ML allowed to take the best of the two approaches in order to predict survival

* NLME to account for longitudinal data

* ML and data science methods to build multivariable models from a large number of features

* **Minimal signature**: 11 baseline clinical features + TK (1 variable – 2 parameters) + BK (4 variables – 8 parameters)

* **Mechanistic modeling** was shown to improve predictions

* Application to clinical oncology could improve **personalized health care**

* Application to **early prediction of trial outcome** could:

* Save a lot of effort (..... and money!)

* Be used to better stratify patients

* Identify signal in early-phase trials
Beyond classical biomarkers:
PIONeeR – QUANTIC and SChISM
# SChISM
## Size CfDNA Immunotherapies Signature Monitoring

**APHM:** S. Salas, Inria / Inserm: S. Benzekry, **L. Nguyen**, Adelis

<figure><img src="image_42.png" /></figure>

<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /></figure>

### Different response profiles and survival prediction

<figure><img src="image_45.png" /></figure>
# The PIONeeR and QUANTIC project

Precision Immuno-Oncology for advanced Non-small cell lung cancer patients with PD-1 ICI Resistance

<figure><img src="image_46.png" /></figure>

Assistance Publique
Hôpitaux de Marseille

<figure><img src="image_47.png" /></figure>

INSTITUT
NATIONAL
DU CANCER

<figure><img src="image_48.png" /></figure>

Inserm

Institut national
de la santé et de la recherche médicale

Aviesan

Alliance nationale
pour les sciences de la vie et de la santé

ITMO Cancer

450 pts

<figure><img src="image_49.png" /></figure>

24,287 variables

1,581 markers

<figure><img src="image_50.png" /></figure>
Roche / Genentech

R. Bruno

P. Chanu

F. Mercier

C. Jamois

<figure><img src="image_51.png" /></figure>

Open PhD /
postdoc positions

sebastien.benzekry@inria.fr

# Acknowledgments

Thank you for your attention!

<figure><img src="image_52.png" /></figure>

https://team.inria.fr/compo/

Patients and families

## Computational

C. Bigarre

M. Karlsen

L. Nguyen - Phuong

R. Taieb

## Clinical oncology

D. Boulate

J. Ciccolini

L. Greillier

X. Muracciole

S. Salas

F. Barlesi

F. Bertucci

L. Padovani

P. Tomasini

....