Predicting survival in prospective clinical trials using weakly-supervised QSP

doi:10.21203/rs.3.rs-4838339/v1

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Predicting survival in prospective clinical trials using weakly-supervised QSP

https://doi.org/10.21203/rs.3.rs-4838339/v1

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Quantitative systems pharmacology (QSP) models of cancer immunity offer a mechanistic understanding of cellular dynamics and drug effects that are often challenging to investigate clinically. Despite their success, these models are limited by their inability to mechanistically represent patient survival as an output, which restricts their utility in the clinical development of anti-cancer drugs. To address this limitation, we propose a novel approach that links virtual patients, generated from a QSP model, to real patients from clinical trials. Utilizing data from atezolizumab clinical trials in non-small cell lung cancer (N = 1641), our findings demonstrate that tumor-based linkage methods can effectively capture survival outcomes. The linked properties of survival and censoring serve as weak supervision labels, enabling the training of survival models on QSP model covariates alone, without the need for clinical covariates. Furthermore, our approach can predict drug effects on survival for treatments not included in the training datasets. Specifically, we accurately estimated the survival hazard ratio (HR) for two external treatments: a chemotherapy monotherapy arm and an atezolizumab + chemotherapy combination arm. The predicted HR was 0.70 (95% PI 0.55–0.86), closely matching the observed HR of 0.79 (95% PI 0.64–0.98) from the IMpower130 clinical trial.

Health sciences/Oncology/Cancer/Cancer models

Health sciences/Oncology/Cancer/Lung cancer/Non-small-cell lung cancer

Biological sciences/Systems biology

Health sciences/Medical research/Clinical trial design/Randomized controlled trials

Quantitative Systems Pharmacology (QSP) is a modeling paradigm where biological interactions are captured mechanistically by systems of differential equations^1,2. It has emerged as a dominant paradigm in recent years in investigating disease mechanisms and drug effects in silico, allowing observation of dynamical properties that may be difficult to investigate clinically. Calibrated using clinical data, QSP models can then be used to generate biologically plausible ‘virtual populations’. Because of their mechanistic structure, QSP models allow the integration of a variety of data sources, and have shown promise in investigating drug combination effects ^3-5. Observation of tumor outcomes or progression using a QSP model is limited to biological outputs represented in the model. For that reason, purely mechanistic models may not readily generate an output of survival as survival is unlikely to be captured in mechanistic terms. This is of importance in cancer immunotherapy where endpoints like objective response rates and progression-free survival, as assessed by RECIST 1.1⁶, may sometimes be discordant with overall survival (OS) ^7,8.

The aim of this work was to generate a prediction of survival from a QSP model of cancer immunotherapy (CIT) by establishing a link between real patients’ survival outcomes and variables from the QSP model, with the goal of training and validating a survival model using a limited set of clinical trial data. We demonstrate that our survival model can be extended to untested treatments, as evidenced by a validated example of a treatment not included in the training data. In addition, we anticipate that the survival model will be applicable to new doses, dosing regimen, or any other conditions that are incorporated and validated in the QSP model.

In order to link virtual patients to real patients on the basis of similarity between the two data types, it was necessary to identify shared variables. An initial challenge was to decide which variables could be used for linkage, given that there were substantial differences between the two data types, with only a few common variables. Tumor size curves were investigated as a means of linkage between the two data types, as previous work in TGI-OS has demonstrated the predictive relationship that exists between tumor growth inhibition (TGI) metrics and OS in the context of clinical trial data ^9–15. Other work has used correlation-based metrics to characterize similarity between tumor size curves, with an aim to characterize heterogeneity in tumor dynamics between individual target lesions, as well as linking this heterogeneity downstream to overall survival ^16,17. We chose tumor size curves as the shared variable to use for linkage, due to compatibility between real and virtual data, and that tumor size metrics have been shown to be predictive of survival across multiple tumor and treatment types ¹⁸.

Following the linkage of a cohort of virtual patients to real patients from clinical trials, the goal was then to impute values of OS and censoring in the virtual population. These labels can then be used to train survival models using only the QSP variables, with the aim of establishing a predictive relationship between these QSP variables and the survival outcome. This is an instance of weakly supervised learning, a branch of machine learning whereby a heuristic process is used to obtain noisy labels for unlabeled data, and these labels are used to train a supervised model^19–21. While this noise may render individual labels inaccurate, it has been shown that models are often able to generalize well, even from very noisy data ²². Figure 1 provides a schematic diagram detailing the whole methodology end-to-end, from patient matching, to model training, to validation.

Several studies have described the creation of virtual patients that either mimic the clinical characteristics of real patients or that are based on actual clinical data. For example, Zhang, et al. ²³ leveraged RNA-seq data to develop virtual patient parametrizations, and Wang, et al. ²⁴ utilized a public portal of immunogenomic data to guide virtual population generation. To the best of our knowledge, only one study has endeavored matching real patients with pre-generated virtual patients to predict clinical outcomes ²⁵, although this methodology has not been applied to survival analysis. Our approach is unique in that it specifically involves imputing overall survival endpoints in the matched virtual population, thereby providing a training set to effectively simulate a virtual clinical trial under new conditions all the way to predicting OS in individual (virtual) patients, along with generating a hazard ratio for the treatment effect.

3.1 Trials and data

3.1.1 Clinical trial data

Data from 5 clinical trials for atezolizumab in non-small cell lung cancer (NSCLC) were used in linking survival labels to virtual patients: BIRCH²⁶, FIR²⁷, OAK²⁸, POPLAR²⁹, and IMpower110³⁰, with total N = 1641. Details for these trials are shown in Table 1. In each of these trials, tumor size was measured by the sum of longest diameters of target lesions (SLD), as per RECIST 1.1⁶. In order for their tumor dynamics to be characterized longitudinally, only those patients with at least one baseline and one post-baseline tumor measurement were retained. Following this selection, the median number of tumor measurements per patient was 5, ranging from 2 to 19.

Table 1

Details of the atezolizumab clinical trials used for OS imputation.
Trial Name	N	ClinicalTrials.gov Identifier	Other Identifier	Indication	Recruitment Status	Phase	Line
BIRCH	580	NCT02031458	GO28754	NSCLC	Completed	II	1L+
FIR	119	NCT01846416	GO28625	NSCLC	Completed	II	1L+
OAK	555	NCT02008227	GO28915	NSCLC	Completed	III	2L+
POPLAR	129	NCT01903993	GO28753	NSCLC	Completed	II	2L+
IMpower110	258	NCT02409342	GO29431	NSCLC	Active, not recruiting	III	1L
Total	1641

3.1.2 Virtual data from the QSP model

Virtual patients were simulated using a QSP model of cancer immunotherapy in NSCLC, which captures the effects of anti-PD-L1 (atezolizumab), as well as chemotherapy (carboplatin plus nab-paclitaxel) ³¹.

Following calibration to clinical data, a cohort of N = 8347 virtual patients (VPs) was selected. Each of these VPs is characterized by a set of treatment-independent attributes (model parameters), along with a set of time-dependent dynamical signals that correspond to treatment responses. For this study, 3 treatment groups were simulated in VPs: atezolizumab, chemotherapy and the atezolizumab + chemotherapy combination. The atezolizumab group was used for training and testing of the survival model, and the chemotherapy and combination therapy groups were used for prediction and validation.

Within this simulated training data, all dynamical signals, including tumor size, were considered over three distinct periods: a pre-treatment period of 40 weeks, a 27-week treatment period, followed by a post-treatment period of variable length. For feature extraction from QSP dynamical signals (see section 3.3), both the treatment period and the full signal were used. The list of QSP model variables that were used for dynamical feature extraction, along with a description of their biological significance, can be found in Table 2.

Table 2

Brief description of the dynamical variables in the QSP model.
Variable	Description
T	Tumor volume
Ag	Tumor antigens in the tumor space
R	Tregs in the peripheral blood
H	T helper 1 cells in the peripheral blood
C	Cytotoxic T cells in the peripheral blood
RT	Tregs in the tumor space
HT	T helper 1 cells in the tumor space
CT	Cytotoxic T cells in the tumor space
Cyde	Total cytotoxic death

When linking tumor curves between real patients (RPs) and VPs (see section 3.2), only the 27-week treatment period is considered, so as to limit matching to periods where both RP’s and VPs are under treatment. In order to compare tumor curves between RPs and VPs, VP SLD curves were scaled relative to the SLD value at the start of the treatment period. Similarly, longitudinal SLD data in RPs were upsampled by linear interpolation to the same frequency as the virtual data, and then scaled relative to their interpolated baseline value at t = 0.

3.1.3 IMpower130 data

IMpower130 was a phase III clinical trial for first-line patients with NSCLC (NCT02367781, 2019), with N = 724 patients initially randomized 2:1 to the atezolizumab + chemotherapy combination and chemotherapy monotherapy arms, respectively. The stratified hazard ratio for the overall survival endpoint reported in this trial was used for model validation purposes. Additionally, an unstratified version was calculated but did not differ from the reported stratified HR.

For the validation data, the chemotherapy (carboplatin + nab-paclitaxel) and atezolizumab + chemotherapy arms were used to compare survival and predict a hazard ratio. After the survival model was trained (details in Section 3.4) using survival endpoints from the atezolizumab monotherapy arms of the clinical trials presented in Section 3.1.1, data from the IMpower130 trial was used to validate the estimated overall survival hazard ratio, as well as the distribution of OS between both arms predicted by our modeling. The predicted HR was then compared against the observed overall survival hazard ratio for the atezolizumab + chemotherapy combination therapy vs chemotherapy monotherapy ³². Atezolizumab therapy was applied for 144 weeks, and chemotherapy was applied for either 4 or 6 cycles of three weeks each, in a 50/50 proportion. This simulated treatment regimen allowed the model validation analysis to 1. mirror the clinical trial conditions in IMpower130 and 2. demonstrate model robustness to out-of-sample data generation and variations in off-treatment durations.

3.2 Linkage methods

In order to impute weak supervision labels of OS and censoring in the virtual population, a number of linkage methods were investigated. The desired outcome of such a method was that the distribution of imputed OS in the virtual cohort would closely match that of the clinical cohort. The full algorithm for matching RPs with VPs is described in Algorithm 1. For each RP, similarity with every VP was characterized by evaluation of mean-squared error (MSE) between tumor curves within the 27-week treatment period, and matches were ranked by smallest MSE values. If an RPs tumor curve was shorter than 27 weeks, the computation of MSE was limited to the duration of the shorter tumor curve.

Having obtained a ranked list of matches for each RP, a cutoff n was selected such that all VPs were represented at least once. Each VP then inherited OS and censoring labels directly from the matched RP. Popular VPs ended up being matched more than once and were over-represented in the resultant sampling distribution, though in each instance with a different label set. This allowed for an over-representation of VPs that were more similar to real patients, while allowing for a high diversity among the VPs represented. The final dataset used to train the model was then sampled from this ‘sampling’ population. In our case, we found n to be 176, leading to a sampling population of VPs of 288816 = 176 x 1641. Figure S1 shows the distribution of copy numbers of each VP in the sampling population, with most VPs being represented 20–30 times on average, very few VPs represented only once (as explained above), and maximal representation being about 250 copies.

3.3 Feature extraction

In order to characterize differences between treatment groups, it was necessary to extract features from the dynamical time series in the QSP model. While each VP is also described by a set of baseline attributes (the model parameter values), these do not vary between treatment groups and so could not account for treatment effects. For each of the 9 signals described in Table 2, 20 features were extracted. These included simple summary statistics, (mean, median, standard deviation, 25th and 75th percentiles), as well as the minimum, maximum, start, end, and absolute differences, characterized both over the whole signal and restricted to the treatment period. In addition, the first-order rate of change between the minimum and maximum of the signal was characterized over the whole signal and treatment period, as well as the periods corresponding to the three most significant frequencies from a Fourier transform of the data over the whole signal. For treatment-period features, a window of 27 weeks was used in feature extraction. All of these dynamical features from the QSP model were used as covariates in the survival model described below.

3.4 Statistical model

From the sampling distribution of VPs with matched OS and censoring, a dataset of 10,000 representative VPs in the atezolizumab treatment group were sampled, and were then split into 90% training and 10% testing sets, with all features being standardized relative to the training set. Data were explored using Cox proportional hazard models, before training a fully parametric log-normal accelerated failure time model, using the Python packages lifelines and scikit-learn ^33,34. For the parametric model, the log-normal distribution used to represent survival was selected among other candidate probability density functions by comparison of the Akaike information criterion (AIC) ³⁵.

In each case, the training set was used to tune the regularization hyperparameter corresponding to the L2 penalty via 5-fold cross-validation, selecting the value that maximized validation c-index ³⁶. Following hyperparameter tuning, models were trained on all of the training data and used to predict on the atezolizumab test data, with imputed OS labels for comparison. The same model was then used to predict on treatment groups in the virtual cohort, providing estimates of survival curves for chemotherapy and atezolizumab + chemotherapy, as well as the associated hazard ratio.

For the log-normal model, we applied a similar methodology as in Claret, et al. ¹⁰, where prediction intervals for hazard ratios were obtained by sampling model parameters 1000 times from the mean and standard error of parameter estimates. For each replicate, the parametric model predicts patient-level survival curves as a function of time, from which median survival time for each VP could be defined. Additionally, a mean survival probability curve for the entire cohort was captured, and was used to plot survival curves in Fig. 2. The OS predictions were used to fit univariable Cox proportional hazards models to provide estimates of hazard ratio, which were then summarized by the median and 95% prediction intervals across the 1000 replicates. Within each replicate, patients with undefined median survival were dropped, and censoring labels were sampled from a Bernoulli-distributed random variable (p = 0.43) to approximate the censoring frequency observed in the clinical trial data.

4.1 Cox model

For each of the features derived from the dynamical time series (see section 3.3 above), a univariable Cox model was fit, providing estimates of hazard ratio as well as statistical significance from a χ 2 test for each parameter estimate. Table 3 shows the 20 most significant features from this analysis, together with their corresponding p-values and hazard ratios. Notably, all of these pertain to the same three time-series from the QSP model, T, the tumor size, Cyde, total cytotoxic death, and Ag, tumor antigens in the tumor space. The most predictive feature was the rate of change between minimum and maximum of the tumor curve within the treatment period, with a hazard ratio of 1.49 predicting greater hazard for tumors with higher growth rates. Figure 3 shows the number of significant features at the 5% level from a univariable model for each of the 9 dynamical signals, and also indicates that features directly related to the tumor (Tumor volume, Tumor cell killing and Tumor antigens) are generally more predictive than those describing immune cells populations. Even though tumor compartment features demonstrate stronger associations with survival, Fig. 3 shows that immune cell signals (from Tregs, CTLs and Th1 cells) all display multiple significant associations with survival in a univariate setting, indicating their complementary role to tumor-derived features in the resultant multivariable model. Importantly, we find that features like those derived from immune cell populations are also predictive of survival, despite not being directly tied to the representation of tumor dynamics in the QSP model. As many of these features were highly correlated, all of them were retained with an L2 penalty performing regularization in lieu of manual feature selection.

Table 3

Top 20 significant features from the QSP model as measured by univariable Cox proportional hazards model, along with their corresponding hazard ratios.
Signal	Feature	Treatment Period	p-value	HR	95% CI
Tumor volume	MinMax rate	TRUE	1.10E-205	1.49	[1.45, 1.53]
Tumor volume	Difference	TRUE	5.46E-205	1.49	[1.45, 1.52]
Tumor cell killing	Difference	TRUE	2.36E-133	0.54	[0.52, 0.57]
Tumor antigens	Difference	TRUE	1.62E-116	0.48	[0.45, 0.51]
Tumor volume	MinMax rate	FALSE	2.72E-116	1.34	[1.31, 1.38]
Tumor cell killing	End	TRUE	3.20E-109	0.61	[0.58, 0.63]
Tumor cell killing	Max	TRUE	1.09E-108	0.62	[0.59, 0.65]
Tumor cell killing	Standard deviation	TRUE	1.51E-104	0.59	[0.56, 0.62]
Tumor cell killing	Baseline	FALSE	2.10E-93	1.27	[1.25, 1.3]
Tumor volume	Difference	FALSE	4.15E-92	1.24	[1.21, 1.26]
Tumor antigens	Difference	FALSE	1.78E-89	0.79	[0.77, 0.8]
Tumor cell killing	Difference	FALSE	5.47E-83	0.74	[0.71, 0.76]
Tumor antigens	End	TRUE	5.28E-70	0.64	[0.61, 0.67]
Tumor cell killing	75th percentile	FALSE	1.91E-64	0.69	[0.66, 0.72]
Tumor antigens	Max	TRUE	1.01E-62	0.67	[0.64, 0.7]
Tumor cell killing	Max	FALSE	8.35E-60	0.68	[0.65, 0.71]
Tumor antigens	Standard deviation	FALSE	1.71E-59	0.66	[0.63, 0.69]
Tumor cell killing	MinMax rate	TRUE	9.00E-54	1.16	[1.14, 1.18]
Tumor antigens	75th percentile	FALSE	1.23E-49	0.71	[0.68, 0.74]
Tumor antigens	Baseline	FALSE	1.34E-49	1.2	[1.17, 1.23]

4.2 Parametric model

Figure 2-A shows model predictions for the final log-normal model on the atezolizumab test data, with a Kaplan-Meier of imputed OS on the test data shown for comparison. Empirically, good agreement is observed between the survival probability curve estimated by the model and that from the Kaplan-Meier model, with some divergence at later times due to censoring in the imputed test data, and small sample size.

Figure 2-B displays the model’s predictions on the VPs across both treatment groups. The simulated Kaplan-Meier curves indicate a qualitative treatment effect, implying a benefit for the combination therapy over chemotherapy monotherapy. The median hazard ratio as well as 95% prediction intervals were derived from 1000 iterates of model parameters. Notably, this model, trained only on atezolizumab data, predicts a treatment effect for combination therapy over chemotherapy with a HR of 0.70 (95% PI 0.55–0.86). This can be directly compared, and is consistent with the observed marginal hazard ratio computed from the IMpower130 data of 0.79 (95% PI 0.64–0.98)³². A posterior predictive check directly comparing the distribution of HR predictions to observed HR is shown in Fig. 4.

This work has demonstrated that by matching clinical patients to virtual patients simulated from a QSP model, it is possible to impute weak supervision labels for survival and censoring in virtual patients. Furthermore, we have demonstrated that using QSP covariates alone, these labels can be used to train survival models that can generalize to different treatment groups, producing estimates of treatment effect consistent with those observed in clinical trials. The fact that we can make a prediction of survival based on QSP covariates alone is a remarkable property of our approach, allowing us to train the model only once and apply it to different clinical settings (that can be represented in the QSP model).

The model predictions for the OS HR demonstrate good alignment with the observed HR in IMPower130. However, it is important to note that the observed HR was derived from an intention to treat (ITT) population. In contrast, our analysis consisted of virtual patients who required at least one post-baseline tumor size measurement to be eligible for matching, which could result in shorter survival times being truncated. Fortunately, patients with only one baseline tumor measurement usually represent only a very small subset of the clinical trial population. While acknowledging the limited presence of patients with a single tumor measurement, we may consider addressing their inclusion in future work to enhance the precision of our findings. Additionally, incorporating stratification of hazard ratio predictions based on other model covariates could help mitigate violations of the proportional hazard assumption and the influence of any other potential sources of bias.

We also investigated using this method to impute clinical covariates in the virtual population, in addition to OS labels, in order to use these clinical covariates as features in the survival model. While we found that they did not significantly alter the performance of the model, future work could explore hybridized approaches to predicting outcomes in virtual populations, that would involve imputing clinical features from real patients in a virtual population, in addition to the survival endpoints imputed in this work.

A unique and valuable aspect of our approach in the context of survival analysis is that our survival model not only benefits from the inclusion of tumor-derived covariates but also from non-tumor-derived covariates, particularly those derived from immune cell populations. This demonstrates that features in the QSP model that are not directly related to tumor growth can exhibit a predictive effect on survival. To the extent that QSP models accurately describe the underlying biology, future work may be able to leverage this kind of methodology to infer molecular or immunological events that are ultimately predictive of survival.

Further improvement in model predictions could be made possible by alternative approaches to matching real patients to virtual patients, for example using immunological markers like PDL1 expression in matching, in addition to tumor dynamics. Further investigation of QSP feature extraction methods would be of interest, both as a means of improving the predictive power of this approach, as well as aiding in providing more detailed biological interpretations.

While survival analysis is a methodology more familiar within traditional statistics, deep learning approaches may add additional predictive power in providing in silico trial endpoints, though perhaps at the cost of some interpretability ^21,37. Deep learning approaches would be suited to unstructured data like time-series, learning informative representations of QSP signals that would not require the heuristic feature extraction performed in this study.

This work provides the first example of an approach that could be applied to QSP models and survival data for other indications and pathways, allowing progression beyond this proof-of-concept by validation across other diseases and drug effects. While this work only considered overall survival as an endpoint, similar approaches could be extended to endpoints like progression-free-survival, which may be of clinical interest.

Competing interests

MW declares no financial or non-financial competing interests. VL, KY and JY are employed by Genentech, Inc. and holds stocks in F. Hoffmann-La Roche Ltd.

Author contributions

MW performed the simulations, engineered the survival methods, and wrote the initial draft of the manuscript. MW and VL co-authored all subsequent versions of the manuscript. MW and VL jointly contributed to formulating the methodological framework of the approach. VL devised the original concept and the principles of the method, supervised the work, developed the QSP model and virtual population (not included in the manuscript), and generated the simulated QSP data. KY and JY provided additional statistical methodological guidance, as well as comments on key versions of the manuscript. All authors read and approved the final manuscript.

Acknowledgements

The authors thank Pascal Chanu for carefully reviewing the manuscript and for providing suggestions to improve the overall readability of the manuscript.

Data availability

The datasets generated in this study are not publicly available due to their proprietary nature.

Code availability

The underlying code for this study is not publicly available for proprietary reasons.

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Algorithm1 is available in the Supplementary Files section.

There is a conflict of interest Matthew West declares no financial or non-financial competing interests. Vincent Lemaire, Kenta Yoshida and Jiajie Yu are employed by Genentech, Inc. and holds stocks in F. Hoffmann-La Roche Ltd.

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Predicting survival in prospective clinical trials using weakly-supervised QSP

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Abstract

Figures

1. Introduction

2. Background

3. Methods

3.1 Trials and data

3.1.1 Clinical trial data

3.1.2 Virtual data from the QSP model

3.1.3 IMpower130 data

3.2 Linkage methods

3.3 Feature extraction

3.4 Statistical model

4. Results

4.1 Cox model

4.2 Parametric model

5. Discussion

Declarations

Competing interests

Author contributions

Acknowledgements

Data availability

Code availability

References

Algorithms

Additional Declarations

Supplementary Files

Status:

Version 1