Explaining in-vitro to in-vivo efficacy correlations in oncology pre-clinical development via a semi-mechanistic mathematical model.

In-vitro to in-vivo correlations (IVIVC), relating in-vitro parameters like IC50 to in-vivo drug exposure in plasma and tumour growth, are widely used in oncology for experimental design and dose decisions. However, they lack a deeper understanding of the underlying mechanisms. Our paper therefore focuses on linking empirical IVIVC relations for small-molecule kinase inhibitors with a semi-mechanistic tumour-growth model. We develop an approach incorporating parameters like the compound's peak-trough ratio (PTR), Hill coefficient of in-vitro dose-response curves, and xenograft-specific properties. This leads to formulas for determining efficacious doses for tumor stasis under linear pharmacokinetics equivalent to traditional empirical IVIVC relations, but enabling more systematic analysis. Our findings reveal that in-vivo xenograft-specific parameters, specifically the growth rate (g) and decay rate (d), along with the average exposure, are generally more significant determinants of tumor stasis and effective dose than the compound's peak-trough ratio. However, as the Hill coefficient increases, the dependency of tumor stasis on the PTR becomes more pronounced, indicating that the compound is more influenced by its maximum or trough values rather than the average exposure. Furthermore, we discuss the translation of our method to predict population dose ranges in clinical studies and propose a resistance mechanism that solely relies on specific in-vivo xenograft parameters instead of IC50 exposure coverage. In summary, our study aims to provide a more mechanistic understanding of IVIVC relations, emphasizing the importance of xenograft-specific parameters and PTR on tumor stasis.

Radius additivity score: a novel combination index for tumour growth inhibition in fixed-dose xenograft studies.

The effect of combination therapies in many cancers has often been shown to be superior to that of monotherapies. This success is commonly attributed to drug synergies. Combinations of two (or more) drugs in xenograft tumor growth inhibition (TGI) studies are typically designed at fixed doses for each compound. The available methods for assessing synergy in such study designs are based on combination indices (CI) and model-based analyses. The former methods are suitable for screening exercises but are difficult to verify in in vivo studies, while the latter incorporate drug synergy in semi-mechanistic frameworks describing disease progression and drug action but are unsuitable for screening. In the current study, we proposed the empirical radius additivity (Rad-add) score, a novel CI for synergy detection in fixed-dose xenograft TGI combination studies. The Rad-add score approximates model-based analysis performed using the semi-mechanistic constant-radius growth TGI model. The Rad-add score was compared with response additivity, defined as the addition of the two response values, and the bliss independence model in combination studies derived from the Novartis PDX dataset. The results showed that the bliss independence and response additivity models predicted synergistic interactions with high and low probabilities, respectively. The Rad-add score predicted synergistic probabilities that appeared to be between those predicted with response additivity and the Bliss model. We believe that the Rad-add score is particularly suitable for assessing synergy in the context of xenograft combination TGI studies, as it combines the advantages of CI approaches suitable for screening exercises with those of semi-mechanistic TGI models based on a mechanistic understanding of tumor growth.

Skipping a pillar does not make for strong foundations: Pharmacokinetic-pharmacodynamic reasoning behind the shape of dose-response relationships in oncology.

Dose-response analysis is often applied to the quantification of drug-effect especially for slowly responding disease end points where a comparison is made across dose levels after a particular period of treatment. It has long been recognized that exposure - response is more appropriate than dose-response. However, trials necessarily are designed as dose-response experiments. Second, a wide range of functional forms are used to express relationships between dose and response. These considerations are also important for clinical development because pharmacokinetic (PK; and variability) plus pharmacokinetic-pharmacodynamic modeling may allow one to anticipate the shape of the dose-response curve and so the trial design. Here, we describe how the location and steepness of the dose response is determined by the PKs of the compound being tested and its exposure-response relationship in terms of potency (location), efficacy (maximum effect) and Hill coefficient (steepness). Thus, the location (50% effective dose [ED50 ]) is dependent not only on the potency (half-maximal effective concentration) but also the compound's PKs. Similarly, the steepness of the dose response is shown to be a function of the half-life of the drug. It is also shown that the shape of relationship varies dependent on the assumed time course of the disease. This is important in the context of drug-discovery where the in vivo potencies of compounds are compared as well as when considering an analysis of summary data (for example, model-based meta-analysis) for clinical decision making.

Association between radiotherapy protocol variations and outcome in the CONVERT trial.

Background: Radiotherapy quality assurance (QA) is integral to radiotherapy delivery. Here we report comprehensive contouring, dosimetry, and treatment delivery QA, describe protocol compliance, and detail the impact of protocol variations on acute grade ≥3 toxicity, progression free survival (PFS), and overall survival (OS) in the phase III CONVERT trial. Materials/Methods: Radiotherapy planning data from one hundred randomly selected patients were requested. Members of the CONVERT Trial Management Group (TMG) recontoured the heart, lung, and spinal cord organs at risk (OAR) according to the trial guideline. The existing radiotherapy plan were re-applied to the new structures and the new dosimetric data were recollected. Compliance with radiotherapy QA components were recorded and radiotherapy QA components were pooled into protocol variations: acceptable, acceptable variation, and unacceptable variation. Univariable analysis with a Cox proportional hazards model established the relationship between protocol variations and patient outcome. Results: Ninety-three cases were submitted for retrospective radiotherapy QA review. Demographics of the radiotherapy QA cohort (n=93) matched the non-QA (n=450) cohort. 97.8% of gross tumour volume (GTV) contours were protocol compliant. OAR contours were non-compliant in 79.6% instances of the heart, 37.6% lung, and 75.3% spinal cord. Of the non-compliant heart contours, 86.5% and 2.7% had contours caudal and cranial to the protocol-defined heart borders. 10.8% did not include the pericardial sac and 2.7% did not include the anterior aspect of the pericardium. Eleven (11.8%) submissions exceeded protocol-defined dosimetric heart constraints; six of which were only noted on the application of protocol-compliant contours. Unacceptable variations were not associated with an increase in grade 3 toxicity (p=0.808), PFS (p=0.232), or OS (p=0.743). Conclusion: Non-protocol compliant heart contours were associated with increased dose delivered to the heart OAR, with 11.8 % of submitted heart structures exceeding protocol-defined constraints. In this QA cohort of patients with small cell lung cancer, unacceptable variations were not associated with acute grade ≥3 toxicity, PFS, or OS. Radiotherapy QA remains the cornerstone of high-quality radiotherapy delivery and should be embedded into clinical trial and non-clinical trial practice; clinical trials should report standardised radiotherapy QA parameters alongside trial outcomes.

Determining bioequivalence possibilities of long acting injectables through population PK modelling.

Long acting injectables (LAI) products are a popular intervention for treating a number of chronic conditions, with their long drug release reducing the administration frequency and thus improving patient adherence. The extended release, however, can provide a major challenge to bioequivalence (BE) testing since the long absorption half-life results in a long washout period, meaning that a traditional BE study can be many months or years in length. The unique PK profile for LAI products also means that it is critical to have appropriate metrics to summarise the plasma concentration profile. In this work, we use paliperidone as a case study to demonstrate how Population PK modelling can be utilised to explore sensitivity of summary metrics to different products. We also determine a range of products that are bioequivalent after both multiple dosing and single dosing. Finally, we show how the modelling can be used in a (virtual) PK study as an alternative approach to determining bioequivalence. This work demonstrates the potential for Population PK modelling in bioequivalence assessment, opening doors to more streamlined product development.

Pretreatment Lymphocyte Count Predicts Benefit From Concurrent Chemotherapy With Radiotherapy in Oropharyngeal Cancer.

PURPOSE: There is a need to refine the selection of patients with oropharyngeal squamous cell carcinoma (OPSCC) for treatment de-escalation. We investigated whether pretreatment absolute lymphocyte count (ALC) predicted overall survival (OS) benefit from the addition of concurrent chemotherapy to radical radiotherapy. PATIENTS AND METHODS: This was an observational study of consecutive OPSCCs treated by curative-intent radiotherapy, with or without concurrent chemotherapy (n = 791) with external, independent validation from a separate institution (n = 609). The primary end point was OS at 5 years. Locoregional control (LRC) was assessed using competing risk regression as a secondary end point. Previously determined prognostic factors were used in a multivariable Cox proportional hazards model to assess the prognostic importance of ALC and the interaction between ALC and cisplatin chemotherapy use. RESULTS: Pretreatment ALC was prognostic for 5-year OS on multivariable analysis (hazard ratio [HR] 0.64; 95% CI, 0.42 to 0.98; P = .04). It also predicted benefit from the use of concurrent cisplatin chemotherapy, with a significant interaction between cisplatin chemotherapy and pretreatment ALC (likelihood ratio test, P = .04): higher ALC count reduced the 5-year OS benefit compared with radiotherapy alone (HR 2.53; 95% CI, 1.03 to 6.19; P = .043). This was likely driven by an effect on LRC up to 5 years (interaction subdistribution HR 2.29; 95% CI, 0.68 to 7.71; P = .094). An independent validation cohort replicated the OS (HR 2.53; 95% CI, 0.98 to 6.52; P = .055) and LRC findings (interaction subdistribution HR 3.43; 95% CI, 1.23 to 9.52; P = .018). CONCLUSION: For OPSCC, the pretreatment ALC is prognostic for OS and also predicts benefit from the addition of cisplatin chemotherapy to radiotherapy. These findings require prospective evaluation, and could inform the selection of good prognosis patients for a de-escalation trial.

Exploring a model-based analysis of patient derived xenograft studies in oncology drug development.

PURPOSE: To assess whether a model-based analysis increased statistical power over an analysis of final day volumes and provide insights into more efficient patient derived xenograft (PDX) study designs. METHODS: Tumour xenograft time-series data was extracted from a public PDX drug treatment database. For all 2-arm studies the percent tumour growth inhibition (TGI) at day 14, 21 and 28 was calculated. Treatment effect was analysed using an un-paired, two-tailed t-test (empirical) and a model-based analysis, likelihood ratio-test (LRT). In addition, a simulation study was performed to assess the difference in power between the two data-analysis approaches for PDX or standard cell-line derived xenografts (CDX). RESULTS: The model-based analysis had greater statistical power than the empirical approach within the PDX data-set. The model-based approach was able to detect TGI values as low as 25% whereas the empirical approach required at least 50% TGI. The simulation study confirmed the findings and highlighted that CDX studies require fewer animals than PDX studies which show the equivalent level of TGI. CONCLUSIONS: The study conducted adds to the growing literature which has shown that a model-based analysis of xenograft data improves statistical power over the common empirical approach. The analysis conducted showed that a model-based approach, based on the first mathematical model of tumour growth, was able to detect smaller size of effect compared to the empirical approach which is common of such studies. A model-based analysis should allow studies to reduce animal use and experiment length providing effective insights into compound anti-tumour activity.

The spindle assembly checkpoint and speciation.

A mechanism is proposed by which speciation may occur without the need to postulate geographical isolation of the diverging populations. Closely related species that occupy overlapping or adjacent ecological niches often have an almost identical genome but differ by chromosomal rearrangements that result in reproductive isolation. The mitotic spindle assembly checkpoint normally functions to prevent gametes with non-identical karyotypes from forming viable zygotes. Unless gametes from two individuals happen to undergo the same chromosomal rearrangement at the same place and time, a most improbable situation, there has been no satisfactory explanation of how such rearrangements can propagate. Consideration of the dynamics of the spindle assembly checkpoint suggest that chromosomal fission or fusion events may occur that allow formation of viable heterozygotes between the rearranged and parental karyotypes, albeit with decreased fertility. Evolutionary dynamics calculations suggest that if the resulting heterozygous organisms have a selective advantage in an adjoining or overlapping ecological niche from that of the parental strain, despite the reproductive disadvantage of the population carrying the altered karyotype, it may accumulate sufficiently that homozygotes begin to emerge. At this point the reproductive disadvantage of the rearranged karyotype disappears, and a single population has been replaced by two populations that are partially reproductively isolated. This definition of species as populations that differ from other, closely related, species by karyotypic changes is consistent with the classical definition of a species as a population that is capable of interbreeding to produce fertile progeny. Even modest degrees of reproductive impairment of heterozygotes between two related populations may lead to speciation by this mechanism, and geographical isolation is not necessary for the process.

Diffusion model comparison identifies distinct tumor sub-regions and tracks treatment response.

PURPOSE: MRI biomarkers of tumor response to treatment are typically obtained from parameters derived from a model applied to pre-treatment and post-treatment data. However, as tumors are spatially and temporally heterogeneous, different models may be necessary in different tumor regions, and model suitability may change over time. This work evaluates how the suitability of two diffusion-weighted (DW) MRI models varies spatially within tumors at the voxel level and in response to radiotherapy, potentially allowing inference of qualitatively different tumor microenvironments. METHODS: DW-MRI data were acquired in CT26 subcutaneous allografts before and after radiotherapy. Restricted and time-independent diffusion models were compared, with regions well-described by the former hypothesized to reflect cellular tissue, and those well-described by the latter expected to reflect necrosis or oedema. Technical and biological validation of the percentage of tissue described by the restricted diffusion microstructural model (termed %MM) was performed through simulations and histological comparison. RESULTS: Spatial and radiotherapy-related variation in model suitability was observed. %MM decreased from a mean of 64% at baseline to 44% 6 days post-radiotherapy in the treated group. %MM correlated negatively with the percentage of necrosis from histology, but overestimated it due to noise. Within MM regions, microstructural parameters were sensitive to radiotherapy-induced changes. CONCLUSIONS: There is spatial and radiotherapy-related variation in different models' suitability for describing diffusion in tumor tissue, suggesting the presence of different and changing tumor sub-regions. The biological and technical validation of the proposed %MM cancer imaging biomarker suggests it correlates with, but overestimates, the percentage of necrosis.

A simple model of a growing tumour.

This paper presents the CellCycler, a model of a growing tumour which aims to simulate and predict the effect of treatment on xenograft studies or in the clinic. The model, which is freely available as a web application, uses ordinary differential equations (ODEs) to simulate cells as they pass through the phases of the cell cycle. However the guiding philosophy of the model is that it should only use parameters that can be observed or reasonably well approximated. There is no representation of the complex internal dynamics of each cell; instead the level of analysis is limited to cell state observables such as cell phase, apoptosis, and damage. We show that this approach, while limited in many respects, still naturally accounts for a heteregenous cell population with varying doubling time, and closely captures the dynamics of a growing tumour as it is exposed to treatment. The program is demonstrated using three case studies.

Resistance models to EGFR inhibition and chemotherapy in non-small cell lung cancer via analysis of tumour size dynamics.

PURPOSE: Imaging time-series data routinely collected in clinical trials are predominantly explored for covariates as covariates for survival analysis to support decision-making in oncology drug development. The key objective of this study was to assess if insights regarding two relapse resistance modes, de-novo (treatment selects out a pre-existing resistant clone) or acquired (resistant clone develops during treatment), could be inferred from such data. METHODS: Individual lesion size time-series data were collected from ten Phase III study arms where patients were treated with either first-generation EGFR inhibitors (erlotinib or gefitinib) or chemotherapy (paclitaxel/carboplatin combination or docetaxel). The data for each arm of each study were analysed via a competing models framework to determine which of the two mathematical models of resistance, de-novo or acquired, best-described the data. RESULTS: Within the first-line setting (treatment naive patients), we found that the de-novo model best-described the gefitinib data, whereas, for paclitaxel/carboplatin, the acquired model was preferred. In patients pre-treated with paclitaxel/carboplatin, the acquired model was again preferred for docetaxel (chemotherapy), but for patients receiving gefitinib or erlotinib, both the acquired and de-novo models described the tumour size dynamics equally well. Furthermore, in all studies where a single model was preferred, we found a degree of correlation in the dynamics of lesions within a patient, suggesting that there is a degree of homogeneity in pharmacological response. CONCLUSIONS: This analysis highlights that tumour size dynamics differ between different treatments and across lines of treatment. The analysis further suggests that these differences could be a manifestation of differing resistance mechanisms.

Complex versus simple models: ion-channel cardiac toxicity prediction.

There is growing interest in applying detailed mathematical models of the heart for ion-channel related cardiac toxicity prediction. However, a debate as to whether such complex models are required exists. Here an assessment in the predictive performance between two established large-scale biophysical cardiac models and a simple linear model Bnet was conducted. Three ion-channel data-sets were extracted from literature. Each compound was designated a cardiac risk category using two different classification schemes based on information within CredibleMeds. The predictive performance of each model within each data-set for each classification scheme was assessed via a leave-one-out cross validation. Overall the Bnet model performed equally as well as the leading cardiac models in two of the data-sets and outperformed both cardiac models on the latest. These results highlight the importance of benchmarking complex versus simple models but also encourage the development of simple models.

Model based analysis of the heterogeneity in the tumour size dynamics differentiates vemurafenib, dabrafenib and trametinib in metastatic melanoma.

PURPOSE: Explore the heterogeneity in dynamics of tumour response to vemurafenib, dabrafenib and trametinib using routinely collected clinical trial imaging data. METHODS: Time-series imaging data from the phase III studies of vemurafenib, dabrafenib and trametinib were collected through a data repository. A mathematical model based on basic mechanisms of tumour growth was placed within a statistical modelling framework to analyse the data. RESULTS: The analysis revealed: (1) existence of homogeneity in drug response and resistance development within a patient; (2) tumour shrinkage rate does not relate to rate of resistance development; (3) vemurafenib and dabrafenib, two BRAF inhibitors, have different variability in tumour shrinkage rates. CONCLUSIONS: Overall these results show how analysis of the dynamics of individual lesions can shed light on the within and between patient differences in tumour shrinkage and resistance rates, which could be used to gain a macroscopic understanding of tumour heterogeneity.

On the relationship between tumour growth rate and survival in non-small cell lung cancer.

A recurrent question within oncology drug development is predicting phase III outcome for a new treatment using early clinical data. One approach to tackle this problem has been to derive metrics from mathematical models that describe tumour size dynamics termed re-growth rate and time to tumour re-growth. They have shown to be strong predictors of overall survival in numerous studies but there is debate about how these metrics are derived and if they are more predictive than empirical end-points. This work explores the issues raised in using model-derived metric as predictors for survival analyses. Re-growth rate and time to tumour re-growth were calculated for three large clinical studies by forward and reverse alignment. The latter involves re-aligning patients to their time of progression. Hence, it accounts for the time taken to estimate re-growth rate and time to tumour re-growth but also assesses if these predictors correlate to survival from the time of progression. I found that neither re-growth rate nor time to tumour re-growth correlated to survival using reverse alignment. This suggests that the dynamics of tumours up until disease progression has no relationship to survival post progression. For prediction of a phase III trial I found the metrics performed no better than empirical end-points. These results highlight that care must be taken when relating dynamics of tumour imaging to survival and that bench-marking new approaches to existing ones is essential.