Bridging responses to a human telomerase reverse transcriptase-based peptide cancer vaccine candidate in a mechanism-based model

Therapeutic cancer vaccines are novel immuno-therapeutics, aiming to improve clinical outcomes with other immunotherapies. However, obstacles to their successful clinical development remain, which model-informed drug development approaches may address. UV1 is a telomerase based therapeutic cancer vaccine candidate being investigated in phase I clinical trials for multiple indications. We developed a mechanism-based model structure, using a nonlinear mixed-effects modeling techniques, based on longitudinal tumor sizes (sum of the longest diameters, SLD), UV1-specific immunological assessment (stimulation index, SI) and overall survival (OS) data obtained from a UV1 phase I trial including non-small cell lung cancer (NSCLC) patients and a phase I/IIa trial including malignant melanoma (MM) patients. The final structure comprised a mechanistic tumor growth dynamics (TGD) model, a model describing the probability of observing a UV1-specific immune response (SI ≥ 3) and a time-to-event model for OS. The mechanistic TGD model accounted for the interplay between the vaccine peptides, immune system and tumor. The model-predicted UV1-specific effector CD4 + T cells induced tumor shrinkage with half-lives of 103 and 154 days in NSCLC and MM patients, respectively. The probability of observing a UV1-specific immune response was mainly driven by the model-predicted UV1-specific effector and memory CD4 + T cells. A high baseline SLD and a high relative increase from nadir were identified as main predictors for a reduced OS in NSCLC and MM patients, respectively. Our model predictions highlighted that additional maintenance doses, i.e. UV1 administration for longer periods, may result in more sustained tumor size shrinkage.


Introduction
Vaccination against cancer antigens is emerging as a novel therapeutic approach, aiming to boost anti-tumor immune responses and improve clinical outcomes with immunotherapy [1].Considering that this type of vaccine is developed to be used in the therapeutic settings where the vaccine-induced response must target an endogenously derived protein, their development process is challenging due to intratumoral heterogeneity, underlying mutations, its immunological status as well as the overall tumor burden [2].Model-based approaches have previously addressed similar challenges for the development of anticancer agents [3].
Human telomerase reverse transcriptase (hTERT) is almost non-existent in human somatic cells but manifests at high levels in the majority of cancer cells [4].Telomerase and its regulatory mechanisms have become attractive therapeutic targets, as well as a possible prognostic or diagnostic biomarkers as a result of its critical role in cellular self-renewal in cancer diseases [4].The activation of hTERT enables cancer cells to evade senescence and acquire the ability of endless replicative potential [5].Previous studies showed that patients with spontaneously primed circulating anti-hTERT T cells present with a better prognosis in non-small cell lung cancer (NSCLC) [6] and associate with clinical response to immunotherapy in melanoma [7].UV1 is a therapeutic cancer vaccine candidate consisting of three synthetic long peptides designed to induce T cell responses directed towards hTERT [8].These peptides were selected based on a screening assay of immune responses towards hTERT in cancer patients previously vaccinated with a 16-mer peptide (GV1001).After vaccination with GV1001, the immune response had broadened towards other regions within hTERT, a phenomenon termed epitope spreading.The peptides selected for the UV1 vaccine harbored highly immunogenic epitopes with broad HLA compatibility and were associated with long-term survival [9].Immunization with UV1 peptides primarily aims to induce CD4+ T cells displaying a Th1 cytokine profile against hTERT antigens presented by cancer cells, leading to the activation of an immune system cascade through stimulating other components of anti-tumor immune response [8], and also induce further epitope spreading to other tumor associated/specific antigens.For instance, the activated CD4+ T cells prompts antigen presentation and the expression of cytokines, CD80, and CD86 co-stimulatory molecules by the dendritic cells (DCs), through binding their CD40L to the CD40 receptors on DCs.These co-stimulatory molecules serve as signal 2 for CD8+ T cells, which, in tandem with the cytokines, facilitate the differentiation, effector functions, and survival of CD8+ T cells [10].UV1 vaccine was administrated in combination with Ipilimumab in phase I/IIa study in malignant melanoma (MM) patients.Ipilimumab is an anti-CTLA-4 monoclonal antibody which causes a rapid expansion of T cells primed by antigen presenting cells [11].As a result, priming immune responses against the tumor with tumor-related antigens prior to or during treatment may improve outcomes with checkpoint inhibitors.This can be achieved through combining ipilimumab with a cancer vaccine [11].
Pharmacometrics is the science in which mathematical and statistical models are employed to describe systems biology, pathophysiological and pharmacology knowledge to develop an informative system [12,13].It can be used as a tool for dose optimization during the clinical development stages of new anticancer modalities (e.g., targeted therapies and biologics), which is the goal of the FDA's Project Optimus, that was launched in 2021 [14].During the model building process, immune events can be characterized to directly or indirectly interact with tumor tissues or other immune biology targets within the cancer immune cycle resulting in antitumor effects [15].Therefore, there is a crucial need to develop mechanism-based models to effectively inform vaccine development and its key decisions [16].
In this work, we present a population mechanism-based model characterizing the time-course of tumor size and UV1-specifc immune response considering the dynamic interaction between the UV1 vaccine peptides, the immune system, and the tumor, at the molecular, cellular, and tissue level.Also, a survival analysis using a parametric time-to event model was performed.In addition, a covariate analysis was conducted to identify predictors for the different outcomes.Eventually, the final framework was used to explore different scenarios such as altering the molar ratios between the vaccine peptides and the dosing schedules.

Study population
Data were obtained from a UV1 phase I clinical trial in patients with stage III or IV NSCLC and a phase I/IIa trial in patients with stage IV cutaneous MM [10,17].UV1 (Ultimovacs ASA, Oslo, Norway) consists of three synthetic hTERT peptides in equimolar ratio; one 30-mer and two 15-mers.It was administrated intradermally to the patients together with 75 µg granulocyte-macrophage colony-stimulating factor (GM-CSF) as an adjuvant.Three different UV1 doses were investigated in NSCLC patients; 100, 300, and 700 µg while only 300 µg was administered in MM patients together with ipilimumab (3 mg/kg) which was administered every 3 weeks for a total of 4 doses.In NSCLC patients, the treatment was given three times during the first week (days 1, 3, and 5) and then week 2, 3, 4, 6, 8, 10, 14, 18, 22, and 26.After week 26, a number of additional doses were given every 3 months.While in MM patients, the treatment was given in a similar manner during the first week and then week 3, 4, 7, 10, 13, 17, and 21.
Tumor response was evaluated in terms of sum of the longest diameters (SLD) using RECIST 1.1 [18] before the first UV1 vaccination and then every 3 months until disease progression.Blood samples were collected for hematological assessments at each treatment visit and 30 days after administration of the last dose of UV1.Immunological assessment of the UV1-specific proliferative response was performed and the stimulation index (SI) was calculated before starting the vaccination, 2 weeks after the first UV1 vaccination, and then, every 4 weeks.Further details are included in Supplementary Material section 1.An SI ≥ 3 was considered as a positive response.Moreover, HLA genotyping was performed for each patient retrospectively [10].Only patients with evaluable tumor size measurements according to RECIST 1.1 [18] and available HLA genotyping were included in the analysis (n = 15 NSCLC patients and n = 10 MM patients).

Mechanistic tumor growth dynamics model
The model was fitted to the longitudinal SLD measurements using a nonlinear mixed-effects modeling strategy.The model involved three levels of biological interactions; (i) molecular level, (ii) cellular level, and (iii) tissue level.

Molecular level
This part characterizes UV1 vaccine peptides uptake and presentation by DCs and is adopted from a previously published model by Chen et al [19].UV1 is administrated intradermally together with an adjuvant, GM-CSF.The vaccine consists of three peptides; two 15-mers and one 30-mer, namely p725, p728 and p719-20 respectively, in equimolar amounts.These vaccine peptides (VP i , with index i = 1, 2, 3 representing the three peptides p725, p728 and p719-20 respectively) were cleared from the dermis with a first order elimination rate constant k VP (Eq.( 1)).
Thereafter, the vaccine peptides were taken up via endocytosis by the dendritic cell (DC) directly into the endosome at rate α E p * VDC VDR , where VDC VDR is a scaling factor which represents the ratio of the volume of DC to that of the injection site (Eqs.(3)-( 4)) (Fig. 1).p719-20 (VP E 3 ) was assumed to be degraded into shorter peptides (VP E p3 ) inside the DC with a first order degradation rate constant k deg (Eqs.(4)-( 5)) as the model assumed that the maximum peptide length that can bind to the free MHC-II receptors is 15-mer [20].In addition, the free MHC-II receptors (MHCII E k ) were represented by a turnover model assuming homeostasis with a turn-over rate constant β M (Eq.( 6)).Inside the endosomes, the vaccine peptides would either interact with MHCII E k to form peptide MHC-II complexes (pMHCII E k,i , with index i = 1, 2, 3 representing the three peptides) or be routed into lysosomes for further degradation with a rate constant k ly (Eqs.(3) and ( 5)).
The strength of the interaction between the vaccine peptides and the free MHC-II receptors is governed by the dissociation constant K Di,k (here, i = 1, 2 represents the two 15-mer peptides and k = 1, 2 represents HLA Class II-DRB1 allele typing for each patient).This dissociation constant is defined as the ratio of the first order dissociation rate constant, k off to the second order association rate constant,k on .K Di,k values were derived using NetMHCIIpan -4.1 online tool [21].Given that the 30-mer peptide was allowed to degrade into shorter peptides, the effective dissociation constant K eff D,k was used instead.The values of K eff D,k were derived based on the method introduced by Yogurtcu et al [22].First, the binding affinities K Dj,k were obtained for all N (15-mer) peptides derived from the 30-mer peptide, j = 1,2,…, N, based on each patient HLA Class II-DRB1 allele typing, k = 1,2, from NetMHCIIpan -4.1 online tool [21].Thereafter, all 15-mer peptides were pooled into a single representative molecule for p719-20 which can bind to MHC-II allele type k with K eff D,k that was calculated as follows; Inside the endosomes, the formed pMHCII E k,i would either undergo exocytosis with rate constant k ex onto the DC surface to be presented (pMHCII sc k,i , with index i = 1, 2, 3 representing the three peptides) or degrade with rate constant β pM (Eqs.( 7)-( 9)).In addition, the free MHC-II receptors (MHCII SC k ) from the dissociated pMHCII sc k,i on the cell surface were allowed to recycle back into the endosomes by rate constant k rec (Eq.( 10)).
The total number of pMHCII molecules presented on the DC surface to activate the UV1 vaccine-specific CD4+ T cells was calculated using Avogadro's number (N AVG ) as follows; Further details on the description of parameters are included in Table 1S.

Cellular level
At this level, immune cell kinetics is characterized.The maturation of DCs at the site of injection via GM-CSF is implemented as previously described by Lai et al [23].As mentioned above, GM-CSF (ADJ) is administrated with UV1 where k ADJ is the first order degradation rate constant of ADJ (Eq.( 11)).
The immature DCs (IMDC) were represented by a turnover model assuming homeostasis with a turn-over rate constant k IMDC .Their maturation was facilitated via GM-CSF, described using non-linear Michaelis-Menten kinetics that was driven by the GM-CSF concentration in dermis [23] (Eqs.( 12)-( 13)).Thereafter, the mature DCs (MDC) would migrate through the lymphatic vessels (Fig. 1).This migration was implemented as a number of transit compartments (indexed with MDC tr,n where n = 1, 2, …, NN) where the DCs were allowed to die naturally with a first order rate constant k MDC (Eqs.( 13)-( 14)).The number of transit compartments was explored to best mimic the delay that occurs before the mature DCs reach the lymph node (MDC LN ) [24] (Eq.( 15)).Only a fraction (f rem ) of the mature DCs carrying the peptide-MHCII complexes reached the lymph node [25].
Once the mature DCs arrive the lymph node, they induce the production of UV1 peptide specific immune response.Two subtypes of UV1 peptide specific CD4+ T cells were considered; transitional effector memory CD4 cells (CD4 TEM ) with a short half-life and central memory CD4 cells (CD4 CM ) with a longer half-life.Both subtypes were assumed to develop in parallel to attain a simplified description of the UV1 induced antitumor immune response [26].Further details on parameter description are included in Table 1S.

Tissue level
A tumor growth dynamics (TGD) model described the patients' SLD measurements over time.Both zero-order and first-order tumor growth rates were evaluated.CD4 TEM and CD4 CM were investigated for their shrinkage effect on the SLD with different relationships being evaluated (ie.linear, E max and Sigmoidal E max ).To describe the potential tumor regrowth, an exponential decay in the CD4 effect was explored.It was also investigated if the debris from the decayed tumor induced an endogenous immune response resulting in tumor effect.
Most of the model parameters were either predetermined such as the initialization of ordinary differential equations (ODEs) (i.e.baselines) and patient-specific HLA typing, or obtained from the literature as summarized in Table 1S.Other parameters were estimated by fitting the model to the longitudinal SLD measurements.

Immune response model
Immunological assessment of the UV1-specific response was performed based on SI measurements where SI was explored as either being continuous or categorical type data.For the former method, the SI was defined as a baseline on which the vaccine effect was evaluated, while for the latter method, the patients were categorized at each visit into either non-immune or immune responders based on SI.A patient with an SI equal to or greater than 3 was classified as an immune-responder, and was otherwise a non-immune responder [10].The transition rate constants ( λ 01 and λ 10 ) from non-immune responder state (S 0 ) to immune responder state (S 1 ) and vice versa were estimated using a two-state continuous time Markov model (Eqs.( 16)-( 17)).Further details are included in Supplementary Material section 2.

Overall survival model
In total, there were 10 death events in the NSCLC trial and 5 death events in the MM trial.The baseline hazard (h 0 (t)) of overall survival (OS) was described using a parametric time to event (TTE) model.Both exponential and Weibull functions were evaluated for describing h 0 (t).

Covariate analysis
All covariates in Table 1 were explored as constant (i.e.baseline values) and as time-varying covariates.The SI was investigated as a time-varying covariate on the TGD model's parameters.For the modelderived predictors, the IPPSE sequential analysis method was implemented resembling the individual PK parameter approach [27,28].Consequently, individual empirical Bayes estimates (EBEs) from the TGD model were used to explore the influence of SLD, CD4 TEM and CD4 CM time-courses on the parameters of the immune response (IR) and TTE models.Given the long computational times of the mechanistic TGD model, a simultaneous estimation approach was not applied.Further details are included in Supplementary Material section 3.

Model development and evaluation
The nonlinear mixed-effects modeling software NONMEM version 7.5.0[30], executed through Perl-speaks-NONMEM (PsN) version 5.2.6 [31], was used for data analysis and simulations.Further details are included in Supplementary Material section 4. R-studio 4.1 was used for data management purposes, model diagnostics, graphical visualization       and evaluations.The parameters' uncertainties were obtained using Sampling Importance Resampling (SIR) [32].Individual fit plots for the TGD model and visual predictive checks (VPCs) for the final models were generated for evaluating the models' predictive performance.

Model predictions
Different scenarios were explored using the final models on the SLD and SI time profiles.This was done to elucidate the influence of changing the molar ratios between the vaccine peptides (eg.2:1:1 and 1:2:2 for 30-mer:15-mer:15-mer peptide) as well as the impact of altering the dosing schedule (eg.dosing three times per week during the first two weeks of UV1 vaccination instead of only the first week and having maintenance doses every three months for a longer period of time than originally used).These scenarios were investigated across the different dose levels (i.e.100, 300 and 700 µg) and K D values (ie.minimum, median and maximum predicted values for each peptide, Table 2S).

Mechanistic tumor growth dynamics model
The final model consisted of 38 ODEs that depict the essential biological interactions required for the initiation of specific UV1 peptide CD4+ T cell immune response that would lead to tumor size regression (Fig. 1).

Molecular level
The model described under section 2.2.1 was adopted.

Cellular level
The production rate of UV1 peptide specific CD4+ T cells (CD4 TEM and CD4 CM ) was stimulated by mature DCs in the lymph nodes (MDC LN ) with a maximum effect (K in ) which also increased as the pMHCII number increased (Eqs.( 18) -( 19)).In addition, K in was stimulated by endogenous peptides presented by the dead tumor tissues through P TUM (Eqs.( 18) -( 19)).

Tissue level
The tumor growth rate was best described by a first order growth rate constant (k GROW,NSCLC ) for NSCLC patients while for MM, a zero-order growth rate (K GROW,MM ) best explained the data (Eqs.( 20) -( 21)).The vaccine-induced tumor shrinkage rate (SHR p where p represents either NSCLC or MM patients) was described as a function of CD4 TEM with a maximum value of k SHR,p .KC 50 , which represents the CD4 TEM required to reach 50 % of k SHR,p , was a shared parameter between NSCLC and MM patients.In addition, for NSCLC patients, immune suppression development over time (t) was significant, which was described as an exponential decay of the shrinkage rate (λ sup,NSCLC ; Eq. ( 20)).
frc is the fraction of CD4+ T cells that differentiate to CD4 CM , MDC 50 is the mature DCs number required for half-maximal production of CD4+ T cells, and ρ TEM and ρ CM represent turn-over rate constants for CD4 TEM and CD4 CM , respectively.Individual SLD baselines were estimated using the observed baselines as well as residuals with variability of the same magnitude as other SLD observations [33].The final model parameters, together with their uncertainties are presented in Table 2.
In the multivariable analysis, λ sup,NSCLC increased significantly with increased levels of lactate dehydrogenase (LDH) as a time-varying covariate, and higher SI values and lower platelet counts (time-varying), were significantly related to higher k SHR,MM .Since these relationships were estimated with low precision, they were however excluded from the final model.
The final model predictions for individual SLD-time profiles corresponded well with the observations as shown in individual fits (Fig. 2), reflecting a good model predictive performance.The final model's predictive performance was further demonstrated by VPC and goodnessof-fit plots (Figures S1-S2).

Immune response model
A two-state continuous time Markov model (Fig. 3) quantified the probability of observing the patient either in a non-immune or in an immune responder state.MTT 01 was shared between the NSCLC and MM patients with an estimated value of 44 years.λ 01 increased approximately 15-fold and 12-fold, respectively, for every 100 units increase in CD4 CM for NSCLC patients and in CD4 TEM for MM patients.Moreover, λ 01 was negatively correlated with the lymphocyte count in MM patients.
No covariate was significant on the backwards transition rate from immune to non-immune responder state (λ 10 ).The final model parameters together with their uncertainties are given in Table 3. VPCs show that the model was able to predict the proportions of immune responders over time (Fig. 4) and the number of simulated transitions between the two states was in a close agreement with the observed numbers (Figure S3).

Overall survival model
A parametric TTE model (Fig. 3) with a Weibull function for NSCLC patients and an exponential function for MM patients best described the hazard of death.In NSCLC patients, the hazard of death was higher for those with high baseline SLD such that the estimated hazard ratio (HR) was 1.51 for every 5 units increase and for those with lower administered dose amounts (i.e., time-constant predictor with HR of 0.007 and 12 for doses of 700 and 100 µg, respectively, compared to a dose of 300 µg).In MM patients, the hazard of death increased with the relative change in SLD from nadir (before the nadir, the relative change was set to zero).The estimated HR was 1.08 for every 1 % increase in SLD from nadir.The final model parameters together with their uncertainties are given in Table 3. Kaplan-Meier VPCs for OS (Fig. 4) illustrate the adequate predictive properties of the model.

Model predictions
The predictions from the final TGD model showed that the CD4 TEM and CD4 CM levels increased with the higher doses and lower K D values (Figure S4).Also, the model-predicted CD4 TEM were sufficient to exceed the KC 50 and achieve the maximum rate of tumor shrinkage during the treatment period resulting in no impact from changing the dose level and the K D value on the UV1 vaccine-induced tumor shrinkage (Fig. 5).However, there was a predicted benefit of higher doses and lower K D values after stopping the vaccine treatment (Fig. 5).This benefit became more pronounced with decreasing values of λ sup,NSCLC for NSCLC patients and k SHR,MM for MM patients.However, there were distinct differences in the probability of observing an immune response in the peripheral blood as the probability increased with increasing dose level and decreasing K D values (Figure S5).This increased probability was associated with the elevated levels of CD4 TEM and CD4 CM levels for MM and NSCLC patients, respectively (Figure S4).
Altering the molar ratio of the three UV1 peptides did not have any noticeable impact on the SLD time profiles at dose level 300 µg and median K D value (Figure S6).This indicates that all proposed ratios resulted in CD4 TEM levels adequate for patients to achieve the maximum shrinkage rate (Figure S7).On the other hand, the molar ratio impacted the probability of immune response (Figure S8) since the CD4 TEM and CD4 CM levels were the highest with molar ratio 2:1:1, followed by 1:1:1 and 1:2:2 (Figure S7).This is due to that the model assumed that the 30mer peptide first degrades before binding to the free MHC-II receptors resulting in a delay in its presentation and an increase of its apparent half-life on DC surface.
Two extra doses of the UV1 vaccine during the second week of the treatment did not influence tumor shrinkage since the maximum response was already achieved with the original schedule at 300 µg and median K D value (Fig. 6).Increasing the maintenance dosing period from approximately one year up to four years for NSCLC patients resulted in a more sustained activation of the CD4+ T cells production in comparison to the original dosing schedule (Figure S9) that is capable of achieving maximum tumor response.Therefore, a delay in the tumor regrowth that became clearer with decreased λ sup,NSCLC values (Fig. 6A) and higher probability of detecting an immune response (Figure S10A) were observed for NSCLC patients.Similarly, for MM patients, adding maintenance doses every three months on top of the original dosing schedule resulted in an increased tumor shrinkage (Fig. 6B) and a more  sustained high probability of observing an immune response (Figure S10B).For both simulated dosing schedules, different dose levels and K D values provided the same results (results not shown).

Discussion
In this work, a mechanism-based pharmacometrics modelling framework was successfully developed using longitudinal SLD, SI and survival data.The mechanistic TGD model included crucial molecular events such as the vaccine peptides processing, their binding to MHC-II receptors, and the peptide-MHC-II receptor complex presentation.Such events have an important role in the development of cancer immune response.It also accounted for the interaction between DCs, UV1specific CD4+ T cells, and tumor, resulting in the vaccine-induced tumor shrinkage effect.The framework quantified the relationships between the SLD time-course, immune response and OS, and managed to elucidate the factors that influence the parameters through covariate analysis.
Based on the final TGD model, the half-life related to maximum vaccine-induced tumor shrinkage rate in NSCLC patients (103 days) for a typical individual was significantly shorter than in MM patients (154 days).However, the inter-individual variability in k SHR was only statistically significant for MM patients with individual half-life values ranging from 51 to 309 days.In addition, emerging immune suppression mechanisms, implemented as a reduction of the vaccine-induced tumor shrinkage effect, was significant for NSCLC patients with an estimated half-life of 4.47 years and individual estimates ranging from 0.0991 to 25.6 years.These findings suggest a gained benefit from the combination of ipilimumab with UV1 vaccine administration in MM patients.Thus, priming anti-tumor immune responses by UV1 vaccine peptides before and during ipilimumab treatment can improve outcomes [11].This could be a reason to why some MM patients had higher shrinkage rates than NSCLC patients in addition to the proven clinical efficacy of ipilimumab in MM [34].Furthermore, ipilimumab can reduce the immunosuppression by blocking CTLA-4 on T regulatory cells in the tumor microenvironment [11].
The choice of the linear tumor growth (Figure S11) in MM patients was supported by a previously developed TGD model in ipilimumabtreated patients with advanced melanoma [35].The estimated tumor growth rate (K GROW,MM = 48.35mm•year − 1 ) was in close agreement with the previously reported growth rates for intermediate and fast growing subpopulations (12.3 and 171 mm•year − 1 , respectively) [35].Furthermore, the shrinkage rate constant estimated in this study (1.643 year − 1 ) was higher than the values previously reported for intermediate and fast growth subpopulations (0.156 and 0.189 year − 1 , respectively) [35], indicating a potential added value of UV1.Our estimate was however somewhat lower than the shrinkage rate constant determined for the no-growth subpopulation (24% of the patients; 2.39 year − 1 ) [35].
In our analysis, dead tumor tissue had a significant stimulatory impact on the production of CD4+ T cells.This is in line with epitope spreading, i.e. endogenous hTERT peptides, as well as other tumor antigens, can be released by the destroyed tumor cells and taken up by the antigen presenting cells, inducing a new wave of immunity by stimulating T cells to attack the tumor.This phenomenon has been suggested as the possible explanation of the late SI peaks observed during the longterm follow-up [10,36,37].Another reason could be subsequent checkpoint inhibitors that some patients received after the end of the vaccination period [10].
The developed framework revealed that the increased levels of the TGD model-predicted CD4+ T cells increase the chances of observing a UV1-specific immune response in the peripheral blood.The NSCLC patients had a more sustainable higher observed proportions of immune responder patients in the post treatment phase of the study (i.e.correlated with CD4 CM ) in comparison to MM patients (i.e.correlated with CD4 TEM ).Unexpectedly, we found that the increasing lymphocyte count over time reduced the chance of observing a vaccine-specific immune response in MM patients which requires further investigation.The ≈ 4fold lower transition rate from immune to non-immune responder in MM patients compared to NSCLC patients could be due to combining the UV1 vaccine with ipilimumab [38].
The model-predicted SLD time profiles showed no discernible difference across different dose levels and dissociation constants during the treatment period (Fig. 5).This indicates that all patients achieved the maximum rate of tumor shrinkage from immune system stimulation induced by the vaccine based on the patients' tumor immune microenvironment status regardless of the dose level and their HLA genotype.Furthermore, the model predictions highlighted a potential beneficial effect from extra maintenance doses on the tumor size shrinkage.
The covariate analysis for the TTE model revealed that the baseline SLD and the relative change from nadir for NSCLC and MM patients, respectively, were the best predictors for OS as previously suggested for other treatments [35,[39][40][41].Moreover, the dose level had a significant impact on the hazard of death with HRs of 12 and 0.007 for 100 and 700 µg, respectively, compared to 300 µg.The strong dose dependence was driven by the fact that there were only five patients per dose group, where only one died in the 700 µg group while all died in the 100 µg group.Our analysis showed that the Markov model-predicted probability of being an immune responder did not have a significant impact on the hazard of death in the NSCLC and MM trials.This observation was further supported by a previous pooled survival analysis of these two trials together with a dataset on prostate cancer concluding that immune responders had longer OS in comparison to non-immune responders (median OS, 54.8 months vs 23.4 months, log-rank p value 0.05), however analyses of individual trials did not show significant associations with longer OS likely due to the smaller sample sizes [10].
There were limitations in this work.It should be acknowledged that the sample size was small resulting in low precision for some of the estimated parameters, and a risk of selection and estimation bias in covariate relationships [42].Small cohorts are however typical for phase I studies and predictors should be further explored in analyses of later phase data.Dichotomizing the SI data into immune and nonimmune responder could result in loss of information and decrease in statistical power.However, the evaluated models could not describe the continuous and fluctuating SI data given the qualitative nature of the immunological assessment test (Figure S12).Factors causing fluctuations include T-cells expansion and contraction, as well as trafficking into lymphoid tissues or tumor microenvironment.
The UV1 vaccine is currently under clinical development, and there were no preexisting datasets for model evaluation, apart from the data incorporated into the analysis.There is an inherent difficulty to capture T cell dynamics within the tumor as repeated biopsies would be unethical and have a low feasibility in clinical praxis.Thus, as there is a lack of quantitative immunological assessment of response to the UV1 vaccine peptides such as TCR sequencing or culturing tumor-infiltrating lymphocytes, we focused on literature in characterizing the underlying CD4+ T cells dynamics in a simplified manner.The model assumed that memory T cells were developed from a subset of the naïve T cell population containing memory precursor genes [26].However, our model structure is flexible for possible refinements and extensions when additional data emerge.In addition, it was assumed that vaccine will always result in a full activation of CD4+ T cells production without considering the role of the T-regulatory cell mediated tolerance in the lymphoid tissues.Nevertheless, the model accounts empirically for the immunosuppression mechanisms by the implementation of the timedependent loss of efficacy.Furthermore, the induced tumor shrinkage effect in MM patients was assumed to be due to the vaccine only as the available data lacked information to quantify the benefit of combining the vaccine with ipilimumab.
To conclude, the mechanism-based pharmacometric framework revealed that the tumor shrinkage was primarily induced by the UV1specific CD4 TEM , that both model-predicted CD4 CM and CD4 TEM were the main drivers for the increased probability of observing an immune response, and that baseline SLD and its relative change from nadir, for NSCLC and MM patients, respectively, were main predictors for OS.To our knowledge, this is the first framework bridging all these clinically collected variables together to better understand their relationships and inter-patient variability, in the therapeutic cancer vaccine area.Currently, large randomized controlled phase II trials, collectively enrolling more than 650 patients, are being conducted to determine the clinical efficacy of UV1 in combination with checkpoint inhibitors which are; pembrolizumab in head and neck cancer, durvalumab in ovarian cancer, and two studies with ipilimumab and nivolumab in melanoma and mesothelioma.Hence, our framework can serve as a valuable model-informed drug development tool via integrating the generated

Declaration of Competing Interest
EIKI and LEF declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.EBE and SMM are employees of Ultimovacs ASA or Ultimovacs AB.SMM controls shares in Ultimovacs ASA via a privately owned company.

Fig. 2 .
Fig. 2. Individual fits for (A) NSCLC patients and (B) MM patients.Dashed lines represent the population/typical model predictions.Solid lines represent the individual model predictions.The dots represent the SLD observations.

Fig. 4 .
Fig. 4. Visual predictive checks of the final immune response model (top) and overall survival model (bottom).The plots show the proportions of the immune responder patients over the study period where the observed proportions are illustrated by solid black lines and the median of the predicted proportions is illustrated by dashed black lines, as well as Kaplan-Meier plots where the observed survival data is illustrated by solid black lines, the median of the predictions illustrated by dashed black lines and the 95% confidence interval illustrated by shaded area.The 95% confidence intervals, derived from 400 simulations from the final models, are illustrated by the shaded blue region (A, left) for NSCLC patients and orange region (B, right) for MM patients.

Fig. 5 .
Fig. 5.The mechanistic tumor growth dynamics model predictions (A) for NSCLC patients and (B) for MM patients.The typical values of λ sup,NSCLC and k SHR,MM were used together with -/+ 0.5 and one standard deviation (SD) of the typical parameter values.The vertical dashed lines represent dosing times.Different colors represent different dose levels while different line types represent different KD values.

Fig. 6 .
Fig. 6.The mechanistic tumor growth dynamics model predictions at dose level = 300 µg and median K D value for (A) NSCLC patients and (B) MM patients.The typical values of λ sup,NSCLC and k SHR,MM were used together with -/+ 0.5 and one standard deviation (SD) of the typical parameter values.The vertical dashed lines represent dosing times.Different colors represent different dosing schedules.Red illustrates the original schedule, orange illustrates the extra added dosing times for alternative schedule 1 (i.e.dosing three times per week during the first two weeks of UV1 vaccination instead of only the first week) and green for alternative schedule 2 (i.e.adding maintenance doses every three months for a longer period of time than originally used).

Table 1
Summary of patients baseline characteristics presented as mean and standard deviation. 9 9 9

Table 2
The final mechanistic tumor growth dynamics model parameter estimates.
a relative standard error (RSE) and confidence interval (CI) were obtained from SIR32.b additive residual error model on log-transformed data.c IIV on λ sup,NSCLC and k SHR,MM had shrinkages of 32% and 48%, respectively, on the standard deviation scale.

Table 3
The final immune response and overall survival model parameter estimates.MTT 01 (MTT 01 = 1/λ 01 ), mean transit time from non-immune to immune responder state for NSCLC and MM patients; MTT 10,NSCLC and MTT 10,MM , mean transit time from immune to non-immune responder state for NSCLC and MM patients, respectively; COV CM , coefficient of the effect of CD4 CM on λ 01,NSCLC (λ 01,NSCLC = 1/MTT 01,NSCLC ); COV TEM and COV LYM , coefficients of the effect of CD4 TEM and time-varying lymphocyte count, respectively, on λ 01,MM (λ 01,MM = 1/MTT 01,MM ); λ OS,NSCLC , scale parameter in Weibull distribution; γ OS,NSCLC , shape parameter in Weibull distribution; β SLD,base and β dose , coefficients of the baseline SLD, parametrized as ln(SLD base /59), and dose level effects, respectively, on death hazard in NSCLC patients; λ OS,MM , baseline hazard; β SLD,RC,NADIR , coefficient of the percent relative change of SLD from nadir on death hazard in MM patients.