A simulation-based sample size analysis of a joint model of longitudinal and survival data for patients with glioma
Daniel Glazar, Solmaz Sahebjam, Michael Yu, Dung-Tsa Chen, Heiko Enderling
Moffitt Cancer Center & Research Institute
Introduction
Patients with recurrent high-grade glioma (rHGG) have poor prognosis with median progression-free survival (PFS) <6 months, and median overall survival <12 months [1]. However, there is a wide heterogeneity in response to treatment in these patients. Predicting which patients will progress early or late on different therapeutic regimens may aid the clinician in deciding which regimen with which to treat the patient. To address this clinical need, we consider a joint model of longitudinal tumor volume and PFS.
However, before applying such a model to clinical data, we note that due to low incidence and accrual rates of early phase clinical trials for patients with rHGG [2]. There is a clinical need , therefore, to determine the minimum sample size necessary to predict patient-specific TTP using longitudinal tumor volumes. As such, we perform a simulation-based sample size analysis of a joint model of longitudinal tumor volume and PFS on an in silico clinical trial for patients with rHGG.
Objectives
1. To develop a joint model of longitudinal tumor volume and PFS for patients with rHGG. This joint model will use tumor volume dynamics as an accurate and precise predictive biomarker of PFS.
2. To perform a sample size analysis on an in silico clinical for patients with rHGG to determine the minimum number of patients needed to make accurate and precise individual Bayesian dynamic predictions of PFS based on longitudinal tumor volumes in order to inform clinical trial design.
Methods
1. We developed a joint model of longitudinal tumor volume and TTP for patients with rHGG. Tumor volumes were modeled using a tumor growth inhibition (TGI) model with mixed effects. TTP was then modeled discretely and defined as the time when tumor volume reached 40% above from nadir. Population parameter estimates of the developed joint model were estimated using quantile information reported in the literature [3] by maximizing the likelihood of joint order statistics [4].
2. We conducted an in silico clinical trial to study the effects of sample size on the predictive performance of the developed joint model to dynamically predict patient-specific PFS. We selected sample sizes of 40, 60, 80,..., 200 as most clinically feasible due to the low incidence of rHGG. We simulated in silico training and test sets and estimated population parameters using the stochastic approximation of expectation-maximization (SAEM) algorithm [5] on the training set. We then dynamically predicted patient-specific TTP for the test patients across landmark times and time horizons [6–8]. Predictive performance was evaluated using time-dependent Brier score (BS) and area under the receiver operating characteristic curve (AUC) [6,9]. Simulations were performed using the Monolix suite software [10].
Results
1. In estimating population parameters, simulated median PFS was between 24 and 30 weeks with the majority of simulated patients having between 3 and 7 observations in agreement with clinical observations [3].
2. For the largest sample size considered (N=200), we evaluated the developed model’s predictive performance for set time horizons of 6, 12, 18, and 24 weeks across all landmark times. The median AUC ranged from 0.55 to 0.63 with median BS ranging from 0.19 to 0.25.
3. Across all sample sizes tested, there was statistically significant albeit small correlation between sample size and AUC (Pearson’s r=0.20, p<1e-15) across all landmark times and time horizons. However, no statistic significance was reached for the correlation between sample and BS (Pearson’s r=-0.0017, p=0.95). When controlling for landmark time and time horizon, the median Pearson’s correlation between sample size and either AUC or BS were r=0.28, 0.07, respectively.
Conclusions
We developed a joint model of longitudinal tumor volume and PFS for patients with rHGG and parameterized according to quantile information reported in the literature. The model was able to capture the dynamics and survival profiles of the patient population. The predictive performance of the model was robust across the sample sizes tested. However, the overall predictive performance of the model was only marginally better than chance as measured by AUC and BS. In future studies, we will explore a larger range of sample sizes to investigate how many patients are necessary to meet various performance benchmarks as measured by AUC or BS.
References:
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