Accuracy in the estimation of the hazard in simultaneous and sequential estimation approaches of tumor size and overall survival (OS) modeling
Sreenath M. Krishnan (1), Lena E. Friberg (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden.
Objectives: Frequently suggested tumor metrics of predicting overall survival (OS) in different tumor types are tumor-size time course (TSt), tumor size ratio at e.g. 6 weeks (TSRw6), time-to-tumor growth (TTG), and the tumor growth rate constant (KG) [1,2]. In addition to the accuracy of tumor metrics, the estimation approach used for connecting tumor metrics to OS might also influence the estimated hazard (HZ) of death, in a similar way as when models of PK are connected to PD models [3]. For example, Empirical Bayes estimates of tumor metrics may be shrunk and thereby affect the estimated OS parameters [4]. Moreover, a tumor size – OS model could ideally be applied early in a treatment to predict the adequacy of the dosing regimen for an individual patient. This study aims to investigate how sequential and simultaneous estimation approaches, as well as the number of tumor size measurements, influence the accuracy of estimated HZ of death for an individual patient.
Methods: Data: Tumor size data for 1000 subjects were simulated using a simplified tumor growth inhibition model for bevacizumab plus chemotherapy in colorectal cancer[5], at baseline(w0), and at 6,12,18,24,36,48,60,72,84 and 96 weeks. Dropout from tumor measurements was considered and forced at an observed increase from the tumor nadir of >20%. The OS data were simulated using a Weibull function and tumor metrics [5]. The accuracy of the estimated HZ was calculated as the percentage deviation from the ‘true’ HZ and the acceptable accuracy was set to 80-125% of the ‘true’ HZ. Sequential approach: (a) The Empirical Bayes estimates were derived from the simulated individual profiles and the prospective evaluation function in PsN[6]. The individuals’ tumor model parameters were applied in the derivation of tumor metrics and the estimation of HZ, similar to ‘Individual PK Parameters (IPP)’ approach. (b) Alternatively, the tumor data and the population tumor parameters were used in the derivation of the tumor metrics and the estimation of the HZ, similar to ‘Population Pharmacokinetic (PK) Parameters and Data (PPP&D)’ approach. Simultaneous (SIM) approach: Tumor parameters and OS parameters were estimated simultaneously using a joint model. In all scenarios, the influence of the number of tumor size observations in the estimation of HZ was investigated.
Results: TSRw6: When w0 and w6 measurements were used, 69% (IPP) and 70% (PPP&D and SIM) of individuals had an acceptable accuracy. By adding w12 measurements, the corresponding percentages were 78% (IPP) and 79% (PPP&D and SIM). The accuracy was little influenced by later observations and accuracy percentages were 81% (IPP) 84% (PPP&D) and 87% (SIM) when all tumor data was used. KG: When tumor data until w6 used, the percentage of the population with acceptable accuracy was 54% (IPP) and 55% (PPP&D and SIM). The accuracy was little affected by adding w12-w24 measurements, while adding tumor data beyond w24 increased the accuracy (median TTG was 23 weeks) and it was 62% (IPP and SIM) and 63% (PPP&D) when all tumor data was used. TTG: The percentage of population with accurate HZ was always lower than 45% for all estimation approaches despite of including more tumor data. With data until w6, the accuracy was 23% (IPP) and 26% (PPP&D and SIM). The accuracy was highest at w36; 36% in IPP, 40% in PPP&D and 43% in SIM. TSt: The accuracy increased with longer tumor follow up. With data up to w6, 39% (IPP and SIM) and 41% (PPP&D When all tumor data was used, the percentages of remaining patients at w96 were 44% (IPP), 46% (PPP&D) and 41% (SIM).
Conclusions: This simulation study demonstrated comparable results between sequential and simultaneous approaches in investigating tumor metrics as predictor of OS. In the scenarios investigated here, the PPP&D approach would be preferable since it had shorter runtimes compared SIM and slightly better results than IPP. The analysis method had little influence on the accuracy of the estimated HZ, while the accuracy in the estimated individual HZ was dependent on which metric that was defined as the true one. When TSRw6 was the predictor, fewer measurements were needed to predict its value [7] and the HZ accuracy was here found to be relatively high already at w12-w18, while longer follow up was needed to improve the accuracy for KG, TTG & TSt metrics and estimated HZ.
Acknowledgements: This work was supported by the Swedish Cancer Society.
References:
[1] Bruno et al., Clin Pharmacol Ther. 2014.
[2] Bender et al., Br J Clin Pharmacol 2016.
[3] Zhang et. Al., J Pharmacokinet Pharmacodyn (2003).
[4] Ribba et al., Clin Pharmacol Ther. 2014.
[5] Claret et al., J Clin Oncol. 2013 Jun 10;31(17):2110-4.
[6] Perl-speaks-NONMEM (PsN). [https://uupharmacometrics.github.io/PsN/index.html]
[7] Krishnan et. al., PAGE abstract 7353. [www.page-meeting.org/?abstract=7353]
