Comparison of partitioned survival modeling with state transition modeling approaches with or without consideration of brain metastasis: a case study of Osimertinib versus pemetrexed-platinum

In cost-effectiveness analyses of anticancer drugs, partitioned survival models (PSM) and state transition models (STM) are the most common model structures applied for oncology drugs [1]. PSM has the advantage of simplicity as it directly uses each survival curve (e.g., progression free survival (PFS) and overall survival (OS)) to estimate the proportion of state membership. However, PSM has limited ability to capture the complexity of a disease with multiple stages because it can only be applied when patients move forward through a set of health states without backward transitions. The STM can be a primary alternative to the PSM. In the STM, the number of patients in each state is dictated by the transition probabilities between mutually exclusive health states. This approach is advantageous owing to its flexibility, although challenges exist in terms of finding robust transition probabilities, especially with multiple health states. It requires more complex methods to reflect time-dependencies in event rates. The STM allows for more health states to be constructed than in PSM, enabling the model to apparently reflect the natural history of the disease. Therefore, it is recommended to use STM alongside PSM to explore uncertainties in the extrapolation period according to the National Institute for Clinical and Care Excellence (NICE) Technical Support Document 19 [2].

The 3-health state transition model (3-STM) is conventionally established with health states of “progression-free (PF),” “post-progression (PP),” and “death.” However, the course of disease sometimes includes heterogeneous health states that lead to higher or lower costs and quality of life (QoL). In these cases, the need for additional health states is highlighted to capture the disease course. However, there is a lack of research on how much the additional health states affect the results of the cost-effective analysis in oncology. To deal with these issues, we developed a 5-health state transition model (5-STM) considering additional health states with heterogeneity.

We conducted a case-study study on Osimertinib, the preferred regimen for first and subsequent line of therapy in epidermal growth factor receptor (EGFR)-mutated non-small cell lung cancer (NSCLC) with or without brain metastases [3]. In South Korea, patients with T790M mutation are eligible for reimbursement of Osimertinib if they experienced disease progression following the prior administration of an EGFR-tyrosine kinase inhibitor (TKI). Patients with EGFR-mutated NSCLC frequently develop brain metastasis [4, 5], which can lead to a higher economic burden, poorer prognosis, and lower QoL compared to metastasis in other sites [6‐8]. In addition, patients with EGFR-mutated NSCLC can continue to use Osimertinib even if brain metastasis progresses [3]. The continuation of Osimertinib treatment despite brain metastasis was observed in the phase 3 AURA3 trial, where the median time to first subsequent therapy or death (16.0 months) was longer than median PFS (10.1 months) [9, 10]. Given these differences, we considered brain metastasis a heterogeneous event from other progressions and included two additional health states: brain metastasis with continuing initial therapy and with subsequent therapy.

This study evaluated the life-years (LY) and quality-adjusted life-years (QALY) estimates for Osimertinib and pemetrexed plus platinum chemotherapy (PPC) as an applied example to explore structural uncertainty. We developed three economic models (PSM, 3-STM, and 5-STM) for patients with EGFR-mutated advanced NSCLC, whose disease had progressed on first-line EGFR-TKI. To estimate the impact of different modeling approaches, we compared PSM and 3-STM. We also built a 5-STM to investigate how adding heterogeneous health states to the 3-STM affects the results of LY and QALY.

In the HIRA database, 3,491 patients with EGFR-mutated advanced NSCLC used Osimertinib or PPC as second-line palliative therapy. After 1:1 matching on the propensity score, 735 patients were included in each of the Osimertinib and PPC cohorts (S2 Fig.). The baseline characteristics of the propensity score-matched cohort were well-balanced, with standardized mean differences of less than 0.1 (S4 Table). The Kaplan–Meier data and fitted parametric curves for OS and TTNT analyzed in the Osimertinib and PPC cohorts are presented in Fig. 2. Model input parameters, including the best-fitting distributions for each survival curve, are listed in Table 1.

The distribution of the patients in each health state over time for each model structure is illustrated in Fig. 3, and the corresponding AUC values are presented in S5 Table. Estimates of the difference in mean LY between Osimertinib and PPC over seven years are reported in Table 2, and were 0.89, 0.90, and 0.91 in PSM, 3-STM, and 5-STM, respectively. The mean QALYs for were 1.90 (PSM), 1.96 (3-STM), and 1.73 (5-STM) for Osimertinib, and 1.07 (PSM), 1.12 (3-STM), and 1.03 (5-STM) for PPC. The incremental QALYs for each model are presented in Table 2, which were 0.83, 0.84, and 0.70 for PSM, 3-STM, and 5-STM, respectively. The incremental QALY for 5-STM was smaller than that for PSM and 3-STM, with differences of -16% and − 17%, respectively. The estimated LYs and QALYs divided by each health state in each model structure are reported in S6 Table. Although similar, PSM predicted slightly fewer LYs for both Osimertinib and PPC. The mean LYs for were 2.40 (PSM), 2.49 (3-STM), and 2.50 (5-STM) for Osimertinib, and 1.51 (PSM), 1.59 (3-STM), and 1.59 (5-STM) for PPC.

The results of one-way sensitivity analyses are presented in Table 3 and S7 Table. The time horizon had the greatest impact on incremental QALYs, ranging from 0.71 to 0.91 (PSM), 0.73 to 0.92 (3-STM), and 0.61 to 0.74 (5-STM). The results were robust to changes in utility sources, exhibiting a less than 10% reduction in incremental QALYs.

In this study, three economic models were constructed to compare the estimates of LY and QALY between the modeling approaches. Despite the different assumptions of the two modeling methods, PSM and 3-STM derived similar results for LY and QALY. In contrast, 5-STM, constructed to reflect the characteristics of Osimertinib, revealed similar incremental LY and lower incremental QALY than those in PSM and 3-STM.

The use of alternative modeling approaches between PSM and 3-STM using time-dependent transition probabilities had little impact on the incremental LY (0.889 versus 0.899) and QALY (0.827 versus 0.840). The difference in the results was attributed to the differences in the method of estimating the proportion of patients in each health state. PSM directly determined the proportion of patients in the death state using the areas under the OS curves. In contrast, 3-STM uses a set of time-dependent transition probabilities between three health states.

Several studies have reported the impact of different model structures within economic models of oncology drugs. Cranmer et al. compared PSM and STM and found that survival estimates were similar within the trial period, but differed after the end of follow-up [14]. Goeree et al. compared the modeling approaches of PSM and STM in patients with advanced NSCLC and reported similar results for LY and QALY, which is consistent with our results [15]. Smare et al. evaluated the survival outcomes of nivolumab and everolimus in renal cell carcinoma and reported differences in survival across three model structures [16]. Smare et al. reported that two variations of STM had higher incremental survival benefits compared with PSM of up to 14%. However, owing to the dissimilarity in the diseases and the longer time horizon a direct comparison with our study would be inappropriate.

In our study, there were considerable differences in incremental QALY (0.840 vs. 0.695) between the 3-STM and 5-STM groups. Incremental LY was greater in 5-STM, but incremental QALY in 3-STM was greater than that in 5-STM. This is likely due, in part, to the fact that patients who developed brain metastases but continued to use Osimertinib were categorized as being in a PFS health state at 3-STM, whereas at 5-STM, they were in a BMIT health state with lower utility. In addition, the impact of lower utility values for brain metastasis states would have been more reflected in the Osimertinib cohort, which survives longer in the brain metastasis states than in the PPC cohort. These results reflect the clinical reality that Osimertinib can be continued in EGFR-mutant NSCLC with brain metastases owing to improved blood-brain barrier penetration [17‐19]. As 5-STM was larger in incremental LY, the results may have differed depending on the difference in utility between the presence and absence of brain metastasis.

Considering the impact on incremental QALY, our findings highlight the importance of selecting an appropriate model structure. It may be necessary to consider additional health states when heterogeneous conditions exist, and the choice of additional health states may vary depending on the type of cancer or treatment. Further research is needed to determine which model structure should be used and when, and a cost analysis should be included to determine the impact on the incremental cost-effectiveness ratio. When incorporating additional health states, cohort STM is suitable as long as the characteristics of the decision problem can be captured with a manageable number of health states [20]. While there is no absolute limit on the number of states in a cohort STM [21], if a large number of additional health states are required, it may be more appropriate to consider another approach, such as the individual-level STM. Also, the model structure and specifications of health states should reflect the understanding of the disease course and adequately capture the benefits of interventions [20].

The strength of this study is that we explored structural uncertainty with the direct calculation of transition probabilities by measuring the time to brain metastasis, which has not been reported in the clinical trial literature. We developed a 5-STM that reflects the disease course of EGFR-mutated advanced NSCLC and compared it with conventional PSM and 3-STM. Real-world clinical outcomes used in the economic models were estimated using a nationwide health insurance claims database covering nearly the entire Korean population. This can provide a more representative sample of patients, with enhanced generalizability, capturing a broader range of age groups and healthcare practices.

This study had several limitations. First, TTNT was used as a proxy for PFS because the HIRA database does not provide information on disease progression. There is a possibility of overestimating PFS given that the Osimertinib cohort exhibited a longer TTNT than PFS in the AURA3 trial [9, 10]. According to previous studies, the TTNT was similar to or exceeded real-world PFS and could be considered a proxy for real-world PFS, although further validation is needed [22‐25]. It is noteworthy that patients not initiating subsequent treatment might introduce bias, especially in cases where individuals with compromised health conditions refrain from treatment, contributing to potential overestimation of PFS. Second, the date of death was extracted using the operational definition described in the Methods section. However, we adapted an operational definition validated in a previous study on lung cancer patients in South Korea to minimize misclassification [26]. Third, long-term data were not available, as reimbursement for Osimertinib was effective from December 2017. However, because this study compared model structures under the same conditions, it was unlikely to have a significant impact on the results. Finally, T790M mutation status is expected to be different between the Osimertinib and PPC cohorts. In South Korea, Osimertinib is reimbursed only for patients with T790M-positive EGFR mutation, but PPC can be reimbursed regardless of the T790M mutation. However, prognostic role of the T790M mutation in EGFR-TKI rechallenge is unclear [27, 28], although several studies have reported that the T790M mutation is associated with poor prognosis in patients with NSCLC [29, 30].

In this study, we developed a PSM and two STMs, with and without additional health states, to explore structural uncertainty through the comparison of different modeling approaches. Our findings demonstrate the considerable impact of incorporating additional health states such as brain metastases into economic models on estimates of incremental QALYs. These results underscore the importance of conducting comprehensive comparisons and justifications of modeling approaches in the economic evaluation of anticancer drugs. Our study suggests that additional health states with a heterogeneous QoL affect the outcomes of cost-effectiveness analysis in oncology.