Model-Based Meta-Analysis of Overall Survival in Vulnerable Platinum-Ineligible NSCLC Populations.

1
Introduction
Atezolizumab was tested versus single‐agent chemotherapy (gemcitabine or vinorelbine as per investigator's choice) in a randomized, controlled global trial in treatment‐naïve non‐small‐cell lung cancer (NSCLC) patients who were deemed unsuitable for platinum‐doublet chemotherapy (IPSOS) [1]. The study enrolled 453 patients across 23 countries regardless of programmed death‐ligand 1 (PD‐L1) expression status. Atezolizumab improved overall survival (OS) compared with chemotherapy (hazard ratio (HR) = 0.78, 95% confidence interval (CI) [0.63, 0.97], p = 0.028).
Although the IPSOS atezolizumab treatment arm demonstrated significant treatment benefit, there remains the question of whether this still holds true when comparing to treatments other than gemcitabine or vinorelbine (investigator's choice per IPSOS protocol). According to the National Comprehensive Cancer Network (NCCN) guidelines [2], docetaxel, gemcitabine, pemetrexed (for non‐squamous histology), or paclitaxel are recommended single‐agent chemotherapy regimens in NSCLC patients who are deemed platinum ineligible. In addition, according to the European Society of Medical Oncology (ESMO) guidelines [3], docetaxel, gemcitabine, pemetrexed, or vinorelbine are recommended single‐agent chemotherapy regimens in this population. Thus, it would be important to understand if the IPSOS control arm of gemcitabine or vinorelbine only would be non‐inferior to a control arm in which a broader choice of single‐agent chemotherapy regimens was allowed.
The purpose of this model‐based meta‐analysis (MBMA) was to quantify the expected OS hazard ratio (HR) of the IPSOS control arm versus historical monotherapies in first‐line treatment in vulnerable/platinum‐ineligible patient populations. The aim was to demonstrate non‐inferiority of the IPSOS control arm vs. historical control with a broader choice of single‐agent chemotherapies.
Historical monotherapies of interest included gemcitabine, vinorelbine (oral and intravenous), docetaxel, paclitaxel, and pemetrexed. Primary analyses were performed using a nonparametric mixed‐effects model of summary‐level longitudinal OS data. To support the MBMA, a literature database that captures treatment effects of first‐line mono‐chemotherapy in NSCLC patients in which platinum‐doublet chemotherapy was not utilized and/or of poor performance status or older age was developed.

2
Methods
Methods follow the principles for systematic reviews outlined by the Cochrane Organization ([4]).
2.1
Literature Search and Data Selection
The PubMed search was conducted for articles published up to 18 September 2023.
The criteria for included studies are as follows:

Population: Treatment‐naïve, advanced or metastatic NSCLC patients in which non‐platinum single‐agent chemotherapies were used (not including targeted therapies such as monoclonal antibody therapies).
Patients with ECOG performance status ≥ 2 or age ≥ 70 years or platinum ineligible.

Intervention: Paclitaxel, docetaxel, gemcitabine, pemetrexed or vinorelbine monotherapies; and absence of platinum doublet as experimental or control group.

Comparison: Same as the list for Intervention (except one trial which also included best supportive care (BSC) as a comparator).

Outcome: Kaplan‐Meier overall survival (OS) curves.
Note that platinum ineligibility was defined by each respective published study.
Study inclusion was reviewed independently by at least two scientists. Discrepancies were discussed via email exchanges and teleconferences until consensus was reached.
Details of the search strategy, including a full list of the search terms, are shown in the Supporting Information S1.

2.2
Data Extraction and Preparation
Trial‐level information from selected studies was extracted manually from included publications according to the data specification in the (Tables S1 and S2).
The following pre‐specified covariates were extracted per study arm: age, percent males, percent Stage 4 disease, Eastern Cooperative Oncology (ECOG) performance status, percent squamous histology, percent adenocarcinoma histology, and percent from Asia.
Age was tested as a covariate as it is reasonable for age to have a potential impact on survival in oncology patients. Sex, disease stage and ECOG PS were identified as factors in an individual‐level meta‐analysis in NSCLC. [5] Asia was tested as a covariate because Asians could have longer survival on immune checkpoint inhibitor therapy treatment ([6]). Since pemetrexed is appropriate for non‐squamous histology only, histology was also tested as a covariate.
Kaplan Meier survival curves were digitized, with data points captured at monthly intervals, using the Engauge digitization software (markummitchell/github.io/engauge‐digitizer Version 12.1).
The dataset was curated by one scientist and checked by a different scientist.
Missing squamous and adenocarcinoma percentages were imputed from selected references that were deemed to have a similar population, if possible. Similar populations were judged based on prior treatment, disease stage, study region, and overlapping investigators. Otherwise, missing squamous and adenocarcinoma percentages were assigned to the median of non‐missing values.
Missing ECOG PS values were first mapped from Karnofsky Performance Scores if available [7]. Otherwise ECOG PS values were imputed by using a logistic regression model to split composite ECOG PS categories (e.g., ECOG PS 0 and 1) into singlet categories by utilizing the estimated odds ratio from other studies with similar ECOG PS inclusion criteria.

2.3
Data Review
Studies and covariates were summarized and tabulated.
Kaplan‐Meier survival curves were plotted by trial and stratified by drug and covariate levels.
All plots and tables were performed with R, version 4.2.2.

2.4
Analysis Methods
MBMA of Kaplan–Meier OS curves was performed using a mixed‐effects non‐parametric conditional probability method [8]. Parameters were estimated using the NONMEM software (ICON PLC, Version 7.5.1).
Figure 1 shows the concept for modeling survival curves. Conditional probability of death is defined to be the percent of subjects dying in a time interval, given survival up to the beginning of that interval. Each conditional death timepoint is assumed to be independent of previous time intervals. In this example, if the survival probability is 85.3% at 3 months and 78.5% at 4 months, then the conditional probability of death between 3 and 4 months is 7.9%.
This method uses similar concepts to Cox‐proportional hazard modeling (i.e., reference survival curve and proportional hazards). This approach assumes that a single reference survival curve with a common but not predefined shape with respect to time (e.g., nonparametric baseline hazard assumption) may be proportionally scaled by random/fixed effects to capture other survival probabilities across the dataset. The log of the HR relative to the reference curve was modeled as a linear combination of covariates and a between‐study random effect. Probabilities were modeled using the Laplacian method in NONMEM [8]. The equation is as follows:An individual‐level meta‐analysis with a large population of NSCLC patients was used to obtain both a list of potential key prognostic factors as well as preliminary estimates of the HR for these prognostic factors to be tested as covariates in the MBMA using summary‐level data [5]. This population used in the individual‐level meta‐analysis included 1231 first‐line epidermal growth factor receptor (EGFR) positive patients from 6 trials that compared EGFR tyrosine kinase inhibitors versus combination chemotherapy. Multivariate prognostic factors for OS included female (HR = 0.83, p = 0.05), ECOG performance status relative to ECOG PS 0 (HR = 2.71 for ECOG PS 2, HR = 1.43 for ECOG PS 1, both with p < 0.001), and Stage IIIB cancer relative to Stage IV cancer (HR = 0.68, p < 0.001).
A statistically significant covariate was defined as a covariate which reduces the objective function value (OFV) by 6.635 points or more (which corresponds to an α of 0.01). The significant covariate would then be retained in the final model.
Using the final model, the IPSOS control arm was compared with the historical control. Non‐inferiority was defined as a hazard ratio < 1 and a 90% confidence interval entirely less than 1 when comparing the IPSOS control arm with the historical control.

3
Results
3.1
Data Collection
3.1.1
Literature Search and Study Selection Results
The literature search yielded 275 references, of which 247 were excluded for the reasons described in Figure 2. Twenty‐eight references were selected for the MBMA analysis, representing 26 unique studies.
Table S3 lists the studies included in the analysis.
Figure S1 illustrates the reference selection process and reasons for exclusion from the analysis dataset.

3.1.2
Analysis Dataset
Table 1 shows a summary of the total number of studies, arms, and participants by drug in the analysis dataset. Only drugs of interest are included in this table. There are more trials reporting results for gemcitabine, vinorelbine, or docetaxel monotherapies than there are for paclitaxel or pemetrexed. Excluded drugs are shown in the (Table S4).
OS data stratified by ECOG performance status were reported for two trials ([9, 10]) and this subgroup data were also included in the analysis database.
Table 2 shows the statistical summary (median and range) of covariates across the studies in the analysis set. Imputed covariate values for ECOG performance status, squamous percentage and adenocarcinoma percentage were incorporated in the statistical summary.
A table of covariates by study both before and after imputation is shown in the (Tables S5 and S6). In total, 30 ECOG PS percentages, 3 squamous percentages, and 5 adenocarcinoma percentages were imputed. Squamous and adenocarcinoma percentages for patients in Lilenbaum et al. [11] were imputed using percentages in Hesketh et al. [12], because the studies had similar patient populations and were analyzed together in a subsequent meta‐analysis [13]. Squamous and adenocarcinoma percentages for patients in Anderson et al. [14] were imputed using percentages in Danson et al. [15], because of similarity in patient populations (population, region, overlapping investigator).
Figure 2a shows all OS survival curves included in the analysis. Figure 2b shows the OS survival curves by drug. Figure 2c shows the OS survival curves by study.
A funnel plot was used to evaluate publication bias (Figure S3). In the plot, the majority of studies symmetrically fall within the funnel shape with a few outliers. Based on this, it appears that in general, there is a lack of publication bias.

3.2
Analysis
3.2.1
Comparison of IPSOS Control Arm to Historical Control
Table 3 summarizes the results from key models comparing the IPSOS control arm with historical trials.
Model 007a estimates the HR of the IPSOS control arm to historical control arms; the estimated value is 0.812 with a 95% confidence interval (CI) of [0.707, 0.934]. In this model, no other covariates were estimated. No adjustment was made for ECOG PS; the hazard ratio (HR) of the composite group ECOG PS 2 and 3 to ECOG PS 0 was fixed to 1, and the HR for the group ECOG PS 1 to ECOG PS 0 was fixed to 1.
Model 007b estimates the HR of the IPSOS control arm to historical control arms by utilizing the HR values for ECOG PS 1 relative to ECOG PS 0 and for ECOG PS 2 relative to ECOG PS 0, from the individual meta‐analysis publication and fixing them to 1.43 and 2.71, respectively. The objective function decreased by approximately 21 points from Model 007a, which is significant at p < 0.001 for two estimated parameters. The estimated HR of the IPSOS control arm relative to historical control arms for Model 007b is 0.528 [0.472, 0.592]. The reason for the change in the model‐estimated HR of Model 007b relative to Model 007a is that 87% of IPSOS patients had ECOG PS 2 or 3 and therefore had worse prognosis relative to most of the historical control arms. Accounting for the effect of ECOG PS widens the gap between the IPSOS control and historical controls.
Model 010 repeats the HR estimation, but also directly estimates ECOG PS HR values from the MBMA dataset instead of fixing them to the values from the individual meta‐analysis publication. The estimated ECOG PS HR values were 1.004 for ECOG PS 1 relative to ECOG PS 0 and 2.158 for ECOG PS 2 and 3. The estimated HR of the IPSOS control arm relative to historical control arms was 0.531 [0.424, 0.664].
The complete listing of models tested is in (Table S7). Other covariates (i.e., age category, sex, disease stage, squamous vs. non‐squamous, adenocarcinoma vs. non‐adenocarcinoma, and Asia vs. non‐Asia geographic region) did not have a statistically significant effect on HR. The Supporting Information also includes the NONMEM model control stream for the final model (Model 010), the final model parameters (Table S8), and model fits to Kaplan Meier curves for each trial (Figure S2).
Figure 3a shows the prediction range of historical trials in comparison to the IPSOS control arm using Model 007a. Figure 3b shows the prediction range of historical trials in comparison to the IPSOS control arm after accounting for the higher percentages of ECOG PS 2 and ECOG PS 3 patients in IPSOS using Model 010.

3.2.2
Comparing Each Monotherapy Chemotherapy, NCCN, and ESMO Regimens With IPSOS Control and With IPSOS Atezolizumab Arms
Three additional comparisons were made. First, a comparison of each specific drug to the IPSOS control arm. Second, a comparison of NCCN and ESMO recommended chemotherapy options to the IPSOS control arm. Third, a repeat of the first two comparisons with the IPSOS atezolizumab arm instead of the IPSOS control arm.
Model 030 in Table 4 shows that docetaxel, gemcitabine, gemcitabine/vinorelbine, pemetrexed, vinorelbine, and paclitaxel all have HR > 1 relative to the IPSOS control arm, after modeling and correcting for ECOG PS. This means that patients in historical control arms had a greater risk of death than patients in the IPSOS control arm, after normalizing for ECOG PS.
NCCN guidelines recommend docetaxel, gemcitabine, pemetrexed, or paclitaxel as treatment in this population ([2]). For the NCCN model, drugs are divided into NCCN or non‐NCCN categories. ESMO guidelines recommend docetaxel, gemcitabine, pemetrexed, or vinorelbine ([3]). For the ESMO model, drugs are split into ESMO or non‐ESMO categories. Model 031 and Model 032 in Table 4 show the comparison of NCCN‐ and ESMO‐recommended control arms to the IPSOS control arm, respectively. The model‐estimated HR is close to 2 in both models. This means that patients in historical control arms according to NCCN or ESMO recommendations had a greater risk of death than patients in the IPSOS control arm, after normalizing for ECOG PS.
Table 4 shows that atezolizumab has a HR of 0.418 compared to historical controls (model 041), 0.420 relative to NCCN‐recommended control arms (model 042), and 0.398 relative to ESMO‐recommended control arms (model 043). This means that patients receiving atezolizumab have less than 50% of the risk of death than patients in historical control arms, after normalizing for ECOG.

3.2.3
Assessing the Impact of Time
Generally, a limitation with retrospective comparisons is that with time there may be medical advancements that prolong survival that are outside of the direct treatment intervention. Thus, additional evaluations were done to see if there was a potential impact with publication year or time.
In the analysis dataset, the O'Brien study published in 2008 used the same chemotherapy regimen as the IPSOS trial of gemcitabine or vinorelbine, and thus could serve as a reference therapy allowing for comparisons controlling for publication year. Table 4 presents an evaluation of each of the monotherapy treatments with O’Brien as the reference arm (Model 047 and 048). Both Model 047 and 048 had similar HR estimates, with CI encompassing 1 for almost all chemotherapy regimens. Furthermore, the results were consistent with the HR estimates when the IPSOS control was used as the reference. However, in Model 047 (and similarly in Model 030), the comparison between O’Brien and the IPSOS control shows that the IPSOS control was superior to O’Brien, despite having the same chemotherapy regimen of gemcitabine or vinorelbine. This suggests that perhaps time may still have an impact, or there may be unknown sources of heterogeneity between O'Brien and the IPSOS control.
Further evaluations were done to assess the impact of publication year, presented in Table 5. The first evaluation conducted was to see if the estimated HR would change if the IPSOS data was removed, as it was the most recent published study. The change in the estimated ECOG PS effect was negligible when both arms of Lee 2023 (IPSOS) were removed from the analysis dataset. Subsequently, the publication year was evaluated as a covariate which resulted in a non‐significant decrease in the OFV. Of note, the publication year covariate was negative, meaning the more recent the year of publication, the lower the log(HR) or hazard compared to the reference. While not significant, this is in line with the hypothesis that therapy could improve over time. The IPSOS HR point estimate for Model 049 compared to Model 010 still supports IPSOS non‐inferiority, but the HR CI for Model 049 now includes 1.
Overall, while these evaluations indicate the impact of time is unclear, all evaluations still support the main analysis results that the IPSOS chemotherapy regimen of gemcitabine or vinorelbine is non‐inferior to other historical monotherapy chemotherapy regimens.

4
Discussion
The purpose of this MBMA was to assess the overall survival hazard ratio of the IPSOS control arm (gemcitabine or vinorelbine) versus various historical single‐agent chemotherapies in first‐line treatment of vulnerable/platinum‐ineligible non‐small‐cell lung cancer (NSCLC) patients. The aim was to demonstrate the non‐inferiority of the IPSOS control arm.
In this analysis, ECOG PS was the only statistically significant covariate identified. After adjusting for ECOG PS, the model‐predicted HR for the IPSOS control arm relative to historic trials was 0.543 (95% CI: 0.435, 0.677). The HR for the IPSOS atezo monotherapy arm relative to historic trials was 0.418 (95% CI: 0.335, 0.522). Thus, the results of the MBMA support the clinical benefit seen in the IPSOS trial.
The IPSOS control arm was shown to be non‐inferior to the NCCN and ESMO guideline recommended therapies based on the MBMA analysis. When comparing the IPSOS control arm relative to the historical control therapies grouped by NCCN guideline therapies, the model‐predicted HR was 0.545 (95% CI: 0.438, 0.678). Similarly, the model‐predicted HR of the IPSOS control arm relative to the ESMO guideline therapies was 0.516 (95% CI 0.418, 0.636).
There were several potential limitations of this analysis. One potential limitation was that most of the studies that were included in the database were published greater than 10 years ago. There could be advances in medical practice such as improved supportive care or a healthier lifestyle of patients resulting in fewer comorbidities that result in longer survival in recent studies that are not directly quantified by the treatment intervention. To address this potential limitation, additional evaluations were conducted including using an older study (O’Brien) as a reference instead of IPSOS, evaluating publication year as a covariate, and excluding IPSOS data from the analysis dataset. While these evaluations were not consistent in characterizing the impact of time, all evaluations still support the main analysis results that the IPSOS chemotherapy regimen of gemcitabine or vinorelbine is non‐inferior to other historical monotherapy chemotherapy regimens.
Another potential limitation is that while the covariate analysis adjusted for the cross‐trial comparison, there could be unknown sources of heterogeneity.
While histology was not a significant covariate, it should be noted that pemetrexed is appropriate for non‐squamous histology only. It should also be noted that in this MBMA, the sample size for pemetrexed therapy was low.
Although the IPSOS atezolizumab arm also showed treatment benefit as compared to historical control, because the initial aim of this analysis was only to show that the IPSOS control arm was non‐inferior to historical control, the analysis for the IPSOS atezolizumab arm is considered exploratory.
Because the datasets were reconstructed from published Kaplan–Meier curves, censoring information indicated by tick marks could not be captured. The absence of censoring data may over‐weight later time points. This was mitigated by removing the tails of the survival curve where the estimated number of surviving patients < 10 or survival probability fell below 10%. Simulation analysis showed that the method accurately estimated hazard ratio distributions under various conditions, including small sample sizes (N < 50), although further work is needed to better define its limitations.

5
Conclusions
To the best of our knowledge, there are no publications utilizing MBMA for the indirect comparison of the control arm in clinical trials; MBMA is typically used for indirect comparison of the investigational arm. This analysis offers a novel approach that could justify the use of specific control arms in clinical trials. Additionally, it facilitates the indirect comparison of alternative historical control arms to the investigational arm, thereby strengthening the clinical results of the trial and potentially enhancing the acceptance of trial outcomes by regulatory health authorities.
This MBMA showed that the IPSOS control arm was non‐inferior to historical controls, which included a broader choice of single agent chemotherapies. This supports the conclusion that the overall survival benefit demonstrated with atezolizumab monotherapy in the IPSOS study population was unlikely to be affected by limiting the choice of chemotherapies to gemcitabine and vinorelbine in the control arm.

Author Contributions
J.C., P.C., R.W., N.Z., B.W., N.K., S.M., V.G., W.Z., and Y.H. wrote the manuscript; J.C., P.C., R.W., N.Z., B.W., N.K., S.M., V.G., W.Z., and Y.H. designed the research; J.C., P.C., R.W., and N.Z. performed the research; R.W. and N.Z. analyzed the data.

Funding
Roche Holding|Genentech (Genentech USA): Joseph Chen; Roche Holding|Genentech (Genentech USA): Russ Wada; Roche Holding|Genentech (Genentech USA): Nancy Zhang; Roche Holding|Genentech (Genentech USA): Vilma Graupner; Roche Holding|Genentech (Genentech USA): Stefanie Morris; Roche Holding|Genentech (Genentech USA): Youyou Hu; Roche Holding|Genentech (Genentech USA): Wei Zhang; Roche Holding|Genentech (Genentech USA): Nastya Kassir; Roche Holding|Genentech (Genentech USA): Benjamin Wu; Roche Holding|Genentech (Genentech USA): Phyllis Chan. Roche/Genentech funded this work as an employer for all of the authors. Note that Russ Wada and Nancy Zhang from Quantx were hired contractors by Roche/Genentech to conduct this work.

Conflicts of Interest
B.W., J.C., N.K., P.C., S.M., V.G., W.Z., Y.H. are employees of Genentech/Roche and receive stock and stock options as part of employment. N.Z. and R.W. are employees of QuanTx and are paid consultants of Genentech in conjunction with this work.

Supporting information

Data S1: psp470197‐sup‐0001‐DataS1.zip.