A Bayesian Approach to Compare Accumulating Survival Data From Clinical Practice With RCT Data: A Case Study in Non‐Small Cell Lung Cancer Patients

ABSTRACT

Survival outcomes observed in randomized controlled trials (RCTs) may not always be generalizable to clinical practice. Evaluating whether treatment outcomes in clinical practice are similar to those in RCTs shortly after a new medicine is introduced is important for making informed decisions. Therefore, we aimed to develop a Bayesian model that compares survival data from clinical practice that accumulates over time with static survival data from RCTs, thereby providing rapid and easily interpretable results that can inform clinical and policy‐related decision‐making. We developed a Bayesian survival model that sequentially updates estimates as new data become available. We designed the model to incorporate static RCT data with accumulating clinical practice data. We used sequential hypothesis testing with Bayes factors to assess the strength of the evidence for different hazard ratio (HR) thresholds (i.e., ranging from HR > 1.0 to > 2.0 and HR < 0.5 to < 1.0). We applied the model to two datasets comprising survival data from clinical practice and an RCT for lung cancer patients treated with pembrolizumab plus chemotherapy (dataset 1) and pembrolizumab monotherapy (dataset 2). For dataset 1, the posterior model checks showed a misfit between the model and the data after 15 months, potentially due to channeling bias. The model fit should be improved before reliable estimates can be obtained. For dataset 2, the model estimated precise HRs 10 months before the end of data accumulation. Sequential hypothesis testing with Bayes factors provided easily interpretable results, with very strong evidence for an HR > 1.0 and strong evidence for an HR > 1.2. In conclusion, provided the posterior check shows an acceptable model fit, our Bayesian survival model with sequential hypothesis testing using Bayes factors can provide rapid and easily interpretable results for decision‐making.

Summary.

• What is the current knowledge on the topic?

  • ○
    Survival outcomes observed in randomized clinical trials (RCT) are not always generalizable to clinical practice. Potential differences in such time‐to‐event outcomes are often assessed using Cox proportional hazards regression models. These models are limited in their application for repeated assessments based on clinical practice data that are accumulating over time.
• What question did this study address?

  • ○
    This study examined whether a Bayesian survival model could be developed to compare accumulating survival data from clinical practice with static survival data from RCTs, in order to provide rapid and interpretable results for clinical and policy‐related decision‐making.
• What does this study add to our knowledge?

  • ○
    We developed a Bayesian survival model that compares survival data from clinical practice that accumulate over time with static survival data from RCTs to investigate whether survival outcomes are similar or different. Provided the posterior check indicates an acceptable model fit, we demonstrated that sequential hypothesis testing with Bayes factors could be used as a statistically sound method for stopping and inferring parameter estimates at the earliest possible time point (i.e., in contrast to the traditional Cox modeling approach, where this is not possible because of practical and statistical concerns). The proposed visualizations allow for direct model interpretation by analyzing model fit and posterior confidence intervals around inferred parameter values.
• How might this change drug discovery, development, and/or therapeutics?

  • ○
    Provided adequate model fit, the Bayesian survival model can enable rapid and interpretable results that can inform clinical and policy‐related decision‐making. For example, very strong evidence that survival in clinical practice is substantially worse than in the trial (e.g., HR > 2) could trigger further investigation into underlying causes and adjustments to treatment strategies.

1. Introduction

Randomized controlled trials (RCTs) are considered the gold standard for determining the efficacy of new medicines [1, 2, 3]. However, outcomes observed in RCT populations may not always be generalizable to clinical practice. Patients treated in clinical practice may be older, less fit, and have more comorbidities [4]. In addition, treatments and follow‐up procedures are often less standardized and consistent in clinical practice than in RCTs. Therefore, it is important to evaluate whether treatment outcomes in clinical practice are similar to those in RCTs shortly after a new medicine is introduced.

Whether effectiveness observed in clinical practice and efficacy observed in RCT are similar has often been investigated, especially for oncology medicines. Survival outcomes such as overall survival and progression‐free survival are typically worse in clinical practice than in RCT populations. For example, the survival of patients with metastatic NSCLC treated with systemic treatments in clinical practice was shown to be nearly 25% shorter than the survival observed in RCTs [4].

A difference between a medicine's efficacy (RCT) and effectiveness (clinical practice) is called an efficacy‐effectiveness gap (EE gap) [5]. The direction and size of an EE gap can vary depending on the type of medicine, setting, and patient characteristics. In cases where an EE gap indicates a clinically relevant difference, it may warrant further investigation and adjustments to treatment strategies.

Time‐to‐event data, such as survival data, are typically modeled with Cox proportional hazards (PH) regression to estimate the hazard ratio (HR). In studies assessing whether there is an EE gap, the HR represents the hazard of an event occurring in the clinical practice cohort divided by that in the RCT cohort, while assuming that the HR is constant over time. An HR of 1 or close to 1 (e.g., an HR between 0.9 and 1.1) indicates similar outcomes for patients treated in clinical practice and those treated in an RCT, whereas an HR above this range indicates worse outcomes and an HR below this range indicates better outcomes for patients treated in clinical practice. However, estimating the appropriate sample size prior to a study is challenging due to variations in the type of medicine, setting, and patient characteristics that may all influence whether treatment outcomes are similar or not. A too small sample size or too‐short follow‐up period may result in a lack of statistical power to detect clinically relevant differences between settings. Conversely, waiting until more patients have been treated or extending the follow‐up period could incur unnecessary delays in investigating a potential EE gap [6].

One potential solution is to compare accumulating clinical practice data repeatedly to RCT data. Bayesian survival models may offer a suitable approach for this type of repetitive evaluation because the Bayesian approach naturally allows sequential updates to model parameters and estimates. Unlike the frequentist Cox PH regression models, Bayesian models are designed to incorporate prior information explicitly, such as data from similar treatments and patient populations [7, 8, 9]. This Bayesian approach allows for the investigation of potential clinically relevant EE gaps as early as statistically justifiable, avoiding the a priori need for larger datasets or extended follow‐up periods. Clinically relevant thresholds can be set to indicate that survival outcomes in clinical practice are worse or better than those reported in RCTs. Moreover, Bayesian models may allow a more intuitive interpretation of uncertainty than frequentist models, making it easier to assess and compare the confidence in estimates at different points in time [10]. This can support clinical and policy‐related decision‐making by indicating whether differences in survival outcomes between clinical practice and an RCT exist, enabling prompt adjustments to treatment strategies if needed.

Therefore, we aimed to develop a Bayesian survival model that compares survival data from clinical practice that accumulates over time with static survival data from RCTs, in order to investigate whether survival outcomes are similar or different, thereby providing rapid and easily interpretable results that can inform clinical and policy‐related decision‐making.

2. Methods

In this section, we describe the key aspects of the development and application of our Bayesian survival model. Bayesian statistics fundamentally rely on Bayes' theorem, which includes three main elements: the observed information in the data, prior information, and posterior distribution. First, we explain the model development by detailing the observed information in the data, prior information, and data assimilation (step 1). Second, we describe the posterior distribution (step 2). Third, we describe the model diagnostics we used to assess the performance of our model (step 3). Fourth, we explain how we used sequential hypothesis testing with Bayes Factors to evaluate potentially clinically relevant differences in survival outcomes (step 4), generating evidential strength in favor of one of the competing hypotheses. Fifth, we describe the prior sensitivity analyses used to assess the robustness of the estimates (step 5). Finally, we describe the two datasets that we used to apply the Bayesian survival model in more detail.

We implement the Bayesian survival model in Python using the PyMC package version 5.16.1 and use the Bayesian Analysis Reporting Guidelines (BARG) to ensure comprehensive and transparent reporting [11]. Full methodological details are available in the Files S1–S12.

2.1. Step 1: Observed Information in the Data (Likelihood), prior Information and Data Assimilation

2.1.1. Observed Information in the Data (Likelihood)

Our Bayesian survival model adopts key characteristics from Cox PH regression modeling. How these characteristics relate to Cox PH regression modeling is discussed in more detail in File S1. The two primary model parameters of interest are the hazard rate and the baseline hazard, which are combined into a hazard function. Similar to Cox PH regression modeling, we assumed that the hazards are proportional and constant over time, and we accounted for right and non‐informative censoring. While the baseline hazard does not need to be specified explicitly in Cox PH regression models, it must be defined in Bayesian models because of their fully parametric nature. Additionally, nuisance parameters for the baseline hazard should be explicitly defined in Bayesian survival modeling. These parameters and their distributions are important for constructing the likelihood function, which quantifies the probability of survival for the observed data. To model the baseline hazard, we used a Weibull distribution with two nuisance parameters $b$ (scale) and $k$ (shape) to model the baseline hazard [12, 13, 14]. Additionally, we incorporated one covariate in our model, representing the setting (clinical practice or RCT). Detailed mathematical information can be found in File S2 and a synthetic validation of our model using simulated data is described in File S3.

2.1.2. Prior Information

Next, we defined weakly informed priors for these three model parameters, to provide some guidance without being overly restrictive. We used a normal distribution for the log hazard rate with $\mu =0$ and a $\sigma =0.5$, with a lognormal distribution for the scale parameter $b$ with $\mu =-3.0$ and $\sigma =1.0,$ and a uniform distribution for the shape parameter $k$ (with $k<1$ indicating the rate decreasing over time and $k>1$ indicating the rate increasing over time), with a range from 0.9 to 1.1. These prior distributions are plotted in Figure S1.

2.1.3. Data Assimilation

The RCT and clinical practice cohorts and associated datasets are described in more detail below. We designed the Bayesian survival model to incorporate the data from the RCT cohort in a fixed manner while accumulating data from the clinical practice cohort over time as new patients are chronologically enrolled and their follow‐up periods prolonged based on their treatment start and end dates. We updated the model at biweekly intervals, incorporating both newly enrolled patients and longer follow‐up of already enrolled patients. Patients who were still alive by the end of follow‐up were censored at the date of their last clinic visit, with the censoring date updated as the follow‐up period was prolonged.

2.2. Step 2: Posterior Distribution

We used Monte Carlo Markov chain (MCMC) simulations to estimate the posterior probability distributions (File S2 and S4). To present the results in an easily interpretable manner, we estimated the HRs over time and their corresponding 50%, 75%, 90%, 95%, and 97.5% credible intervals, which were derived from the posterior distribution. The Bayesian credible intervals provide an easily interpretable result, as they express the probability of a parameter falling within a specific range: a 95% credible interval reflects a 95% probability that the true value lies within that interval based on the accumulated data at a specific point in time.

2.3. Step 3: Model Diagnostics

Kaplan–Meier curves were constructed to visualize the data and to check whether the HRs are proportional and constant over time. Prior predictive checks were performed to evaluate the suitability of the chosen priors, ensuring alignment with data distributions before model fitting (File S5). After applying the model, posterior predictive checks were used to assess the model fit, comparing model‐generated data with the observed data (File S6). Good model fits are necessary to obtain reliable estimates.

2.4. Step 4: Bayesian Hypothesis Testing

To determine whether any observed differences in survival outcomes between patients treated in clinical practice and those in the RCT were clinically relevant, evidence for clinically relevant HR thresholds was calculated at each model update. HR thresholds from > 1.0 to > 2.0 were used to indicate worse survival outcomes (i.e., higher risk of death) in clinical practice compared to the RCT, while thresholds from < 0.50 to < 1.00 were used to indicate better survival outcomes (i.e., lower risk of death).

However, repeated evaluations can lead to multiple testing issues, increasing the likelihood of false positive conclusions. To mitigate this issue, we used the Bayes factor that quantifies the strength of the evidence provided by the data for the null hypothesis H₀ compared to the evidence for the alternative hypothesis H1. A Bayes factor of 1 signifies inconclusive evidence for H1, a Bayes factor between 1 and 3 indicates anecdotal evidence for H1, a Bayes factor between 3 and 10 suggests moderate evidence for H1, a Bayes factor between 10 and 30 indicates strong evidence for H1, and a Bayes factor greater than 30 represents very strong evidence for H₁ [15]. The Bayes factor is updated as new data are available, providing insight into which hypothesis (H₀ or H₁) is better supported by the evidence for every updated model [15]. To provide interpretable results at each model update, the Bayes factors with the different levels of evidence were plotted for all competing hypotheses testing different HR thresholds. For hypotheses that consistently reached very strong evidence in consecutive model updates, the graph was limited to this level. Details on Bayes factor hypothesis testing are reported in File S7.

2.5. Step 5: Prior Sensitivity Analysis

To evaluate the robustness of the estimates, sensitivity analyses with different priors and a different baseline hazard were conducted (Files S8 and S9). For the baseline hazard parameterization, a Gompertz distribution (instead of a Weibull distribution) was used.

2.6. Application of the Bayesian Survival Model to Two Datasets

To evaluate the performance of the Bayesian survival model in multiple settings, the model was applied to two datasets of patients with metastatic NSCLC (mNSCLC) treated with either pembrolizumab plus chemotherapy (dataset 1) or pembrolizumab monotherapy (dataset 2). These datasets were readily available and therefore suitable to evaluate the performance of the model.

2.6.1. Design and Setting of Dataset 1: Pembrolizumab Plus Chemotherapy

The first dataset contains survival data from two cohorts of patients with mNSCLC who were treated with first‐line pembrolizumab plus chemotherapy: one derived from the phase III KEYNOTE‐189 RCT (n = 410) [16], with survival data reconstructed with the algorithm of Guyot et al. [17], and one clinical practice cohort (n = 512) derived from electronic health records from the same seven non‐university Dutch teaching hospitals of the Santeon Group. The RCT included patients treated and followed up between February 2016 and March 2017, with a median follow‐up of 10.5 months. The clinical practice cohort included patients treated and followed up between January 2019 and December 2021, with a median follow‐up of 15.5 months. Previous research from Verschueren et al. (2024) demonstrated that the survival outcomes for patients treated in the clinical practice cohort were worse than the survival outcomes for patients treated in the RCT, as assessed with Cox PH regression modeling (HR 1.50; 95% confidence interval 1.26–1.79) [18]. The distribution of patient and disease characteristics over time is described in File S10 and Table S3. More details regarding the clinical practice cohort and data analysis can be found in their publication.

2.6.2. Design and Setting of Dataset 2: Pembrolizumab Monotherapy

The second dataset contains survival data from two cohorts of patients with mNSCLC who were treated with first‐line pembrolizumab: one derived from the phase III KEYNOTE‐024 RCT (n = 154) [19] and one clinical practice cohort (n = 83) derived from electronic health records from seven non‐university Dutch teaching hospitals (Santeon Group). We used the algorithm developed by Guyot et al. to reconstruct survival data from the Kaplan–Meier curves of the RCT [17]. The RCT included patients treated and followed up between September 2014 and October 2015, with a median follow‐up of 11.2 months. The clinical practice cohort included patients treated and followed up between January 2015 and January 2019, with a median follow‐up of 15.5 months. Previous research from Cramer et al. (2021) demonstrated that the survival outcomes for patients treated in the clinical practice cohort were worse than the survival outcomes for patients treated in the RCT, as assessed with Cox PH regression modeling (HR 1.55; 95% confidence interval 1.07–2.25) [20]. The distribution of patient and disease characteristics over time is described in File S10 and Table S4. More details regarding the clinical practice cohort and data analysis can be found in their publication.

3. Results

3.1. Dataset 1: Survival Outcomes Associated With Pembrolizumab Plus Chemotherapy

3.1.1. Kaplan–Meier Curves

The Kaplan–Meier curves of overall survival outcomes associated with pembrolizumab plus chemotherapy for the RCT cohort and the complete clinical practice dataset (i.e., comprising of all patients and complete follow‐up) are presented in Figure 1.

FIGURE 1.

Kaplan–Meier curves of overall survival outcomes for patients treated with pembrolizumab plus chemotherapy in clinical practice versus the KEYNOTE‐189 RCT.

3.1.2. Model Diagnostics

The MCMC procedure demonstrated good convergence and resolution, as detailed in Table S1 and Figure S3. Figure S5 shows that the predictive prior checks demonstrated good alignment between the prior and the observed data, indicating that the chosen priors are appropriate. Figure S7a–j provides a visualization of the model fit at subsequent time intervals, through posterior predictive checks. Initially, there was a good overlap between the data and the posterior, indicating a good model fit. However, after 15 weeks of data accumulation, there was a consistent mismatch between the data and the posterior model fit, suggesting that the model may be unable to capture certain complexities in the data over time. This indicates that the model should be improved (e.g., through including additional covariates) before reliable estimates can be obtained and any meaningful conclusions can be drawn.

3.1.3. Posterior Distribution

Figure 2a shows the HR estimates for each consecutive model with credible intervals from 50% to 97.5%. Initially, in the first 15 months of data accumulation, the HR estimates fluctuated but showed an overall upward trend toward 2.20, indicating worse survival outcomes for patients treated in clinical practice compared to those treated in the RCT. As more data accumulated (i.e., more patients and longer follow‐up), HR estimates decreased and reached a plateau at around 1.5 after approximately 35 months. When all data were included, the HR was 1.54 (95% credible interval 1.33–1.78) (File S11 and Table S5).

FIGURE 2.

Hazard Ratio (HR) represents the hazard of a survival event occurring in the clinical practice cohort divided by that in the RCT cohort for patients treated with pembrolizumab plus chemotherapy (A) HR distribution over time with 50%, 75%, 95%, and 97.5% credible intervals. (B) The Bayes factor for competing hypotheses testing different HR thresholds for each model update. The gray circle indicates the point at which there is very strong evidence for either H₁ or H₀ for every further updated model.

3.1.4. Bayesian Hypothesis Testing

Figure 2b shows the Bayes Factor over time for different competing hypotheses, evaluating whether the observed HR falls above certain thresholds (ranging from HR > 1.00 to > 2.00) or below certain thresholds (ranging from HR < 1.00 to < 0.50). In the first 5 months of data accumulation, there was strong to very strong evidence that the observed HR is above 1, indicating worse survival outcomes in clinical practice. At 15 months of data accumulation, there was very strong evidence that the observed HR is above 2. After 15 months of data accumulation, the strength of evidence for observing HRs above 2 decreased, and when all data were included, there was strong evidence that the observed HR was above 1.0 and below 2.0, indicating that the survival of patients treated in clinical practice was worse than the survival for those treated in RCTs.

3.1.5. Prior Sensitivity Analyses

The prior sensitivity analysis, detailed in File S8, Figures S12 and S13, demonstrated that variations in the range of priors did not impact the results, confirming the robustness of the chosen prior. Similarly, the application of a different baseline hazard parameterization (using a Gompertz instead of a Weibull baseline hazard) did not affect the results, confirming robustness against baseline hazard parameterization (File S9). Dataset 2: Survival outcomes associated with pembrolizumab monotherapy.

The results of the Bayesian survival model for dataset 2 are reported in File S12. All model diagnostics were good, with posterior checks demonstrating a good fit between the model and observed data. After about 20 months of data accumulation, the model estimated precise HRs (Figure S20). When all data were included, the HR was 1.49 (95% credible interval 1.11–1.98) (File S11 and Table S6), indicating worse survival outcomes for patients treated in clinical practice than those treated in the RCT.

4. Discussion

We aimed to develop a Bayesian survival model that compares survival data from clinical practice that accumulates over time with static survival data from RCTs to investigate whether survival outcomes are similar, thereby providing rapid and easily interpretable results that can inform clinical and policy‐related decision‐making. Using two datasets comprising survival data from clinical practice and an RCT, we demonstrated that our Bayesian survival model enabled efficient comparisons of survival outcomes. For dataset 2, the model estimated precise HRs using part of the available data from clinical practice. The HR at the end of data accumulation was 1.49 for pembrolizumab monotherapy, indicating worse survival outcomes for patients treated in clinical practice than for those treated in the RCTs. In addition, these obtained estimates were equivalent to the ones obtained by traditional Cox PH regression modeling [18]. Furthermore, we demonstrated that sequential hypothesis testing with Bayes factors can be used for efficient and easily interpretable results that can inform clinical and policy‐related decision‐making, with very strong evidence for the HR being > 1.0 and strong evidence for HR being > 1.2 before the end of data accumulation. For dataset 1, the posterior model checks showed a misfit between the model and the data after approximately 15 months, indicating that the data generation process was not well captured by the model. Thus, the model fit should be improved before reliable estimates of this dataset can be obtained.

In dataset 1, we observed that the HR initially exceeded 2 in the first 15 months before decreasing to 1.54 by the end of data accumulation, suggesting worse survival outcomes for patients who started pembrolizumab plus chemotherapy shortly after it became available in clinical practice. This trend may reflect ‘channeling’ of novel treatments in clinical practice, where initially treated patients experience poorer outcomes due to use in more advanced disease or less optimized conditions. Over time, as protocols improve and clinicians gain experience, outcomes tend to improve [21]. To explore this phenomenon, another variable should be added to the model that explicitly captures the effect of treatment timing by linking the date of treatment initiation to its first availability. Importantly, this trend did not appear in the pembrolizumab monotherapy dataset, probably because patients receiving monotherapy in clinical practice represented a more homogenous population. As the first available first‐line immunotherapy, pembrolizumab monotherapy was probably administered with more caution, leading to stricter patient selection than for pembrolizumab plus chemotherapy. Such variation in the data between the two datasets highlights the importance of rigorously monitoring posterior checks in Bayesian modeling, since these checks help to identify the model's limitations in capturing certain complexities in the data over time. Furthermore, further model developments are needed to improve the model fit in dataset 1, such as incorporating a variable that reflects the timing of treatment initiation relative to its availability.

Provided a good model fit—as with all models for statistical analysis—the Bayesian survival model developed in this study offers two key advantages: (i) it facilitates earlier insights into potential differences in survival outcomes between accumulating clinical practice data and static RCT data, and (ii) it facilitates easy interpretation of results to support clinical and policy‐related decision‐making. First, the model provided precise HR estimates for differences in survival outcomes between clinical practice and the RCT before including all data, indicating its potential to facilitate insights as early as statistically justifiable. Precise HR estimates were achieved approximately 10 months before the end of data accumulation (total 30 months) in dataset 2. As far as we are aware, no studies have applied a Bayesian approach for this specific context. In one study, a Bayesian survival model was developed for a post hoc analysis of two clinical trials with overall survival as the endpoint. The authors demonstrated that sequential Bayesian analyses provided earlier insights into treatment effects than frequentist Cox PH regression, with precise estimates available 6 months before the trial's data lock point [22].

The second key advantage of the developed Bayesian approach is that it provides easily interpretable results to support clinical and policy‐related decision‐making. The model could generate early signals for treatment strategies that may be more or less effective in clinical practice than pre‐specified HR thresholds specific to the type of medicine and clinical setting. For example, when the model shows a good posterior fit and there is very strong evidence that survival in clinical practice is substantially worse than in the trial (e.g., HR > 2), this could trigger further investigation into underlying causes and inform adjustments to treatment strategies. Currently, our Bayesian model incorporates only one variable (clinical practice versus RCT), providing HR estimates for the overall patient population rather than for specific subgroups. Ideally, additional variables, such as patient, disease, treatment, and setting variables, could be added to the model to provide direct insights for specific subgroups of patients. Adding other variables could also provide insights into how differences between clinical practice and RCT populations impact the observed HR estimates, as patients in clinical practice are often older, less fit, and more comorbid, with less standardized treatments and follow‐up procedures. Although the model's explicit structure allows for this flexibility, the unavailability of individual patient data from RCTs limits the incorporation of such detailed characteristics for the current datasets. To still gain insight into the potential impact of patient and disease characteristics within the clinical practice population, we examined their distribution over time (File S10; Tables S3 and S4). The distributions remained relatively stable, suggesting that changes in these characteristics are unlikely to explain the observed variation in HR over time.

In this study, the model has been applied to two datasets with different oncological treatments, investigating whether survival outcomes are similar for patients treated in clinical practice and those in RCTs. Beyond this application, the model can evaluate other time‐to‐event outcomes, such as time‐to‐treatment failure or time‐to‐next treatment, across various treatments and populations. Additionally, the model can compare time‐to‐event outcomes between two treatment strategies within clinical practice, offering valuable insights when head‐to‐head RCT data are unavailable. However, this requires further development to the model to allow the incorporation of patients, disease, and treatment variables.

Despite its advantages, our Bayesian survival model has several limitations. First, the use of a simple model with one covariate limited our ability to explore the impact of other covariates on the observed survival outcomes. However, as the study's primary focus was to design a proof‐of‐concept Bayesian framework to evaluate its feasibility and potential value in comparative effectiveness studies, a simple model was chosen to keep modeling concise and easily reproducible. However, it did not always provide an optimal fit, suggesting that other covariates may need to be screened for relevance and incorporated into the model to better fit the data. Additionally, the high level of censoring toward the end of the dataset suggests that parametric models may be less suitable, underscoring the need to investigate more flexible approaches, such as semi‐parametric and non‐parametric models.

5. Conclusion

We developed a Bayesian survival model that compares survival data from clinical practice that accumulates over time with static survival data from RCTs to investigate whether survival outcomes are similar or different. Provided the posterior check shows an acceptable model fit, we demonstrated that sequential hypothesis testing with Bayes factors could be used to allow an accelerated route for informing clinical and policy‐related decision‐making. This approach provides a statistically sound method for stopping and inferring parameter estimates at the earliest possible time point (i.e., in contrast to the more traditional Cox modeling approach, where this is not possible because of practical and statistical concerns). The proposed visualizations allow for direct model interpretation by analyzing model fit and posterior confidence intervals around inferred parameter values. However, further developments to the model are needed to improve its ability to capture complexities in the data over time, such as incorporating a variable that captures the timing of treatment initiation relative to its availability. Additionally, incorporating patient, disease, and treatment characteristics into the model will facilitate investigating their impact on the observed survival outcomes.

Author Contributions

M.V.V.: conceptualization, data curation, investigation, methodology, visualization, writing – original draft and writing – review and editing. D.V.V.: conceptualization, formal analysis, investigation, methodology, software, visualization, writing – original draft and writing – review and editing. E.M.W.G.: conceptualization, supervision, methodology, funding acquisition and writing – review and editing. L.T.B.: conceptualization, investigation, supervision, methodology, writing – original draft and writing – review and editing.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Data S1.

Data Availability Statement

Project name: BayesianSurvival. Project home page: https://github.com/danielverschueren/BayesianSurvival, Programming language: Python.