Abstract
Background
Adaptive clinical trials enable modifications to the study design based on accumulating evidence. The Bayesian predictive probability approach offers a framework for estimating the likelihood of achieving a successful outcome in a future analysis, based on current interim data.
Objective
To estimate the predictive probability of success for binary outcomes in patients with Alzheimer's disease or Ataxia treated with NeuroEPO plus.
Methods
A retrospective Bayesian analysis was conducted using data from exploratory phase II trials as prior information for confirmatory phase III trials in Alzheimer's disease. Predictive probabilities were calculated at interim points with sample sizes of 50, 100, 150, and 176 patients.
Results
The analysis demonstrated that the trial could have been stopped early due to a high probability of success or failures before reaching the full planned sample size.
Conclusions
Bayesian predictive probability is a valuable tool for decision-making in rare diseases, particularly when alternative treatments are limited or ineffective, or when baseline heterogeneity affects outcomes unevenly. This approach enhances interim evaluations by incorporating historical or non-informative priors, allowing for more accurate and efficient trial designs.
Introduction
In recent years, the study of neurodegenerative diseases has increasingly focused on the development of innovative therapeutic strategies to slow cognitive decline and improve patients’ quality of life. One such approach is the use of NeuroEPO plus, a non-hematopoietic formulation of erythropoietin administered intranasally, which has shown promising neuroprotective and cognitive effects in patients with Alzheimer's disease, Parkinson's disease, and hereditary ataxias.1–3 Clinical trials such as the ATHENEA study have demonstrated the safety and efficacy of NeuroEPO plus in improving neuropsychological performance, with favorable cognitive and behavioral outcomes. 4 The therapeutic potential of NeuroEPO plus, along with its tolerability and minimal side effects,5,6 positions it as a candidate for broader clinical application.
However, conducting confirmatory trials in neurological disorders presents several challenges, particularly in designing studies with sufficient power to detect meaningful clinical effects in relatively small and heterogeneous populations. Traditional fixed-sample designs can be inefficient and may not accommodate the complexities of disease progression or treatment response variability. In this context, Bayesian predictive probability (PP) models offer a powerful framework for adaptive trial design, allowing for interim decision-making based on accumulating evidence.7,8 Unlike frequentist approaches, Bayesian methods can incorporate prior information—such as results from earlier phase trials—and continuously update the probability of success as data accrue.9,10
The utility of Bayesian PP becomes particularly relevant in trials involving NeuroEPO plus, where phase II data has already provided evidence of cognitive improvement in various neurodegenerative conditions.3,11 By integrating historical data, Bayesian designs reduce the ethical and financial costs of lengthy trials and can trigger early stopping for efficacy or futility, especially in scenarios where patient recruitment is slow or endpoint assessment is complex.12,13 Predictive analytics thus serve as a bridge between methodological rigor and clinical feasibility in neurotherapeutic research.
Moreover, the application of predictive analytics is supported by advancements in open-source statistical tools and simulation-based modeling. Software packages such as WinBUGS and MLPowSIM allow researchers to evaluate the impact of design choices on trial outcomes and optimize sample size based on realistic assumptions.13,14 These tools are critical when designing studies for populations with high variability or limited treatment options, as is the case with Alzheimer's disease, Parkinson's disease, and rare ataxias. The integration of Bayesian PP with such platforms ensures that trials are not only statistically robust but also adaptable to real-world constraints.15,16
Adaptive clinical trials allow adaptation based on new information acquired. The Bayesian predictive probability approach enables estimation of the likelihood of achieving a successful outcome in a future analysis, given current interim data. This paper explores the use of Bayesian predictive probability models in the context of NeuroEPO plus clinical trials. Using data from phase II studies as prior information, we performed retrospective Bayesian analyses to estimate the probability of trial success at different enrollment milestones. Our goal was to evaluate whether predictive probabilities could have informed earlier decisions to stop or continue the trial, thus enhancing efficiency without compromising scientific integrity. This approach illustrates the value of Bayesian adaptive design in neurodegenerative disease research, where timely and informed decisions are critical for both patient care and resource allocation.
Methods
Statistical model for binary outcomes
Suppose you have interim data from a randomized two-arm experiment with a binary outcome, and the following data have been observed:
Assume a prior θA and θB are independently distributed as beta(a,b).
Assume also that
These assumptions imply that, a posteriori,
Denote the future data by the following table:
At the end of the experiment, the total number of observations on arm A will be
The values NA and NB are the planned total samples sizes. Now,
This formulation allows for Bayesian predictive modeling of trial outcomes by integrating prior beliefs with observed and projected data.
Interim analysis for binary outcomes
The most common use of this software is performing an interim analysis of a clinical trial. This is useful, for example, when determining whether a trial should continue to enroll patients. This functionality can be accessed by going to the Interim Analysis menu as shown in Figure 1A. This will bring up the main form for this method as shown in Figure 1B.

Bayesian predictive probability workflow for binary interim analysis. Panel A shows the interface for initiating a binary interim analysis, where users specify study parameters and define interim checkpoints. Panel B illustrates the main analysis form, which allows input of event counts, prior distributions (flat or historical), and sample size parameters, generating predictive probability estimates for trial continuation or early termination.
Entering current data. For binary data, the current data section of the user interface is shown in Figure 1B. The “# of Success” is the current number of patients that have had a \success” according to the protocol definition and “# of Failures” is the corresponding number of non-successes. The totals will automatically be updated as you enter data.
Specifying priors. The prior parameters are entered into the portion of the user interface shown in Figure 1B. Typically, the prior parameters are chosen so that the prior mean, E(πi) = a/(a + b), is set to the historical probability of success. Parameter a can be interpreted as the prior number of success and b can be interpreted as the prior number of patient failures.
For convenience, a Parameter Solver utility has been provided to aid in specifying the prior. By right-clicking on either “Treatment A” or “Treatment B” you will get a menu which will activate the Parameter Solver. You may use the Parameter Solver to determine the priors for that arm based and export these values to the prior parameter fields.
Two prior distributions were considered in the Bayesian analysis. The first was an uninformative prior, specified as a uniform Beta distribution with hyperparameters α = 1 and β = 1 representing minimal prior knowledge about the treatment effect. The second was a refined accumulated prior derived from historical clinical data. For this, a Beta distribution was parameterized using a mean and variance estimated from relevant prior evidence, reflecting accumulated knowledge from earlier studies. Analyses were conducted using both priors, and the results were compared to evaluate the robustness of the conclusions. This dual-prior approach allowed assessment of whether the choice of prior meaningfully influenced predictive probabilities. Explanations of the prior derivation and interpretation were provided in accessible terms to facilitate understanding among readers without advanced Bayesian expertise.
Additional information. The planned number of patients on treatment A” is the number of patients that one expects to have been assigned treatment A at the end of patient accrual. This must be at least as large as the current number of patients on treatment A. Similar remarks apply to treatment B. If the planned number of patients on both A and B are equal to the current quantity of patients, the predictive probability will return either 1 or 0, depending on the value of P(πi > πj |data). See above for a discussion of the Bayesian and frequentist methods of analyzing the trial. In practice, the methods often give very similar results.
Clinical trials analyzed. Table 1 shows the report of four clinical trials of NeuroEPO plus in healthy volunteers, in patients with Parkinson's disease, spinocerebellar ataxia type 2 or Alzheimer's disease. The product was identified as NeuroEPO plus. In all studies, the intranasal route and the dose 1 mg were used; and the dose 0.5 mg was also evaluated. The frequency of drug administration and the duration of the intervention were variable. This table presents a chronological overview of clinical trials evaluating the safety and efficacy of intranasal NeuroEPO plus in different patient populations, from healthy volunteers to individuals with neurodegenerative disorders.
Clinical trials of the neuroprotective potential of NeuroEPO.
Phase I (RPCEC00000157): Conducted in 25 healthy volunteers, this study evaluated intranasal NeuroEPO plus at doses of 0.5 mg or 1.0 mg administered three times daily for four days. The treatment was well tolerated, with only mild adverse events (ADVs) that were resolved without intervention. Importantly, no hematological alterations were observed, indicating safety and no erythropoietic stimulation. Key finding: NeuroEPO plus is safe and well tolerated via nasal administration.
Phase I–II (RPCEC00000187): In 34 patients with spinocerebellar ataxia type 2 (SCA2), NeuroEPO plus or placebo was administered intranasally (0.5 mg or 1.0 mg) three times per week over six months. The study showed no severe adverse events and observed improvements in motor function and saccadic eye movements, with no hematological effects. Key finding: NeuroEPO plus is safe and may provide modest benefits in motor and cognitive symptoms in ataxia.
Phase II–III (RPCEC00000233 – mAkEUP study): In 102 patients with early-stage Parkinson's disease, participants received NeuroEPO plus (0.5 mg or 1.0 mg) or placebo intranasally three times weekly for nine months. Results demonstrated a dose-dependent improvement in cognitive function, with greater effects in younger patients and those with higher educational levels. Key finding: NeuroEPO plus positively impacts cognitive performance in Parkinson's disease, particularly in younger and better-educated individuals.
Phase II–III (RPCEC00000232 – ATHENEA study): A large trial with 174 patients with mild-to-moderate Alzheimer's disease assessed NeuroEPO plus using different dosing strategies over 48 weeks. The study found cognitive and behavioral improvements, supporting NeuroEPO's role in slowing cognitive decline. Key finding: NeuroEPO plus shows efficacy in attenuating the progression of cognitive impairment in Alzheimer's disease.
Parameter Solver. The Parameter Solver is a utility that will determine the distribution parameters of a random variable given either two quantiles or a specific mean and variance. The Parameter Solver is also available as a stand-alone program which supports more distribution families than just the beta and inverse gamma families used in this application. For more information, see https://biostatistics.mdanderson.org/SoftwareDownload/.
Results
Clinical trial NeuroEPO plus in Alzheimer's disease
Table 2 presents the results of a Bayesian predictive probability analysis using interim data from a confirmatory trial of NeuroEPO plus versus placebo, incorporating prior information from a Phase II subset (EC170, Sosa et al., 2023 4 ). The analysis was done with the first 35 patients included, then with 67, 98 and 116 patients included. It was found that the trial could be stopped before including the total number of patients and aimed to estimate the likelihood of trial success at different stages of patient enrollment, using both uninformative and cumulative priors. At the first milestone (n = 35; 18 treated versus 17 placebo), 83.3% of patients receiving NeuroEPO plus showed cognitive improvement (ADAS-Cog11 ≤ −4), compared to 41.2% in the placebo group (p = 0.010). At this early point, the Bayesian PP indicated a 97% chance of success using an uninformative prior and 99% using a cumulative prior. As sample size increased to 67, 98, and finally 116 patients, the treatment effect remained consistent or improved, with predictive probabilities reaching 100% at N = 99 and beyond. Notably, even with just 25% of the full sample size, the Bayesian approach identified a high probability of success, suggesting that the trial could have been stopped early. These findings highlight the value of Bayesian PP tools in adaptive trial designs, supporting more efficient and ethically sound decision-making in clinical research.
Bayesian PP provided a high probability of success with just the 25% of the sample size.
As observed in Table 2, the posterior probabilities with both uninformative and cumulative prior distributions are high, very close to or equal to 1, which is interpreted as a high probability of concluding in favor of the NeuroEPO plus 0.5 mg treatment in all estimated interim analyses. It begins with a Beta distribution with a mean and variance based on historical data and the hyperparameters were estimated with the parameter solver.
Clinical trial NeuroEPO plus in ataxia
Table 3 presents a Bayesian predictive probability (PP) analysis conducted using data from a confirmatory trial of NeuroEPO plus versus placebo, incorporating prior information from the Phase II study EC152.3 The outcome measure was SCAF (a functional clinical score), with a threshold of ≥ 0.75 considered indicative of clinical improvement. The analysis was performed at an early stage of enrollment, using both the intention-to-treat (ITT) and per-protocol (PP) populations. In the ITT analysis (n = 34; 17 patients per group), 35.3% of patients receiving NeuroEPO plus achieved clinical improvement compared to 11.8% in the placebo group. Although the Fisher's exact test p-value (0.225) did not reach statistical significance, the Bayesian predictive probability was high—96.2% using an uninformative prior and 96.4% using a cumulative prior. Similarly, in the per-protocol analysis (n = 29; 13 NeuroEPO plus versus 16 placebo), the response rate was 46.2% versus 12.5%, respectively. The p-value decreased to 0.092, and the predictive probabilities rose to 98.2% (uninformative prior) and 98.4% (cumulative prior). Despite the small sample size (only 25% of the planned enrollment), the Bayesian PP analysis suggested a high probability of eventual trial success. This supports the potential for early trial termination and highlights the utility of Bayesian methods for adaptive decision-making, even when conventional statistical significance has not yet been reached. The analysis was done with the first 50 patients included, then with 100, 200 and 405 patients. It was found that the trial could be stopped before including the total number of patients.
Bayesian PP provided a high probability of success with just the 25% of the sample size.
As appreciated in Table 3, the posterior probabilities with both uninformative and cumulative prior distributions are high, very close to or equal to 1, which is interpreted as a high probability of concluding in favor of the NeuroEPO plus 0.5 mg treatment in all estimated interim analyses. The hyperparameters of the Beta distribution were estimated with the parameter solver using a mean and variance based on historical data.
Discussion
The results of this retrospective Bayesian analysis suggest that the predictive probability approach can be an effective and efficient strategy for interim decision-making in clinical trials involving NeuroEPO plus for neurodegenerative disorders such as Alzheimer's disease and ataxia. The possibility of stopping trial early due to high predictive probability of success not only reduces exposure to potentially ineffective treatments but also allows for better resource allocation and faster clinical translation in rare or high-need populations.
Our findings align with the theoretical framework outlined by Saville et al. 7 and Wathen et al., 8 who demonstrated the utility of Bayesian predictive probabilities for adaptive monitoring in clinical trials. In our study, using interim data and incorporating either flat or historical priors, such as those derived from earlier phase II trials, allowed for robust estimations of future success. This is particularly relevant in contexts where frequentist approaches may fail to capture the uncertainty and dynamic nature of evolving trial data.9,12
From a statistical modeling perspective, the Bayesian approach offers flexibility in handling heteroscedasticity and imbalances in baseline characteristics, which are common in trials involving patients with neurodegenerative conditions. As demonstrated by Browne et al., 13 simulation-based methods are valuable for modeling sample size requirements under random effects, and our analysis supports this by showing the potential to adjust the trial trajectory in response to emerging data. Tools such as WinBUGS 12 and PSPP, 14 as referenced in their respective manuals, are critical to implementing these models accurately and reproducibly.
Clinically, the outcomes observed in prior studies of NeuroEPO plus—such as improved cognitive performance and behavioral outcomes in Alzheimer's disease and Parkinson's disease patients2,4,5 —strengthen the rationale for using early-phase data to inform subsequent trials. This approach ensures that promising treatments like NeuroEPO plus can be evaluated more efficiently, particularly when patient recruitment is limited, and the burden of disease progression is high.3,11 Importantly, our findings support broader integration of predictive modeling in clinical trial design, especially for neurological conditions where inter-individual variability and limited therapeutic alternatives are significant concerns.
Predictive probability methods offer a valuable enhancement to traditional clinical trial methodology. When applied with rigor and supported by high-quality prior data, they provide a more accurate and efficient framework for decision-making, especially in complex and resource-limited therapeutic areas. Future studies should continue to explore the integration of Bayesian predictive tools across diverse clinical contexts to validate their impact on trial outcomes and ethical conduct. 17
Yoshimoto et al. 18 proposed a Bayesian predictive probability framework for single-arm phase II trials that jointly evaluates binary efficacy and safety endpoints using a bivariate index vector. This method enhances trial efficiency by enabling adaptive decisions, such as early stopping for success or futility, while accounting for both treatment benefits and risks. Through simulation studies, the authors show that the approach maintains strong operating characteristics and offers a more transparent assessment of efficacy-safety trade-offs compared to traditional designs. Although the method assumes binary outcomes and requires careful prior specification, it provides a flexible and ethically sound tool for early-phase clinical trials.
On the other hand, Turner et al. 19 explored practical Bayesian approaches for determining sample size in non-inferiority trials with binary outcomes, addressing challenges in balancing statistical rigor with feasibility. Their methods incorporate prior information and predictive distributions to assess the probability of declaring non-inferiority, offering greater flexibility than traditional frequentist calculations. The authors illustrate how Bayesian criteria can guide more efficient and ethically sound trial designs, particularly when historical data are available. While the approach requires careful prior specification and may be computationally intensive, it enhances decision-making in early planning stages of non-inferiority studies.
Traditional frequentist interim monitoring, such as group-sequential designs, relies on pre-specified statistical boundaries (e.g., O’Brien–Fleming, Pocock) to decide whether to stop a trial early for efficacy or futility while controlling the type I error. In contrast, the Bayesian predictive probability (PPoS) approach estimates the probability that the trial will ultimately meet its success criteria if continued to full enrollment, given the current interim data. This forward-looking perspective integrates parameter uncertainty and future data projections, often leading to earlier, clinically intuitive stopping decisions without compromising statistical rigor.20,21,22
While posterior probability quantifies the likelihood that a treatment is effective given the data already collected, predictive probability projects the chance of success with future data. The posterior addresses “What is the probability of efficacy now?” whereas predictive probability addresses “What is the probability we will declare success if we continue?” This distinction is critical in interim monitoring: high posterior probability may coexist with low predictive probability if future success is unlikely, supporting early futility stopping.21,22
Predictive probability offers several advantages over frequentist conditional power and posterior probabilities alone. It provides an intuitive probability of trial success that stakeholders can easily interpret, accounts for uncertainty in both current and future data, and often reduces trial duration and patient exposure. Comparative studies have shown that Bayesian predictive designs can yield similar or improved efficiency compared with frequentist group-sequential methods.20,21,22
Conclusions
The Bayesian predictive probability can be particularly valuable for decision-making in the context of rare diseases, where alternative treatments may be ineffective, unavailable, or inaccessible. They are also useful when heteroscedasticity is present and baseline variables impact outcomes in non-uniform ways. The predictive probability approach allows interim analyses to incorporate either historical prior information or non-informative (flat) priors, enabling more flexible and responsive trial designs. Leveraging all available information improves the accuracy of outcome predictions and supports more informed, timely decisions regarding trial continuation or early termination.
Footnotes
Acknowledgements
The authors express their deepest gratitude to the patients and their families who generously participated in these clinical trials. Their willingness to contribute, often in the context of challenging health conditions, made this research possible.
Ethical considerations
This study was conducted in accordance with ethical standards. All participants provided informed consent prior to inclusion in the study.
Consent to participate
All procedures performed in these studies were conducted in accordance with the ethical standards and with the 1964 Helsinki Declaration and its later amendments. Written informed consent was obtained from all individual participants included in the trials.
Consent for publication
Not applicable.
Author contribution(s)
Funding
The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by CIM (Center of Molecular Immunology) and La Universidad de Las Américas.
Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Data availability statement
The data supporting the findings of this study are available from the corresponding author upon reasonable request.
