A Review on Bridging CAM and Modern Statistical Tools: An Introduction to Bayesian Methods

Abstract

Complementary and Alternative Medicine (CAM) modalities, encompassing practices such as acupuncture, yoga, and herbal therapy, are experiencing a notable increase in their utilization as supplementary or alternative options to conventional medical interventions. Nonetheless, the scientific appraisal of these modalities is frequently hindered by methodological issues, including the personalization of treatments, limited sample sizes, and multifaceted, multidimensional outcomes. Such constraints often render traditional frequentist statistical techniques inadequate for evaluating the efficacy of CAM interventions. This review highlights the potential of Bayesian statistical approaches as a transformative solution for the study of CAM.Through an extensive review of existing literature and the development of hypothetical models, we illustrate the advantages of Bayesian methodologies in tackling the specific challenges associated with CAM research. Review findings include the capacity to integrate prior knowledge derived from historical and observational data, thereby effectively addressing issues related to small sample sizes and facilitating adaptive trial designs that enhance resource allocation.Furthermore, Bayesian hierarchical models adeptly accommodate heterogeneity across varied patient demographics and therapeutic modalities, while allowing for the seamless integration of multidimensional outcomes into a cohesive analytical framework. Despite challenges such as computational intensity and the subjective nature of prior selection, advancements in computational software and educational resources are improving the accessibility of Bayesian methodologies. This paradigm presents a robust, evidence-based framework for the validation of CAM therapies, thereby promoting their incorporation into clinical practice. By effectively addressing methodological intricacies, Bayesian statistics has the potential to elevate CAM research to align with the standards of contemporary evidence-based medicine, thereby encouraging wider acceptance within healthcare systems.

Introduction

I. INTRODUCTION

Complementary and Alternative Medicine (CAM) encompasses a wide array of healthcare methodologies and practices that fall outside the traditional boundaries of conventional medical paradigms, thereby incorporating diverse approaches that have not been historically recognized within the conventional medical framework. The CAM practice comprises of various modalities including, but certainly not limited to, acupuncture, homeopathy, herbal medicine, chiropractic care, meditation, yoga, naturopathy and Traditional Chinese Medicine (TCM), each of which is rooted in distinct historical and cultural backgrounds(1). The defining feature of CAM lies in its holistic perspective, which significantly emphasizes the intricate interrelationship among the body, mind, and spirit, thereby striving to achieve a comprehensive state of overall health and well-being. In contrast to conventional medicine, which frequently emphasizes treatments that are specific to particular diseases or conditions, CAM adopts a more individualized approach that is meticulously tailored to address the unique needs, preferences, and circumstances of each individual patient (2).

The World Health Organization (WHO) acknowledges the vital role that CAM plays within global healthcare systems, especially in geographical regions where traditional healthcare practices are deeply embedded within the fabric of cultural traditions and societal norms (3). Practitioners of CAM often employ a combination of diverse techniques, which may include natural therapies and lifestyle modifications, to proactively prevent illness and enhance overall health; thus, positioning CAM as a complementary resource that can work synergistically alongside mainstream medical methodologies (1).

Despite the growing popularity and acceptance of CAM among various populations, the integration of these practices into the realm of evidence-based medicine encounters numerous significant challenges that hinder its broader acceptance within the medical community. A primary concern pertains to the absence of standardized methodological frameworks that can effectively evaluate CAM interventions, which are often characterized by their multifaceted and context-dependent nature, rendering traditional evaluation mechanisms less applicable (4).

Randomized controlled trials (RCTs), which are widely regarded as the gold standard for establishing evidence within conventional medical research, frequently fail to adequately capture the intricate and individualized aspects of CAM therapies, thereby limiting the ability to draw definitive conclusions regarding their efficacy (2).Moreover, there exists a notable discourse within the scientific community concerning the fundamental mechanisms that regulate Complementary and Alternative Medicine (CAM) practices, which presents an additional challenge to its acceptance and incorporation. For instance, phenomena such as the placebo effect and the intricacies of patient-practitioner dynamics are often disregarded as merely anecdotal evidence, despite their potential therapeutic ramifications and significant contributions to patient outcomes (5). Furthermore, a considerable number of CAM studies are susceptible to scrutiny due to their limited sample sizes, considerable variability in treatment methodologies, and inadequate reproducibility, all of which further complicate the effort to establish a solid and rigorous evidence base (6).

Traditional statistical methodologies, particularly frequentist approaches, predominantly rely on the application of large sample sizes, controlled experimental settings, and fixed hypotheses, all of which often prove to be impractical when applied to the unique context of CAM research. For example, frequentist statistical models necessitate the establishment of a strict null hypothesis, which inherently limits their capacity to explore the dynamic, adaptive, and often personalized nature of CAM interventions (7). Additionally, the conventional RCT framework may not adequately encapsulate the individualized outcomes associated with CAM, which frequently fluctuate based on a multitude of factors including patient characteristics, cultural backgrounds, and contextual influences (2).Furthermore, the dependence on p-values within frequentist statistical methodologies has encountered substantial scrutiny, particularly due to its inadequacy in producing significant insights within the domain of Complementary and Alternative Medicine (CAM) research. For example, the dichotomous interpretation of statistical significance thresholds frequently results in a reductive acceptance or rejection of therapeutic interventions without sufficiently accounting for the broader clinical context or the specific variables pertinent to the individual patient (8). This intrinsic limitation establishes a considerable impediment to attaining a holistic comprehension of the intricate effects of CAM therapies, which frequently do not align neatly with the binary framework delineated by frequentist analysis.

Conversely, probabilistic approaches such as Bayesian statistics offer a more versatile and nuanced analytical paradigm that is particularly advantageous for confronting the complexities inherent in CAM research. Bayesian methodologies enable researchers to integrate prior knowledge, encompassing historical data, expert perspectives, and findings from observational studies, into their statistical evaluations, thereby enhancing the overall interpretation of the data (5). This attribute is especially beneficial within the context of CAM research, where the evidence often arises from a heterogeneous range of sources, including traditional knowledge and anecdotal accounts that may not adhere to conventional scientific frameworks (4).

A. Bayesian Statistics: A Contemporary Framework for Complementary and Alternative Medicine (CAM)

1) Key Principles of Bayesian Methods and How They Differ from Frequentist Approaches

The foundation of Bayesian statistics is firmly grounded in the principles outlined by Bayes' theorem, which serves as a mathematical construct for the calculation of the probability of a particular event occurring by taking into account both previously held beliefs and the evidence that has been observed. In stark contrast to the methodologies employed by frequentist approaches, which depend exclusively on the data derived from sample populations to draw conclusions, Bayesian methods integrate prior probabilities into their analyses, thereby facilitating a more all-encompassing and contextually aware evaluation of the data at hand (6). The Bayesian analytical process is characterized by three components that are essential for its application:

1. Prior probability: This represents the initial beliefs or knowledge that researchers possess regarding the parameter of interest before any new evidence is considered. 
2. Likelihood: The probability linked to the observation of the current dataset, conditional upon the veracity of the parameter under examination.
3. Posterior probability: This denotes the revised beliefs about the parameter after the new evidence has been taken into account,
   reflecting an updated understanding based on the integration of prior knowledge and observed data.

Bayes’ theorem can also be articulated in a mathematical framework as follows:

P(H?D): This symbolizes the posterior probability, which is the recalibrated probability of the hypothesis H subsequent to the observation of data D.

P(D?H): This stands for the likelihood, which encapsulates the probability of obtaining the data D if the hypothesis H is indeed accurate.

P(H): This represents the prior probability, which mirrors the initial belief concerning H prior to the analysis of any data.

P(D): This refers to the marginal likelihood, which functions as a normalizing constant that ensures the total probabilities sum to one.

This iterative and dynamic framework empowers researchers to continuously refine and enhance their understanding as additional data emerges, thereby rendering Bayesian techniques particularly well-suited for studies in the realm of CAM, where the available evidence is often subject to incremental evolution over time (5).

For instance, within the context of CAM, the prior might consist of historical data pertaining to the effectiveness of acupuncture as a treatment for chronic pain, while the likelihood could signify the observable outcomes documented in a recent research study, and the posterior would encapsulate the recalibrated probability reflecting the treatment's efficacy based on the new evidence (4).

2) Bayesian Methods are Suited to CAM's Holistic and Individualized Nature

The principles inherent in Bayesian methodologies resonate profoundly with the foundational tenets of CAM, which emphasize both personalization and adaptability in treatment approaches. CAM therapies characteristically involve the customization of interventions to meet the unique needs of individual patients, a process that can be adeptly modeled through the application of Bayesian techniques. For example, Bayesian models have the capacity to integrate patient-specific variables, including but not limited to genetic predispositions, lifestyle choices, and personal preferences, in order to predict treatment outcomes, thereby offering a more tailored assessment compared to traditional statistical methods (4).

Furthermore, Bayesian statistics demonstrate exceptional proficiency in scenarios characterized by small sample sizes, a frequent challenge encountered in the research of CAM modalities. By effectively utilizing prior knowledge in conjunction with observational data, Bayesian techniques can yield significant insights even when confronted with constrained datasets, thereby enhancing the credibility and validity of studies conducted in the CAM field (2). This unique capability positions Bayesian statistics as an indispensable instrument for the advancement of evidence-based practices in CAM, all while honoring and respecting its holistic philosophical underpinnings.

II. METHODS

This review aims  to comprehensively investigate and elucidate the profound significance and implications of Bayesian statistics within the specialized domain of research pertaining to Complementary and Alternative Medicine (CAM). The systematic search methodology employed a meticulously crafted combination of highly specific keywords and Boolean operators, which were strategically utilized to optimize the relevance and precision of the results obtained from freely accessible academic databases that house a plethora of scholarly articles. The aforementioned keywords encompassed terms such as "Bayesian statistics," "Complementary and Alternative Medicine," "CAM validation," "Bayesian adaptive trials," and "Bayesian networks in healthcare," thereby ensuring a targeted and thorough exploration of the intersection between these two fields of study. Furthermore, Boolean operators, including "AND" and "OR," were judiciously applied to refine the search parameters further, thereby capturing the intricate intersections that exist between CAM research and the methodologies rooted in Bayesian statistics.

Inclusion and Exclusion Criteria for Studies

The inclusion criteria were designed to focus on studies that directly examined the application of Bayesian methods in CAM research. Articles were included if they:

1. Discussed Bayesian statistical frameworks relevant to healthcare or CAM.
2. Provided case studies, clinical trials, or theoretical discussions on Bayesian applications in CAM.
3. Were published in peer-reviewed journals.

Exclusion criteria included studies that:

1. Focused solely on frequentist methods without comparison to Bayesian approaches.
2. Lacked sufficient methodological detail on Bayesian frameworks.
3. Were published in non-peer-reviewed or predatory journals.

A narrative synthesis approach was systematically employed to effectively organize and analyze the findings that emerged from the selected studies. This particular method places significant emphasis on thematic analysis, which is instrumental in identifying and elucidating recurring patterns, themes, and insights that may arise across a diverse array of sources. It is especially well-suited for the synthesis of literature that spans multiple academic disciplines, such as the interrelated fields of CAM and Bayesian statistics.

The synthesis process was conducted through a series of methodical steps for identifying key applications of Bayesian Statistics in CAM Research that included the following:

Data Extraction: This initial step involved the meticulous extraction of comprehensive details concerning the objectives, methodologies, and results of the studies selected, with a particular emphasis placed on the application and utilization of Bayesian approaches.

Categorization: In this step, the extracted studies were systematically grouped into thematic categories, which included but were not limited to Bayesian adaptive trials, Bayesian networks specifically within CAM research, and models tailored for personalized treatment approaches.

Integration: The final step entailed the summarization of critical insights into how Bayesian methodologies effectively address the distinctive challenges inherent to CAM, such as the issues posed by small sample sizes and the complexities associated with multifaceted interventions.

Bayesian methodologies can be adeptly and effectively applied to real-world scenarios within the realm of CAM, where patient-centered approaches and adaptive methodologies are of paramount importance and relevance.

Personalized Treatment Models: Bayesian frameworks possess the capability to incorporate a wide array of individual patient characteristics, including genetic predispositions or lifestyle factors, in order to accurately predict the probability of success for various CAM interventions, such as herbal therapies or acupuncture techniques.

Adaptive Clinical Trials: In the context of trials that evaluate the efficacy of CAM therapies, Bayesian methodologies empower researchers to make informed adjustments to the trial design based on interim data, thereby enhancing the overall efficiency of the study and reducing the consumption of valuable resources.

Modeling Uncertainty: Bayesian networks have the potential to model intricate relationships that exist among various variables, such as the level of patient trust, perceived effectiveness, and the frequency of utilization of CAM therapies, as evidenced by studies focused on Traditional Chinese Medicine.

These diverse applications underscore the capacity of Bayesian methodologies to effectively address the unique and multifaceted challenges that are characteristic of CAM research, thereby providing robust and actionable insights that can be immensely beneficial to both practitioners and researchers operating within this field.

III. RESULTS

A. Bayesian Networks for Understanding CAM Usage

Bayesian networks have been recognized as an exceptionally robust analytical instrument for the intricate modeling of the multifaceted relationships that are inherently present in the domain of Complementary and Alternative Medicine (CAM) research, with a particular emphasis on elucidating patient behaviors and the various usage patterns that characterize this field of study. For instance, in their 2021 research, Eigenschink et al. undertook the development of a comprehensive Bayesian network model specifically designed to investigate public perceptions regarding Traditional Chinese Medicine (TCM) within the geographical context of Austria. This sophisticated model effectively integrated a diverse array of factors including, but not limited to, the level of awareness among the public, the degree of trust placed in practitioners of TCM, and the perceived scientific validity of the treatment modalities, all of which collectively contributed to the prediction of trends associated with CAM usage. Such an innovative approach empowered researchers to quantitatively assess the complex interplay between these various variables, thereby providing a nuanced and detailed understanding of the myriad factors that influence the adoption of CAM practices (9).

In another study, Bayesian networks were utilized to conduct a thorough analysis of the various factors that contribute to patient satisfaction levels concerning CAM therapies. By meticulously incorporating a wide range of data encompassing patient-practitioner interactions, treatment outcomes, and pertinent demographic variables, the model yielded actionable insights that could be effectively harnessed to enhance the quality and effectiveness of CAM services (7). These examples distinctly underscore the capacity of Bayesian networks to facilitate a comprehensive and holistic analysis of CAM, thereby reflecting the fundamentally patient-centered philosophy that underpins this approach to healthcare.

B. Bayesian Adaptive Designs in Clinical Trials for CAM Interventions

Clinical trials for CAM therapies often face challenges such as small sample sizes and high variability in treatment protocols. Bayesian adaptive designs offer a solution by allowing researchers to modify trial parameters in real time based on interim data. For instance, Herman et al. (2005) discussed the use of Bayesian adaptive designs in trials evaluating acupuncture for chronic pain. These designs enabled the reallocation of participants to more effective treatment arms, optimizing resource utilization while maintaining statistical rigor.

Bayesian adaptive trials are particularly suited for exploratory CAM research, where flexibility and iterative learning are crucial. They provide the ability to test multiple hypotheses simultaneously and incorporate patient-specific factors, reducing the time and cost associated with traditional trial designs (5).

C. Quantifying Uncertainty and Personalization in CAM

Examples of Bayesian Models Used for Personalized Treatment Predictions

Bayesian models excel in capturing the variability and individualization central to CAM practices. For example, Berna et al. (2019) utilized Bayesian frameworks to predict the effectiveness of herbal medicine based on patient-specific factors such as age, lifestyle, and genetic predispositions. The model updated probabilities iteratively, providing personalized treatment recommendations that aligned with the holistic approach of CAM.

Another example comes from studies on homeopathy, where Bayesian models were used to evaluate the likelihood of treatment success for specific symptoms. By integrating historical data with patient-reported outcomes, the models offered predictions tailored to individual patients, enhancing the precision of CAM interventions (2).

Insights from Studies Demonstrating How Bayesian Methods Enhance CAM Outcomes

Studies have shown that Bayesian methods not only improve the accuracy of predictions but also enhance patient outcomes. For instance, Bayesian frameworks applied to acupuncture studies demonstrated superior efficacy when treatment protocols were personalized based on Bayesian inference. This approach allowed practitioners to refine interventions in real time, leading to improved symptom management and patient satisfaction (4).

Similarly, Bayesian networks analyzing public perceptions of CAM therapies revealed key insights into the role of trust and education in influencing treatment outcomes. These findings have informed strategies for improving CAM accessibility and acceptance among diverse populations (9).

D. Comparison with Frequentist Approaches in CAM Studies

Limitations of Frequentist Methods in Capturing the Dynamic and Individualized Nature of CAM

Frequentist statistical methods, which rely on fixed hypotheses and p-value thresholds, are often ill-suited for CAM research. These methods struggle to account for the dynamic and individualized nature of CAM practices, where interventions are tailored to each patient's unique needs. For example, frequentist analyses in CAM studies often yield inconclusive results due to small sample sizes, variability in treatment protocols, and the difficulty of standardizing holistic interventions (5).

Additionally, the reliance on p-values in frequentist methods has been criticized for its binary interpretation of significance, which fails to capture the probabilistic nature of CAM outcomes. This limitation is particularly problematic in exploratory research, where the goal is to generate hypotheses rather than test predefined ones (8).

E. Bayesian Models as a Solution to These Limitations

Bayesian models address these limitations by providing a flexible and iterative framework for analyzing CAM data. Unlike frequentist methods, Bayesian approaches allow for the integration of prior knowledge, such as historical evidence and expert opinions, with new data. This capability is particularly valuable in CAM research, where traditional evidence hierarchies often exclude anecdotal or experiential knowledge (4).

For instance, Bayesian adaptive trials in CAM have demonstrated the ability to optimize resource allocation and improve trial efficiency, even with small sample sizes. By updating probabilities in real time, these models provide a more accurate and nuanced understanding of treatment effects, enabling researchers to capture the complexity of CAM interventions (7).

In comparative studies, Bayesian methods consistently outperform frequentist approaches in their ability to model uncertainty and provide actionable insights. This superiority has positioned Bayesian frameworks as a cornerstone for advancing evidence-based CAM research, bridging the gap between traditional practices and modern scientific methodologies (6).

IV. DISCUSSION

A. Strengths of Bayesian Approaches in CAM Research

One of the primary advantages of Bayesian methodologies lies in their capacity to synthesize existing knowledge within statistical frameworks. In Complementary and Alternative Medicine (CAM), where therapeutic approaches frequently draw upon historical practices and experiential insights, Bayesian techniques empower researchers to amalgamate this antecedent information with emerging data, thereby fostering a more thorough analytical paradigm (5).

Moreover, Bayesian methodologies facilitate the continual refinement of evidence as novel data becomes accessible. This adaptive characteristic is of paramount importance in CAM research, wherein interventions are frequently exploratory and subject to evolution over time. For example, Bayesian models employed in acupuncture studies have effectively enhanced treatment protocols by integrating real-time patient outcomes, resulting in heightened efficacy and tailored patient care (2).

Another significant merit of Bayesian approaches is their ability to quantify uncertainty, thereby yielding nuanced perspectives on treatment effects. This capability is particularly critical in CAM investigations, where limited sample sizes and variability in outcomes can render conventional statistical techniques less reliable (4). By quantifying uncertainty, Bayesian frameworks present a more lucid depiction of the probability of therapeutic success, thereby enabling practitioners to make well-informed decisions.

Importantly, Bayesian models align seamlessly with CAM’s holistic and patient-centered principles. CAM therapies often prioritize individualized care, emphasizing the interplay of physical, emotional, and environmental factors. Bayesian frameworks accommodate this complexity by allowing for the inclusion of multiple variables and their interactions, making them a natural fit for CAM’s philosophy of integrative healthcare (9,10).

B. Challenges and Barriers to Adoption

Despite their strengths, Bayesian methods face several challenges that may hinder their adoption in CAM research. One significant barrier is the computational complexity of Bayesian analyses. Unlike frequentist methods, which rely on simpler calculations, Bayesian models often require advanced programming skills and substantial computational resources, particularly when dealing with large datasets or complex models (7).

Another challenge lies in the selection and interpretation of prior probabilities. While the inclusion of prior knowledge is a strength of Bayesian methods, it can also introduce biases if the priors are not chosen carefully or are overly subjective. In CAM, where evidence is often anecdotal or context-dependent, the risk of bias in prior selection may be heightened (6).

The limited availability of training programs in Bayesian reasoning further exacerbates these challenges. Many CAM practitioners and researchers lack formal training in advanced statistical methods, creating a knowledge gap that may impede the broader adoption of Bayesian approaches in the field (4).

C. Integration of Bayesian Statistics into CAM Practice

To overcome these challenges, there are significant opportunities to integrate Bayesian reasoning into CAM practice. Training programs designed specifically for CAM practitioners can bridge the knowledge gap, equipping them with the skills needed to understand and apply Bayesian methods.

Collaborative approaches are also essential for enhancing the scientific credibility of CAM. Partnerships between CAM experts, statisticians, and biomedical researchers can facilitate the development of rigorous studies that leverage Bayesian methods. For instance, collaborative teams can work together to design adaptive trials or develop Bayesian models that address specific CAM challenges, such as small sample sizes or complex interventions.

D. Future Directions for Research and Practice

The future of Bayesian methods in CAM research lies in the development of user-friendly tools that simplify complex analyses. Software platforms with intuitive interfaces and pre-built templates for Bayesian modeling can make these methods more accessible to CAM practitioners without advanced statistical training.

Expanding the applications of Bayesian methods is another critical direction for future research. Beyond efficacy studies, Bayesian approaches can be applied to cost-effectiveness analyses, enabling policymakers to evaluate the economic value of CAM interventions. Real-world observational studies are another promising area, where Bayesian models can account for variability in treatment settings and patient populations, providing robust insights into the practical effectiveness of CAM therapies.

By addressing these opportunities, Bayesian methods can further bridge the gap between CAM practices and modern evidence-based paradigms, paving the way for their integration into mainstream healthcare systems.

Conclusion

Bayesian methods represent a transformative statistical framework for CAM research, offering tools to integrate prior knowledge, update evidence iteratively, and quantify uncertainty. These features make Bayesian approaches uniquely suited to the dynamic, individualized, and holistic nature of CAM practices. Their ability to address the limitations of traditional statistical methods positions them as a cornerstone for advancing evidence-based CAM research.

References

[1] Nguyen LT, Davis RB, Kaptchuk TJ. Use of complementary and alternative medicine and self-rated health status: results from a national survey. J Gen Intern Med. 2011;26(4):399-404. doi:10.1007/s11606-010-1542-3 [2] Herman PM, Craig BM, Caspi O. Is complementary and alternative medicine (CAM) cost-effective? A systematic review. BMC Complement Altern Med. 2005;5(1):11. doi:10.1186/1472-6882-5-11 [3] Traditional, complementary and integrative medicine [Internet]. Who.int. [cited 2024 Dec 29]. Available from: https://www.who.int/health-topics/traditional-complementary-and-integrative-medicine [4] Chiappelli F, Prolo P, Rosenblum M, et al. Evidence-Based Research in Complementary and Alternative Medicine II: The Process of Evidence-Based Research. Evid Based Complement Alternat Med. 2006;3(4):477-482. doi:10.1093/ecam/nek017 [5] Rutten, L. (alb), & Stolper, E. (cf). (2015). Complementary alternative medicine, plausibility and statistics. European Journal of Internal Medicine, 26(4), e5. [6] Berna F, Göritz AS, Mengin A, Evrard R, Kopferschmitt J, Moritz S. Alternative or complementary attitudes toward alternative and complementary medicines. BMC Complement Altern Med [Internet]. 2019;19(1):83. Available from: http://dx.doi.org/10.1186/s12906-019-2490-z [7] Pandolfi M, Carreras G. Why Current Statistics of Complementary Alternative Medicine Clinical Trials is Invalid. J Clin Med. 2018 Jun 7;7(6):138. doi: 10.3390/jcm7060138. PMID: 29880738; PMCID: PMC6025062. [8] Ramsey SD, Zeliadt SB, Blough DK, Fedorenko CR, Fairweather ME, McDermott CL, Penson DF, Van Den Eeden SK, Hamilton AS, Arora NK. Complementary and alternative medicine use, patient-reported outcomes, and treatment satisfaction among men with localized prostate cancer. Urology. 2012 May;79(5):1034-41. doi: 10.1016/j.urology.2012.01.023. PMID: 22546381; PMCID: PMC3489914. [9] Eigenschink M, Bellach L, Leonard S, Dablander TE, Maier J, Dablander F, et al. Cross-sectional survey and Bayesian network model analysis of traditional Chinese medicine in Austria: investigating public awareness, usage determinants and perception of scientific support. BMJ Open [Internet]. 2023 [cited 2024 Dec 29];13(3):e060644. Available from: https://bmjopen.bmj.com/content/13/3/e060644 [10] Goligher EC, Heath A, Harhay MO. Bayesian statistics for clinical research. Lancet. 2024 Sep 14;404(10457):1067-1076. doi: 10.1016/S0140-6736(24)01295-9. PMID: 39277290.

Copyright

Copyright © 2025 Shashi Shekhar Singh, Setu Singh Gehlot. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.