Synthesis Methods for Meta-Analysis: A Scoping Review

1. INTRODUCTION

Meta-analysis or “analysis of analyses” [1, 2] refers to results obtained by combining and analyzing data from different studies conducted on similar research topics [3]. In statistical terms, meta-analysis is defined as a technique for amalgamating, summarizing, and reviewing previous quantitative research [4]. The primary objective of meta-analysis is to increase statistical inference and provide more precise estimates of effect size by pooling data from multiple smaller studies [5]. Additionally, meta-analysis typically leads to narrower confidence intervals and more stable effect estimates, reflecting stronger evidence than any single study can provide [6]. However, meta-analytical methods rely on sufficient, consistent data across individual studies [7]. Missing or partial reporting, such as lack of correlations or variances, limits the ability to include such studies in quantitative synthesis [8, 9]. Without sufficient overlap in reported outcomes, combining results statistically becomes inconsistent or biased [10, 11].

To address this problem, Samsa et al. proposed a multivariate meta-analytic modeling method called “synthesis analysis,” which refers to the challenge of integrating information from studies that lack complete multivariate data [12]. They used the term synthesis for their new statistical method even though the general idea of “synthesis in research” is understood as the integration and interpretation of multiple pieces of evidence to produce a new, coherent understanding [13]. In statistics, synthesis analysis is a methodology that constructs a multivariate regression model by integrating univariate regression coefficients and pairwise correlations from multiple independent studies or data sources [4]. This method is particularly useful in settings where individual studies are incomplete, reporting only subsets of predictors or univariate associations. It enables researchers to estimate comprehensive multivariate relationships when no single dataset contains all predictors of interest together with the outcome variable [12].

Over the years, research on synthesis analysis has been scattered across methodological and applied domains. In 2005, the pioneering work on synthesis analysis described a methodological innovation which used widely reported univariate estimates and correlations for continuous outcomes [12]. The newly emerged synthesis method was extended in 2009, improving the method by eliminating the normality assumption, reducing bias, and allowing for variance estimation [4]. Soon after, synthesis analysis appeared in genetic studies [14], followed by a methodological framework for binary outcomes, building logistic regression prediction models [15, 16]. All these methods created theoretical frameworks for various statistical outcomes, including simulation-based studies and related examples. The applied approach of synthesis analysis showed the development of multivariate disease prediction models in scenarios where a comprehensive dataset containing both disease outcomes and all relevant predictors of interest is not available [17, 18].

For example, the Framingham Coronary Heart Disease (CHD) model is widely recognized as a comprehensive tool, but it does not include several important risk factors such as body mass index (BMI), family history of CHD, and C-reactive protein [19–21] for risk prediction. To address this gap, Hu et al. provided a new CHD prediction model by incorporating additional risk factors through the novel synthesis modeling approach [17, 22]. Thus, developing and validating these methods would enable more robust and generalizable risk prediction for clinical decision-making, particularly in contexts of non-communicable diseases, i.e., stroke, coronary heart disease, and cancer.

However, most existing studies have concentrated on a narrow range of statistical methods and have been applied primarily within specific medical domains, such as stroke and coronary heart disease, limiting their generalizability to other types of statistical responses. Given the increasing role of clinical decision-making in public health practice, it is essential to deepen the understanding of how commonly used statistical outcomes are applied in real-world settings, such as time-to-event outcomes. A thorough understanding of synthesis analysis practices in public health can help identify existing challenges and support efforts to improve the reporting and interpretation of statistical outcomes. Therefore, a scoping review was conducted to systematically examine how synthesis methods are currently applied and analyzed in the literature. Specifically, this research aimed to: (1) identify existing synthesis analysis methodologies across various statistical response types, summarize their current applications, and highlight areas where further research is needed; and (2) describe how synthesis methods were applied in clinical practice to estimate risk prediction models.

2. MATERIALS AND METHODS

This review was conducted per the Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews (PRISMA-ScR) checklist and explanation (https://www.prisma-statement. org/scoping). The PRISMA-ScR was developed based on published recommendations by the EQUATOR (Enhancing the QUAlity and Transparency Of health Research) Network for reporting guideline development.

The electronic databases PubMed, Google Scholar, and Scopus were searched. Studies were identified in the search using the following keywords: “synthesis analysis,” “meta-analysis,” “linear model,” “logistic model,” “combining statistical models,” “multivariate model,” and “prediction model”. These keywords were selected to incorporate relevant publications through specific terms like “synthesis analysis,” “multivariate model,” “linear model,” and “logistic model,” as well as more general terms such as “prediction model” and “combined statistical model” to ensure comprehensive literature extraction.

All eligible studies identified via the “snowballing” search strategy were included in the review [23]. Studies were included if they met the following criteria: (1) the study was published as a peer-reviewed journal article; (2) the article presented methodological development and applied examples of the synthesis method for statistical outcomes; (3) the publication appeared between 2000 and 2025; (4) the manuscript was written in English.

Exclusion of studies was based on specific eligibility criteria such as: (1) the article described synthesis analysis or meta-analysis without providing sufficient methodological or applied detail for implementation; (2) the primary objective of the method was not the analysis of statistical responses. For example, articles with random-effects meta-analysis or synthesis of correlated endpoints were excluded [24, 25]; (3) publications appeared before 2000; (4) the article was not written in English.

The selected articles were reviewed, and relevant data were manually extracted using Microsoft Word and organized into a tabular format. The extracted data included authors, article title, year of publication, study aims, methods, outcome measures, findings, and significance of the results (Supplemental File 1). The table facilitated the identification of methodologies, techniques/ applications, advantages, and disadvantages within the included studies. The collected details were then summarized and presented in a narrative format.

3. RESULTS

The initial database search in Google Scholar, PubMed, and Scopus identified 248 studies as potentially relevant. After removing duplicates, the screening process included titles, abstracts, and method sections to further narrow the search. Of these, only 10 studies published between 2004 and 2017 addressed methodological and implementation research across various contexts of synthesis analysis and were included in this review. A flow diagram of the study showing the identification of studies via databases is shown in Fig. (1). The PRISMA checklist is attached as an additional file (Supplemental File 2).

4. DISCUSSION

The purpose of this review is to present an overview of the published literature on synthesis analysis methods, summarize their applications, and identify areas requiring further research. Through a comprehensive examination of the literature, this review highlights how synthesis analysis has evolved as both a statistical concept and an applied tool across diverse research domains. The findings indicate a scarcity of studies focused specifically on statistical methodology and a limited amount of research regarding its implementation in this area.

It is important to note that the term “synthesis” was not used consistently across the studies included. While some explicitly described their approach as synthesis analysis, others described related methods (e.g., multivariate meta-analysis) that shared the same goal of integrating incomplete or heterogeneous information across studies. These were included to provide a comprehensive overview of developments relevant to synthesis analysis. Based on the primary contribution of each article, the findings were distinguished into two parts: methodological and applied synthesis analysis. Section 3.1 focuses on methodological developments, i.e., studies whose primary contribution is the theoretical or statistical formulation of synthesis analysis (e.g., estimation frameworks, assumptions, simulation performance). In contrast, Section 3.2 focuses on applied implementations, where synthesis analysis is used as a tool to enhance real-world prediction models (e.g., CHD and stroke risk scores).

The methods of synthesis analysis have evolved from univariable approaches to more advanced multivariable frameworks that incorporate incomplete or heterogeneous data from various studies. Advancements in methodology have enhanced estimation under non-normal distributions for continuous outcomes, enabled the modeling of correlated predictors, and improved prediction accuracy using only summary-level inputs. For binary outcomes, the methodological framework provided improved performance with increased sample size, especially for normally distributed data. These methodological frameworks provided real data examples, such as National Health and Nutrition Examination Survey (NHANES) data, which enable researchers to derive more accurate estimates of multivariate model coefficients, in contrast to the less rigorous approach of using univariate model coefficients to represent multivariate relationships.

Applied studies have effectively enhanced clinical risk models, including the Framingham Risk Score and Stroke Risk Score, showing improvements in discrimination, calibration, and practical significance. Synthesis analysis has contributed to significant and wide-ranging benefits for public health. The method enables the construction of multivariable risk prediction models without the need for large-scale primary data collection, which is particularly valuable in resource-limited settings where conducting comprehensive longitudinal studies is financially unfeasible [12]. The use of multiple risk factors within a single model also strengthens risk stratification across populations. This improvement helps earlier recognition of individuals at high risk and supports more efficient delivery of preventive interventions such as lifestyle modification programs and pharmacological treatments [22]. Furthermore, the method allows accumulated epidemiological evidence to be converted directly into practical clinical risk tools. This accelerates the translation of evidence into practice and removes the need to repeat expensive primary studies [26]. However, a consistent limitation across all studies is that synthesis analysis remains confined to continuous and binary outcomes.

To date, no research has proposed or assessed a synthesis framework for time-to-event or survival data, which are essential in medical research and clinical decision-making [28]. Survival analysis (also called time-to-event analysis or failure-time analysis) is a set of statistical procedures that focus on time-to-event data, with the outcome variable being the time until an event (e.g., death, disease relapse, or recovery) occurs [29]. Extending synthesis analysis to time-to-event outcomes would be a valuable and novel meta-analytic approach that could synthesize information from various public health studies. Without a synthesis analysis approach for time-to-event outcomes, valuable information from multiple incomplete studies remains underutilized, limiting our ability to provide robust, evidence-based survival predictions and inform patient care [30].

Future research should prioritize the development of synthesis methods for time-to-event and other statistical outcomes, including ordinal and repeated-measures outcomes. This statistical framework can be applied to address infectious diseases and undiagnosed health conditions, including obesity, elevated serum cholesterol levels, hypertension, dietary and nutritional status, as well as cardiovascular and cognitive health [31, 32].

Therefore, expanding the statistical scope of synthesis analysis, alongside improving usability and transparency, will be critical for broader implementation.

CONCLUSION

This scoping review highlights synthesis analysis as a promising approach for building multivariate models from incomplete data sources. While effective for continuous and binary outcomes, current methods lack support for time-to-event and other complex responses. Addressing this gap is crucial for broader application in public health and clinical decision-making.

REFERENCES