Statistical Methods in Medical Research

Statistical prediction models for binary outcomes are becoming increasingly popular. One significant challenge is calibrating these models to suit the characteristics of a target population that is structurally different from the original population. Calibration is especially challenging when there is no training data available from the target population. To address this problem, we propose a novel calibration method, SimCal, which uses synthetic data generated from the model development data in conjunction with marginal statistics from the calibration cohort. We show that expert judgment modeling (EJM) may be used for calibration if cross-sectional data from the target population are available comprising expert judgments about the potential outcome and the covariates. We describe three alternative calibration approaches when calibration data are lacking: similarity-binning averaging (SBA), adaptive calibration of predictions (ACP), and Elkan calibration. In a simulation study, we compare SBA, ACP, Elkan calibration, and SimCal. R code for applying these methods is provided from the re-analysis of data on coronary artery disease. We illustrate all 5 calibration approaches with a real data set for predicting functional outcome after stroke and all approaches but EJM in the re-analysis of the Cleveland Clinic data. None of the approaches performed convincingly well in all situations. SimCal performed well when model parameters were correctly specified. EJM failed on the stroke data. Further research is urgently required for calibration in the absence of calibration data.

Cancer therapy balances between two competing objectives - treatment efficacy against the tumour and the risk of treatment related severe adverse events, including patient death. Most existing optimal control theory (OCT) formulations rely on optimising heuristic cost functionals that lack direct clinical interpretability. In clinical practice treatment efficacy and patient tolerability are primarily assessed through survival metrics and adverse event rates. Here we introduce the Continuous Lifetime Payoff (CLP), a novel OCT objective functional that directly links treatment decisions to patient survival. It explicitly incorporates tumour dynamics, tumour eradication, and patient mortality from tumour progression, drug-related toxicity and age. We fit age-related mortality from life tables and infer parameters from simulated survival data. The CLP provides a clinically grounded framework for optimising chemotherapy regimens.

Abstract Purpose This study introduces a novel approach to address unmeasured confounding in terminal event studies using the prior event rate ratio (PERR) method. The proposed approach PERR_{proxy} used a proxy event to replace the original terminal event in the pre-exposure period, enabling the application of PERR in terminal event settings. Additionally, we also applied difference in difference (DID) regression, which is conceptually analogous to PERR to estimate the standard errors and confidence intervals of PERR_{proxy}. Methods We conducted numeric simulations to evaluate the validity of PERR_{proxy} approach and assessed its performance under varying levels of unmeasured confounding effects, baseline hazard ratios, and the correlation between the proxy and terminal events. To demonstrate its practical applicability, we also performed an empirical analysis to investigate the impact of severe hospitalized COVID-19 on circulatory system disease mortality using the PERR_{proxy}. Results In simulation studies, PERR_{proxy} effectively reduced the unmeasured confounding effects compared to the conventional methods. The performance of PERR_{proxy} was influenced by the strength of unmeasured confounding, baseline hazard ratios, and the correlation between the proxy and terminal outcomes. In addition, difference in difference (DID) regression had much faster computational speed for estimating standard errors and confidence intervals compared to bootstrap. In the empirical analysis, PERR_{proxy} identified that severe hospitalized COVID-19 as a significant risk factor for the circulatory system disease mortality and reduced the unmeasured confounding effects. Conclusions The PERR_{proxy} approach extends the applicability of the original PERR method to terminal event studies, offering a promising solution for addressing unmeasured confounding. Additionally, the DID regression framework provides a computationally efficient alternative for parameter estimation in PERR-based studies. However, careful consideration is still required in PERR_{proxy} for proxy events selection and other underlying assumptions of the PERR method to ensure valid results. Keywords: prior event rate ratio, unmeasured confounding, proxy event, terminal event study, observational study, electronic health records

Instrumental variable (IV) methods are widely used in health and social sciences to estimate causal treatment effects among compliers. In certain research settings, the instrument-treatment association (first stage) and the instrument-outcome association (reduced form) are each estimated from a different dataset. Two-Sample Instrumental Variables (TSIV), proposed by Angrist and Krueger (1992), addresses this by combining first-stage and reduced-form estimates from separate data sources into a single causal effect estimate. However, TSIV identification requires that instrument compliance behavior be consistent across the two samples, a condition that is rarely verified in practice. We show mathematically and empirically that when compliance differs between samples, the raw TSIV estimator does not converge to the true Local Average Treatment Effect (LATE) and instead attenuates toward a predictably biased limit proportional to the ratio of first-stage compliance rates between the two samples. To address this, we formalize a framework for estimating LATE with TSIV under two key assumptions: (1) Covariate Overlap, requiring that the two samples share sufficient common support in their covariate distributions, and (2) Compliance Transportability, requiring that compliance behavior is identical across populations after conditioning on observed covariates. We consider a setting in which a health policy instrument and outcomes are recorded in administrative claims while treatment and covariates are collected in a survey. We use a C-statistic derived from pooled covariates to detect population mismatch and an Inverse Probability Weighting (IPW) correction that reweights the first-stage sample to approximate the administrative covariate distribution. In Monte Carlo simulations across eight scenarios calibrated to a survey-Medicaid setting, IPW-TSIV reduces bias in estimating the LATE, achieving 88% reduction in the primary scenario, 82% under severe selection, and 79% when state-level expansion policy drives compliance heterogeneity. We further validate this framework using the Oregon Health Insurance Experiment, where partitioning the public-use lottery data (N = 24,646) into two non-overlapping samples with substantively meaningful compliance heterogeneity yields a verifiable benchmark against the true causal effect. IPW-TSIV reduces mean absolute bias by 71.6% relative to the oracle S2-specific LATE across 10 independent replications (C-statistic = 0.78), outperforms naive TSIV in all 10 splits, and reduces mean bias relative to the full-data LATE from +0.016 to +0.008. This framework provides applied researchers with actionable diagnostic thresholds to detect sample mismatch, validate transportability assumptions, and determine when structural TSIV estimation is reliable.

Background. Self-exciting (Hawkes) point processes are a natural model for the temporal clustering of human physical activity (PA) recorded by accelerometers, yet they have seldom been used in this setting---in part because the usual maximum-likelihood fitting is challenging due to potential estimation bias and convergence failures on these data. A moment-based alternative---estimating the Hawkes branching ratio from the dispersion index, the variance-to-mean ratio of event counts---is kernel-independent and computationally trivial, but it has not been evaluated for accelerometry or adapted to the intensity-marked recordings accelerometers provide. Methods. Treating each minute above a sedentary threshold as an event, we estimated the Hawkes branching ratio $n$ by maximum likelihood and, as a kernel-independent and far cheaper alternative, from the dispersion index. We compared four dispersion-based estimators---event-count-based, intensity-mark-weighted using the mark-moment ratio, and time-of-day (TOD) adjusted variants of each---against the marked and unmarked maximum-likelihood estimates. Estimators were evaluated for mutual agreement, goodness of fit, and finite-window results in two National Health and Nutrition Examination Survey (NHANES) accelerometry cohorts (hip-worn, $n=2{,}560$; wrist-worn, $n=3{,}132$). We related the resulting temporal clustering measures to all-cause mortality using survey-weighted Cox models, adjusting for PA frequency, Peak30 (the average of the 30 highest PA values), and demographic covariates. Results. Event-count-based dispersion estimates agreed strongly with maximum-likelihood branching ratios ($r\approx0.74$ in both cohorts); the intensity-marked variant incorporating PA intensity variability agreed less well. Marked and unmarked Hawkes models yielded similar excitation and decay parameters, suggesting PA intensity added little clustering information beyond event timing. In the survival analysis, temporal clustering was associated with all-cause mortality independently of PA frequency and Peak30; the direction of association differed between the hip- and wrist-worn cohorts. Conclusions. A scalable dispersion-index estimator recovers the Hawkes branching ratio and matches maximum-likelihood estimates without requiring kernel specification or iterative optimization. It offers a practical tool for quantifying temporal clustering in accelerometry, enabling decomposition of temporal PA patterns into its exogenous initiation and endogenous persistence. Such temporal patterns carry health-relevant information beyond PA intensity and volume. Keywords: dispersion index; Hawkes process; branching ratio; temporal clustering; point process estimation; accelerometry; mortality

Objective To evaluate the feasibility, safety, patient acceptance, and preliminary clinical relevance of automated self-operated transvaginal ultrasound for ovarian stimulation monitoring. Design Prospective observational pilot study. Subjects Ten women undergoing ovarian stimulation for in vitro fertilization or fertility preservation at a single high-volume private IVF center. Exposure Participants performed investigational self-operated transvaginal ultrasound examinations immediately following standard monitoring visits. Patients inserted and stabilized the ultrasound probe while ovarian and endometrial imaging was acquired through controlled motorized probe rotation without real-time anatomical guidance. Main Outcome Measure(s) The primary outcome was feasibility, defined as the generation of evaluable imaging datasets suitable for ovarian stimulation monitoring. Secondary outcomes included bilateral ovarian visualization, procedural safety, patient-reported outcomes, follicular assessment, and agreement of endometrial thickness measurements with standard transvaginal ultrasound. Result(s) Nineteen investigational scan attempts were performed, yielding 18 evaluable datasets (94.7%). Bilateral ovarian visualization was achieved in 16 of 18 evaluable examinations (88.9%), whereas partial ovarian visualization occurred in 2 examinations (11.1%). No adverse events, adverse device effects, vaginal injury, bleeding, or infection were observed. Patient-reported outcomes demonstrated high procedural acceptability, with all participants expressing willingness to reuse the system. Compared with standard transvaginal ultrasound monitoring, investigational self-operated acquisition significantly improved overall examination experience (Wilcoxon p=0.002). Investigational imaging demonstrated clinically relevant agreement with standard transvaginal ultrasound for follicular categorization and endometrial assessment. Counts of follicles [≥]14 mm correlated strongly with mature oocyte recovery for both investigational and standard ultrasound measurements (Spearman {rho}=0.83 and {rho}=0.80, respectively). Endometrial thickness measurements also demonstrated strong correlation between modalities (Spearman {rho}=0.91). Conclusion(s) This prospective pilot study demonstrates the feasibility of automated self-operated transvaginal ultrasound during ovarian stimulation monitoring. Investigational imaging generated clinically relevant monitoring information without observed safety concerns and was associated with high patient acceptance. These findings support further investigation of patient-operated acquisition strategies and standardized imaging workflows in reproductive medicine.

Recently, Hu et al. (2024) conducted a benchmarking study showing that most existing Mendelian randomization (MR) methods exhibit substantial bias and inflated type-I error rates in real data. They attributed these failures to two largely neglected sources of bias: winner's curse and polygenicity-induced bias. Although a few methods have been developed to address one or both of these issues, existing approaches either do not fully account for both biases or are restricted to the univariable setting. In this paper, we propose a multivariable Rao-Blackwellization that corrects winner's curse while accounting for polygenicity and sample structure in a unified framework. Unlike univariable Rao-Blackwellization, where instrument selection yields a truncated normal statistic amenable to a Mills-ratio correction, multivariable Rao-Blackwellization conditions on a noncentral $\chi^2$ statistic, for which no analogous correction is available. We derive closed-form conditional moments under this instrument selection model and use them to construct bias-corrected summary statistics that can be integrated into a wide range of existing MR methods. Simulations and real data analyses show that, when combined with methods such as MR-cML and MR-BEE, the proposed correction substantially improves type-I error control and yields more robust inference.

Meta-analysis usually reduces each study to an effect estimate with a standard error and pools these by inverse-variance weighting: fixed effect (FE), random effects (RE), or unrestricted weighted least squares (UWLS). We propose information-geometric meta-integration (IGMI), representing each study by its sampling distribution, the Gaussian N(theta_i, Sigma_i), and pooling studies as a weighted Frechet mean (barycenter) under Bures-Wasserstein (BW), Fisher-Rao, or Wasserstein-Fisher-Rao (WFR) geometry. In the scalar fixed-variance case the BW barycenter mean is exactly the FE estimate; the minimized Frechet functional reproduces the Higgins-Thompson I^2 and DerSimonian-Laird tau^2 heterogeneity statistics; and a Frechet-scatter pivot reproduces the Hartung-Knapp-Sidik-Jonkman interval at m = 1 and yields an exact Hotelling F(m, K-m) region for m outcomes under proportional total covariances. WFR adds a robust outlier-resistant pool: as its length scale delta grows without bound it converges monotonically to BW, whereas finite delta gives a redescending M-estimator with rejection point exactly pi*delta. Simulations show calibrated multivariate coverage at small K, where Wald intervals undercover, and strong resistance of the equal-weight WFR pool to contamination. In 2,445 Cochrane meta-analyses, WFR most often wins leave-one-out predictive scoring. In 835 bivariate meta-analyses, the closed-form BW barycenter matches REML multivariate meta-analysis predictively and is exactly invariant to the unreported within-study correlation, unlike the likelihood estimate.

Progestin-IUD use was more frequent among IUA cases (29.9%) than polyp (3.4%) or infertile (11.1%) comparison groups. Compared to infertile comparators, any prior progestin-IUD use was independently associated with IUA (aOR 3.12; 95% CI 2.01, 4.85). There was a duration-response pattern: use of 5 years or less was modestly associated with IUA case status (aOR 1.99; 1.09, 3.64), whereas use >5 years conferred more than a seven-fold increase (aOR 7.26; 3.27, 16.11). The association persisted among surgically naive women (aOR 3.98; 2.44, 6.48) and was concentrated in those who were nulliparous, where use beyond five years conferred an approximately twelve-fold increase in odds (aOR 12.74; 5.25, 30.92). Progestin-IUD use was less frequent in polyp controls relative to IUA and infertile comparators, suggesting a possible role for progestin exposure in preventing endometrial polyp formation. The case control design does not allow for estimation of absolute risk for an individual and cannot inform causation. Further prospective studies are needed to better assess the relationship between progestin-IUD's, particularly when used beyond five years, and adverse fertility outcomes.

In meta-analyses of continuous outcomes, the sample mean and standard deviation (SD) are essential for synthesizing effect sizes across studies. However, clinical studies frequently report alternative summary statistics, such as the median, quartiles, and range. To enable inclusion of such studies, various methods have been proposed to estimate the sample mean and SD from these reported summaries. We propose the Bayesian Order Statistics-based Estimator (BOSE), which leverages the joint likelihood of observed order statistics together with weakly informative priors to obtain the full posterior distribution for the mean and SD without relying on computationally intensive iterative procedures such as Markov chain Monte Carlo algorithms. Our numerical studies demonstrate that BOSE performs competitively with existing approaches in estimating the mean, while achieving superior performance for estimating the SD across all evaluated scenarios, particularly in small-sample settings. Under non-normal distributions including skewed, heavy-tailed, and bimodal settings with mild or moderate deviations from normality, BOSE remains robust and stable, whereas methods specifically designed for skewed distributions may become unstable or even inapplicable. Beyond point estimation, BOSE naturally provides empirically validated posterior credible intervals, enabling researchers to formally quantify uncertainty for study-level estimates and make reliable, evidence-based decisions in meta-analytic research synthesis. A publicly accessible web application implementing BOSE and competing methods is also provided to facilitate practical use in meta-analytic research.

Infectious disease transmission evolves as a dynamic process shaped by biological mechanisms, population behavior, and intervention policies, yet public health responses are often driven by lagging indicators. Accurate short- and long-term disease forecasting is essential for the timely deployment of intervention strategies, healthcare capacity planning, and uncertainty-aware, risk-informed decision-making. To address this challenge, three broad classes of forecasting models have traditionally been used: statistical, machine learning, and mechanistic approaches. However, each of these modeling paradigms faces fundamental limitations. In particular, traditional statistical models often lack the flexibility needed to capture complex disease dynamics, machine learning approaches require large, high-quality data streams, and mechanistic models are notoriously difficult to calibrate. To overcome these challenges, we propose a novel physics-informed machine learning (PIML) framework for forecasting infectious disease dynamics. Our approach simultaneously forecasts new case and hospitalization counts, along with other key epidemiological quantities such as the time-varying reproduction number. This is achieved through the design of a machine learning model and estimation strategy regularized by a system of differential equations that encode disease dynamics of the SIHR model, thereby bridging the gap between purely data-driven and mechanistic models. We demonstrate the proposed methodology through in-depth numerical studies and an application to COVID-19 data collected in the state of South Carolina.

Mendelian randomization (MR) analysis is widely used to estimate causal relationships between risk factors and outcomes of interest. Two-sample MR approaches have gained increasing attention in genetic epidemiology due to the growing availability of Genome-Wide Association Study (GWAS) summary statistics from public databases. A critical step in two-sample MR is the selection of genetic variants as instrumental variables (IVs). Although genome-wide significant variants are typically preferred, the inclusion of variants with weaker association p-values is considered, as they may potentially improve power through an increased instrument number of instruments, while they may introduce weak instrument bias and attenuate effect estimates towards the null. Our simulation results show that even modest levels of pleiotropy substantially increase the variability of causal effect estimates, while the inclusion of weak IVs does not substantially affect the direction and variability of causal effect estimates in most cases. In real data analyses, we used two released versions of FinnGen GWAS summary statistics with different sample sizes as exposure GWASs to assess the influence of weak IVs. Here, the inclusion of IVs with higher exposure-association p-values resulted in weakened estimated effect sizes, particularly when the exposure GWAS sample size was small. These findings suggest that incorporating weak IVs is reasonable when the exposure GWAS sample size is large, but it poses a risk of falsely concluding null associations when the exposure GWAS sample size is small.

Superspreading events (SSEs) produce extreme, rare bursts of disease transmission that standard compartment models, which assume population homogeneity, fail to capture. This inability to model heterogeneity in transmission rates can result in biased estimates of transmissivity. To address this limitation, we present a modular framework that treats SSEs as statistical outliers in case count time series and incorporates them into SIR-type models via pulse terms that transfer SSE cases directly from susceptible to infected compartments. This separation isolates anomalous SSE-driven transmission from background spread, which reduces bias when estimating mean transmission rates. We validate the approach on synthetic data generated by a stochastic model with embedded SSEs, demonstrating accurate recovery of the true non-SSE transmission parameter. We then apply the method to COVID-19 outbreaks in Hong Kong and the German district of Gutersloh, showing improved model fits and more robust estimates of background transmissivity both for a period with constant transmission and for a period with temporally structured NPI-driven heterogeneities. The framework's interchangeable outlier-detection, compartment, and SSE modules make it adaptable to diverse diseases and data contexts.

Standard demographic models of age-related hearing loss (presbycusis) predominantly utilize symmetric functions, such as log-normal distributions for age-binned thresholds and 4-parameter logistic curves for prevalence estimates. While these models capture early-to-moderate degradation effectively, they structurally struggle to characterize the heavy tails associated with severe clinical impairment. In this study, we present a statistical critique using a secondary analysis of the historical Medical Research Council (MRC) National Study of Hearing (1980-1986) dataset. By applying Generalized Extreme Value (GEV) distribution theory, we demonstrate that as severity increases, the underlying statistical geometry of hearing loss shifts. The asymmetric, heavy-tailed GEV distribution provides a parsimonious description of severe impairment, requiring fewer parameters than standard symmetric models. However, we explicitly acknowledge that utilizing static population data to infer progression introduces an ecological fallacy. Furthermore, the dataset's historical nature embeds unquantified generational cohort effects. We conclude that while extreme value statistics offer a compelling mathematical framework for modeling the variance of severe presbycusis, true longitudinal datasets are required to isolate physiological degradation from historical cohort variance.

Preclinical cancer sojourn time, defined here as the duration a cancer is undetected but detectable, is important for understanding disease progression and evaluating screening policies. This study aims to robustly characterise empirical evidence and existing knowledge over mean sojourn times across 21 stageable tumour sites, including stage-specific preclinical cancer sojourn times and the sojourn time of circulating tumour DNA (ctDNA)-positive cancers. We updated an existing systematic review through to February 2025 to extract population-level empirical sojourn time estimates derived from mathematical models of primary screening data. To synthesise this heterogeneous literature, quantify uncertainty, and obtain estimates for cancer-sites lacking empirical evidence, we conducted a formal Structured Expert Elicitation involving 15 clinical experts. The elicitation was grounded on the systematic review results, supplemented by an evidence dossier that included survival data and outcomes from relevant ctDNA cancer studies. The systematic review revealed heterogeneity in existing literature, which focused on a small subset of screened cancers (e.g., breast, cervical, colorectal). The elicitation successfully generated comprehensive probability distributions of overall mean sojourn times for all 21 cancer-sites (representing the site of tumour origin), as well as stage-specific sojourn times and overall sojourn times for ctDNA-positive cancers across 14 cancer-sites. This study used robust methodology to quantitatively describe existing evidence and experts' beliefs on the sojourn time of multiple cancer-sites, also describing uncertainty. Such estimates are important for future evaluations of the clinical impact, potential for overdiagnosis and subsequent cost-effectiveness of emerging screening technologies, including multi-cancer detection tests.

Introduction: For oncology patients with limited treatment options, clinical trials may be a critical lifesaving pathway. Identifying relevant trials, however, is a time-consuming and difficult task. Several patient-trial matching processes incorporating large language models (LLMs) have been proposed to alleviate the burden on patients and oncologists. We aim to explore the benefits and practical challenges of zero-shot LLM-assisted trial matching processes by analyzing the results for a single pancreatic cancer patient. Materials and Methods: The results of a simple zero-shot LLM-assisted clinical trial matching process for our patient were compared to those of a "human benchmark," which was developed manually by two of the authors interfacing directly with ClinicalTrials.gov. Performance metrics -- sensitivity, specificity, precision, and accuracy -- were calculated. In addition, a qualitative content analysis (QCA) of LLM reasoning text was done to identify patterns in "errors," which we define as a human-LLM discrepancy in final patient eligibility. Implications and severity of errors are discussed. Results: The zero-shot LLM-assisted process returned potential trials with a sensitivity, specificity, and precision of 81.1%, 89.3%, and 86.5% respectively compared to the human benchmark. Qualitative error analyses revealed that about 73% of errors could potentially be alleviated with improved prompting and information access. Overall performance seemed comparable to that of human reviewers. Conclusion: The results from this preliminary real-world case study provide additional evidence to the literature in support of the integration of LLMs in clinical trial matching to provide benefit to patients with metastatic cancer with limited options.

Vaccination can be a useful intervention for reducing infectious disease burden. Estimating numbers of vaccine-prevented health outcomes is one approach to quantifying the benefits of vaccination. Here we improve a method described by Foppa et al. (1) that assumes vaccination has only direct effects, that is, it cannot prevent infection or onward transmission of the disease. We rederive this method and derive an improved method that increases estimation accuracy with minimal additional analytical complexity. To evaluate the improved method, we simulated disease outbreaks and compared the accuracy of the two methods for estimating prevented disease outcomes. In 84% of simulations performed over a wide parameter space, the improved method had an equal or smaller estimation error compared to the original Foppa method, with 7.9-fold smaller mean error and 44-fold smaller standard deviation of errors. Our study improves a method for estimating prevented burden when assuming vaccination has only direct effects.

Modeling the circadian impact of seasonal clock changing requires precise synchronization between solar and social time. This report critiques a recent study that associated disease prevalence in the United States with seasonal clock exposure. We identify a fundamental computational error in which a sign reversal of the longitudinal offset effectively inverted the US East-West axis, cross-correlating local health data with the circadian burden of hypothetical locations on the opposite side of a time zone. We outline the methodology for a correct modelization of the circadian process in the context of US geography.

Compartmental models of infectious disease transmission make assumptions about human behaviors. Specifically, they parameterize interactions across population groups, assumed to have distinct epidemiologically-relevant behavioral patterns, primarily through contact matrices stratified by demographic variables such as age, gender, or socioeconomic status. Although such demographic characteristics are readily measurable, they may inadequately capture the social and psychological forces that govern protective behaviors. Drawing on 20 waves of a national survey conducted throughout the COVID-19 pandemic in the United States, we show that institutional trust - particularly trust in public health agencies, physicians, and hospitals - is a dominant predictor of protective behavior adoption. For mask wearing during periods of strongest pandemic activity, for example, institutional trust explains more behavioral variance across population groups than age, income, education, and partisan affiliation combined. In unadjusted analyses, the difference in protective behavior adoption between individuals with the highest and lowest trust in the CDC was four- to six-fold larger than the corresponding differences by age, income, or educational attainment, and exceeded the difference between Democratic and Republican respondents. This association was institutionally specific (e.g., the relationship attenuates for trust in banks), and behaviorally specific (e.g., trust in the CDC is associated with protective behaviors but not visiting a doctor). The latter suggests that trust modifies voluntary compliance with public health recommendations rather than access to or use of healthcare. We conclude that compartmental models of disease transmission would be substantially improved by incorporating institutional trust as a stratifying variable. We additionally offer a trust-integrated mathematical modeling framework and recommendations for the data infrastructure needed for its implementation.

Background: Public health initiatives increasingly target multiple overlapping high-risk groups to maximize impact. However, a common challenge in modelling these initiatives is to capture these overlapping risk factors, leading to potential misallocation of resources and biased effectiveness estimates. Using China's tuberculosis (TB) control program as an example, this study explores different possible frameworks to account for population heterogeneity and risk overlap. Methods: We examined four risk allocation frameworks: (i) Direct Summation (DS), a simple additive benchmark; (ii) Probabilistic Union Deduplication (PUD), using inclusion-exclusion principles; (iii) Risk population combination (RPC), modeling interaction effects; and (iv) Agent-Based Framework (ABF), a granular microsimulation. To show how these frameworks could be used in epidemiological modelling, we embedded each within a deterministic transmission model of TB epidemiology in China, to simulate the impact of China's National Tuberculosis Strategic Plan (NTSP). We explored each framework when implemented in both static and dynamic versions. We compared them using methodological principles and indicators of intervention cost (screening volume) and benefits (cases/deaths averted). Results: Under the static version, the detection yield of active cases followed a consistent hierarchy: DS > PUD > RPC {approx} ABF. The DS method systematically overestimated yields by double-counting overlapping populations, while PUD corrected for overlap but ignored interaction. The RPC and ABF methods provided the most granular estimates by incorporating Risk population combinations. Additionally, comparing static versus dynamic versions revealed that for the same multi-risk screening framework, mortality reductions remained stable and incidence reductions varied significantly. Conclusion: This study presents potential screening frameworks for overlapping risk populations. The RPC method offers optimal balance of real-world plausibility and computational efficiency. We propose the dynamic RPC method as the preferred tool for routine analysis where multimorbidity and intersectional risks exist, providing a robust evidence base for optimizing resource allocation in heterogeneous populations.