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Objectives The number needed to treat (NNT) is a widely used efficacy and effect-size measure in epidemiology and meta-analysis, originally defined as the average number of patients who need be treated to obtain one additional beneficial outcome. In this study, we introduce novel direct and indirect formulations of the NNT, the number needed to be exposed (NNE) and the exposure impact number (EIN) - quantifying the average number needed to treat (expose) to achieve benefit via the treatment's direct and indirect effects in the respective treatment group. Methods Using nested potential outcomes, we formally define the direct effect NNT, NNE, and EIN (DNNT, DNNE, and DEIN, respectively) and the indirect effect NNT, NNE, and EIN (INNT, INNE, and IEIN, respectively). We then derive their identification conditions in observational studies. We introduce an estimation method and illustrate it with two analytical examples. Results The identification results provide explicit conditions under which the novel direct and indirect indices are estimable in observational studies. Simulation studies demonstrate that the proposed estimators are consistent and that the associated analytic confidence intervals attain their nominal coverage rates. Two analytical examples clarify implementation and interpretation. Conclusions We formalize novel path-dependent efficacy measures - DNNT, INNT, DNNE, INNE, DEIN, and IEIN - and derive their identification conditions for observational studies. We also introduce an estimation method and demonstrate its efficiency and accuracy using theoretical results and a simulation study. The widespread use of NNT and NNE, together with the need for path-dependent reporting, supports the utility of the proposed indices. These indices can help disentangle direct and indirect benefits and guide the choice among intervention strategies in public health, clinical practice, and other policy decision-making contexts.

External validation is critical in risk prediction model development to assess the model’s performance on independent datasets before clinical application. Sample size determination (SSD) is a pivotal aspect for external validation, ensuring sufficient precision, adequate power, appropriate ethical considerations, and affordable resource allocation. SSD for external validation of a risk model with binary outcomes can be performed targeting the most commonly used evaluation criterion, the area under the receiver operating characteristic (AUROC) curve, for two study designs: one focusing on margin-of-error and another on hypothesis testing. Sample sizes for external validation are estimated using various AUROC variance estimators. In this article, we conduct extensive simulations to compare the performance of different AUROC-based SSD methods for external validation under the two study designs. These simulations involve models developed using various machine learning (ML) algorithms, different sets of predictors, and data generated under diverse distributions. The simulation results show significantly different sample size estimates based on the chosen SSD methods. Based on empirical evidence from these simulations, we recommend the Hanley and McNeil method or the rules-of-thumb approach for margin-of-error–based designs, given their balance between reliability and feasibility. For hypothesis testing designs, the Hanley and McNeil method demonstrates superior operating characteristics and is recommended for achieving adequate power. We also demonstrate the application of these AUROC-based SSD methods in the external validation of a risk prediction model for forecasting 1-year overall survival (OS) in pediatric patients who underwent allogeneic hematopoietic cell transplantation (alloHCT). Our findings highlight the importance of selecting appropriate SSD methods for external validation and provide practical guidance for implementing SSD in clinical prediction model validation.

Despite modern medical developments, infectious diseases continue to impact millions worldwide. Malaria, for instance, is a significant cause of mortality and suffering in developed and developing countries. The most challenging hurdle for scientists to control this disease is the parasite’s propensity to develop resistance to novel medicines and treatment approaches. In response, this study develops a novel compartmental model of malaria transmission with memory between human-to-mosquito and mosquito-to-human that integrates drug resistance development and therapy as a preventative measure. The memory is incorporated using the Caputo fractional derivative. The existence and stability of the disease-free and endemic equilibrium have been investigated using the Routh-Hurwitz criterion. Numerical simulations have been performed to establish the role of different crucial parameters and variables in the proposed model. In addition, sensitivity analysis has been performed to demonstrate the variation of findings for the different parameters. The results demonstrate that decreasing the order of derivative reduces the basic reproduction number and that early detection of resistance levels can help minimize transmission. The research has broad implications for healthcare, including the need to achieve high rates of treatment and immunity development while minimizing the emergence of drug resistance due to treatment failure. In summary, this research sheds light on this terrible pandemic’s nature by assessing the impact of treatment rates and resistance levels.

Objectives This study investigates the use of multilevel models within capture-recapture experiments, a common procedure to estimate the size of an elusive population, accounting for random effects to accurately calculate the probabilities of being observed. Methods We review single data-source capture-recapture estimators. We provide a general framework to account for random effects to accurately calculate the probabilities of being observed and apply the method to estimate the number of powder cocaine, crack cocaine, heroin users and people who inject drugs in France in 2019. Using two-level, random-intercepts logistic regression models that account for both individual and center factors, we conduct the calculations once with fixed effects only, and once with predicted center-level random effects. Results There are substantial differences between estimates based on fixed-effects only predictions and fixed and random effects combined, reflecting the influence of the treatment center-level. The application of multilevel modelling in capture-recapture allows the researcher to include individual and contextual information, and provide estimates at a large geographical scale. Conclusions Multilevel capture-recapture modelling offers a credible alternative to estimate the size of elusive populations in large geographical settings. The influence of higher-level clusters in capture-recapture studies using multilevel modelling should be explicitly considered in future studies.

Compartmental models have emerged as useful tools in epidemiology due to their mechanistic nature. They provide insights into complex dynamic systems and allow predictions under different scenarios. However, despite their widespread use, there is still a gap in the literature, concerning their statistical formalization and a systematic discussion of the statistical methods suitable for both tasks of inference and forecasting. In this work, starting from the fundamental distinction between deterministic and stochastic compartmental models, we focus on how the formulation of the likelihood function becomes a necessary and challenging step in the transition from a deterministic to a stochastic framework. We then analyse the various difficulties encountered in evaluating the likelihood function associated with discrete-time stochastic models. We distinguish two reasons for the intractability of the likelihood function, the high dimension of missing data and the complexity of the model structure, and discuss suitable methods for addressing the problem both from a frequentist and Bayesian perspective. We overview likelihood-based methods and explore the use of likelihood-free approaches in this framework, namely approximate Bayesian computation algorithms and a method that combines model calibration with a parametric bootstrap procedure. We emphasize their ability to make inferences from data that are partially observed, or only observed in some aggregated form. To showcase their feasibility and reliability, we compare the likelihood-free and likelihood-based methods at work with a toy example of the Susceptible-Infected-Removed. Finally, we explore the relevance of likelihood-free methods in a real-world framework through an example of a complex compartmental model developed to study smoking dynamics in Tuscany (Italy).

In observational studies, performing a sensitivity analysis for unmeasured confounding is recommended alongside estimating the causal effect of an exposure on an outcome. This study extended sensitivity analysis frameworks to evaluate the joint effects of two binary exposures, accounting for potential unmeasured confounders. We applied this approach to assess the joint impact of household wealth and maternal education on child nutritional status using data from the 2019 Bangladesh Multiple Indicator Cluster Survey (MICS). A log-binomial regression model was employed to estimate the causal effect in the relative risk scale after adjusting for observed confounders by inverse probability weighting (IPW). Sensitivity analysis explored the robustness of the estimated causal effect under different scenarios of unmeasured confounding. The findings indicate that higher levels of wealth and maternal education significantly reduce the risk of child malnutrition independently and jointly, and the joint effects are robust against unmeasured confounders. Such conclusions underscore the need to account for both exposures in causal inference and provide a framework to assess robustness when unmeasured confounders are a concern in public health studies.

Objectives The use of substances in adolescents is an increasing public health problem. Many high schools in Canada have implemented school-based programs to mitigate student substance use, but their utility is not conclusive. Polysubstance use data collected on students from multiple schools may be subject to informative cluster size (ICS). The objective of this study was to investigate whether a multivariate analysis approach that addresses ICS provides different conclusions from univariate analyses and methods that do not account for ICS. Methods We used data from the 2018/2019 cycle of the Cannabis, Obesity, Mental health, Physical activity, Alcohol, Smoking, and Sedentary Behaviour (COMPASS) study, an ongoing prospective cohort study that annually collects data from Canadian high schools and students. We compared results from four analytical approaches that estimate marginal associations between each school substance program and the four substance use behaviours (binge drinking, cannabis, e-cigarette, and cigarette): univariate generalized estimating equations (GEE), univariate cluster-weighted GEE (CWGEE), multivariate GEE, and multivariate CWGEE. Results We observed that the proportion of students who engage in each of the four behaviours was higher in small schools and lower in large schools. In general, the univariate and multivariate analyses produced comparable results. Some differences existed between multivariate CWGEE and GEE. CWGEE indicated that the school program on cannabis had an odds ratio (OR) and 95 % confidence interval (CI) of 0.83 (0.73, 0.95) on all substance use, but GEE produced a null association with an OR (95 % CI) of 0.92 (0.79, 1.07). Conclusions When ICS is present in clustered school data, weighted and unweighted analyses may produce different results. Care is needed to investigate the relationship between cluster size and the outcome, and use appropriate methods for analysis. Certain substance programs may influence student behaviour in other substances, highlighting the need for a multivariate analytical approach when studying the use of substances by adolescents.

When data on multiple indicators of underlying psychosocial constructs are collected, they are often intended as closely related assessments of a relatively unified phenomenon, or alternatively as capturing distinct facets of the phenomenon. Establishing distinctions among construct phenomena, assessments, or indicators is sometimes described as establishing discriminant validity. In the philosophical literature, often extreme instances or limit cases, actual or hypothetical, are used to identify settings in which one phenomenon is present and the other is not, to establish distinctions. We put forward an empirical analogue of this philosophical principle applied to distinctions amongst survey item responses. The quantiles of extreme differences matrix characterizes, for each pair of indicators, how large differences are between indicators at relatively extreme quantiles of the distribution of those differences. We discuss potential uses and properties of this matrix and related matrices for identifying relevant distinctions among indicators or facets of underlying construct phenomena.

Objectives In clinical and epidemiological studies, the modified Poisson and least-squares regression analyses for binary outcomes have been used as standard multivariate analysis methods to provide risk ratio and risk difference estimates. However, their ordinary Wald-type confidence intervals can suffer from finite-sample biases in the robust variance estimators, and the coverage probabilities of true effect measures are substantially below the nominal level (usually 95 %). To address this issue, new accurate inference methods are needed. Methods We propose two accurate inference methods based on the estimating equation theory for these regression models. A remarkable advantage of these regression models is that the correct models to be estimated are known, that is, conventional binomial regression models with log and identity links. Using this modeling information, we first derive the quasi-score statistics, whose robust variances are estimated using the correct model information, and then propose a confidence interval based on the regression coefficient test using χ 2 -approximation. To further improve the large sample approximation, we propose adapting a parametric bootstrap method to estimate the sample distribution of the quasi-score statistics using the correct model information. In addition, we developed an R package, rqlm (https://doi.org/10.32614/CRAN.package.rqlm), that can implement the new methods via simple commands. Results In extensive simulation studies, the coverage probabilities of the two new methods clearly outperformed the ordinary Wald-type confidence interval when the regression function assumptions were correctly specified, especially in small and moderate sample settings. We also illustrated the proposed methods by applying them to an epidemiological study of epilepsy. The proposed methods provided wider confidence intervals, reflecting statistical uncertainty. Conclusions The current standard Wald-type confidence intervals may provide misleading evidence. Erroneous evidence can potentially influence clinical practice, public health, and policymaking. These possibly inaccurate results should be circumvented using effective statistical methods. These new inference methods would provide more accurate evidence for future medical studies.

Objectives Advantages of panel data, i.e., difference in difference (DID) design data, are a large sample size and easy availability. Therefore, panel data are widely used in epidemiology and in all social science fields. The literature on causal inference in panel data settings or DID designs has been expanding, although existing studies often focus on the exposed group (or treated group), limiting the development of mediation analysis methods. Methods In this study, we present a methodology for conducting causal mediation analysis in a DID design and panel data setting that encompasses the entire population including both exposed and unexposed groups, by proposing a general common trend assumption which has a form of exchangeability. We provide formal counterfactual definitions for controlled direct effect and natural direct and indirect effect in panel data setting and DID design, including the identification and required assumptions. We also demonstrate that, under the assumptions of linearity and additivity, controlled direct effects can be estimated by contrasting marginal and conditional DID estimators whereas natural indirect effects can be estimated by calculating the product of the exposure-mediator DID estimator and the mediator-outcome DID estimator. A panel regression-based approach is also proposed. Results The proposed method is then used to investigate mechanisms of the effects of the Covid-19 pandemic on the mental health status of the population. The results revealed that mobility restrictions mediated approximately 45 % of the causal effect of Covid-19 on mental health status. Conclusions The proposed approach offers a framework for mediation analysis in DID and panel data settings, addressing limitations of existing studies by including both exposed and unexposed groups.

In the prevailing era of cardiovascular and chronic diseases, the causes of death seldom operate in isolation. We aim to assess the impact of distortions in statistically significant associations between causes of death on the overall structure of cause of death dependencies. Focusing on the causes of death for USA in 2019, we study all possible scenarios for independence of diseases by optimizing the marginal distributions in the respective contingency tables. We select the independence scenario that corresponds to the minimal intervention in the contingency table and study the effect of setting up independence between diseases i and j on the relationships between i and k (or j and k ). Disrupting associations between leading cause of death pairs would generally lead to decreases in the strength of relations these diseases have with others outside the disrupted pair. The most pronounced effects are observed in the loss of association between mental and behavioral disorders with other respiratory diseases; heart diseases with endocrine, nutritional, and metabolic disorders; and heart diseases with mental and behavioral disorders. Changes in odds ratios between leading cause of death pairs do not occur in isolation from other diseases. Our results may serve as a reference point for optimizing strategies for multimorbidity prevention.

Despite the various advantages of online surveys, such as their cost-effectiveness and broad reach, the infiltration of bots can result in data distortion, eroding trust and hindering effective decision-making. Identifying bot responses within survey data is paramount, and epidemiologic and public health researchers can utilise various tactics such as email authentication and scrutiny of response times, to detect fraudulent responses. This paper discusses the authors’ experience of bot spamming in an online survey, which skewed our findings. We discuss the actions taken to detect and invalidate bot responses within survey data and discuss potential forms of bot prevention. To detect fraudulent responses, the authors investigated the time taken to complete the survey, recruitment rates, invalid email addresses, and invalid free-format responses. Supplementary strategies, such as data validation methods and monitoring tools, can complement reCAPTCHA systems to alleviate the adverse effects of bot activity on survey data accuracy. However, employing other methods that require challenges, or additional questions may reduce the recruitment rate and deter potential participants. Given the advancing sophistication of bots, ongoing innovation in authentication techniques is imperative to protect the dependability and accuracy of survey data in the future.

Objectives A stochastic version of the deterministic model for meningitis epidemic by Yaga and Saporu (A study of a deterministic model for meningitis epidemic. J Epidemiol Methods 2024;13:20230023) is developed. Method The stochastic mean system of equations for possible state of an individual in the model and the extinction probabilities for carrier and infective are derived. Comparison of the system of stochastic mean equations and its deterministic analogue of profiles for the various compartments and the case-carrier trajectories show similar pattern with a time shift difference. Results This indicates that there must be caution in using the deterministic analogue as an approximating system of the stochastic mean equations for inferential purpose. Simulation studies of the comparison of the compartmental profiles for the general case; model I, with the assumption that a proportion ( φ ≠0), of the infected susceptible can move directly to the infective stage and that of the special case, model II, when φ =0 is examined for various values of ϵ (odds in favour of a carrier transmitting infection) ≤ 2 $\le 2$ . It is only when ϵ =2 that model II can approximate model I in all compartments except that of the carrier. Transmission rate, β , loss of carriership rate, σ and ϵ are identified as the most sensitive parameters of the extinction probabilities. Threshold results derived for carrier and infective extinction probabilities are distinct but bear some relation, transmission rate required for carrier extinction is square of that for infective. Conclusion It is concluded that carriership play a more prominent role in the transmission of meningitis epidemic and efforts aimed at control should be targeted at reducing the transmission rate and increasing the loss of carriership.

Exposure to the media can have a significant impact on the transmission of infectious diseases. In this study, we examine the role and importance of information intervention in the fight against infectious illnesses. A four-class mathematical model: H S , H I , H R , and H Z has been developed. The first three classes, denoted as H S , H I , and H R , stand for the population’s subclasses, susceptible, infected, and removed people, respectively. The fourth class, denoted as H Z , stands for the population’s information density. Another component of this model is time delay ( τ ), which accounts for the delay in people’s taking preventive action due to their decision-making period between the report and action times. Essential properties, like boundedness and non negativity of the solutions of the model have been studied. We have addressed the existence and local stability of both the equilibrium points: disease-free and endemic. Conditions for global stability of disease-free and endemic equilibrium points have been obtained. Also, the critical value of delay is obtained, which, when crossed leads to a switch in stability and thus Hopf bifurcation. Finally, to support these analytical findings, numerical simulations have been performed. We have explored the relationship between the number of infective people and the rate of illness transmission, information intervention, and reaction intensity. We have also fitted our model to the actual data of COVID-19 of India for the month of April 2021. Based on the findings, policymakers are recommended to create suitable policies that limit the degree of disease transmission and accelerate the dissemination of information.

Objectives EpiEstim is a popular statistical framework designed to produce real-time estimates of the time-varying reproductive number, R t ${\mathcal{R}}_{t}$ . However, the methods in EpiEstim have not been tested in small, non-randomly mixing populations to determine if the resulting R ̂ t ${\hat{\mathcal{R}}}_{t}$ estimates are temporally biased. Thus, we evaluate the temporal performance of EpiEstim R ̂ t ${\hat{\mathcal{R}}}_{t}$ estimates when population structure is present, and then demonstrate how to recover temporal accuracy using an approximation with EpiEstim . Methods Following a real-world example of a COVID-19 outbreak in a small university town, we generate simulated case report data from a two-population mechanistic model with an explicit generation interval distribution and expression to compute true R t ${\mathcal{R}}_{t}$ . To quantify the temporal bias, we compare the time points when true R t ${\mathcal{R}}_{t}$ and estimated R ̂ t ${\hat{\mathcal{R}}}_{t}$ from EpiEstim fall below the critical threshold of 1. Results When population structure is present but not accounted for R ̂ t ${\hat{\mathcal{R}}}_{t}$ estimates from EpiEstim prematurely fall below 1. When incidence data is aggregated over weeks the estimates from EpiEstim fall below the critical threshold at a later time point than estimates from daily data, however, population structure does not further affect timing differences between aggregated and daily data. Last, we show it is possible to recover the correct timing when by using the lagging subpopulation outbreak to estimate R ̂ t ${\hat{\mathcal{R}}}_{t}$ for the total population with EpiEstim . Conclusions R t ${\mathcal{R}}_{t}$ is a key parameter used for epidemic response. Since population structure can bias R t ${\mathcal{R}}_{t}$ near the critical threshold of 1, EpiEstim should be prudently applied to incidence data from structured populations.

To represent uncertainty in survival analysis, the Kaplan–Meier estimator is frequently presented, along with pointwise confidence intervals, though rarely with confidence bands. Using theoretical reasoning and simulations, this paper investigates the coverage properties and interpretation of pointwise confidence intervals. In addition, we examine the technicalities and potential pitfalls of confidence bands. As both the sample size and the number of events increase, the simultaneous coverage of pointwise confidence intervals decreases. The portion of the survival curve covered by interconnected pointwise confidence intervals corresponds to the nominal coverage of pointwise confidence intervals. Contrary to expectations, most confidence bands cover only a portion of the survival curve. The coverage of confidence bands built for the entire curve may be below the nominal coverage. Despite their limitations, pointwise confidence intervals remain practical and easy to use for illustrating uncertainty in survival estimates. They do not cover a continuous portion of the survival curve but, on average, cover a portion equal to the pointwise nominal confidence level.

Objectives In drug development, there is increasing interest in leveraging real-world data (RWD) to augment trial data and generate evidence about treatment efficacy. However, comparing patient outcomes across trial and routine clinical care settings can be susceptible to bias, namely due to differences in how and when disease assessments occur. This can introduce measurement error in RWD relative to trial standards and lead to bias when comparing endpoints. We develop a novel statistical method, survival regression calibration (SRC), to mitigate measurement error bias in time-to-event RWD outcomes and improve inferences when combining trials with RWD in oncology. Methods SRC extends upon existing regression calibration methods to address measurement error in time-to-event RWD outcomes. The method entails fitting separate Weibull regression models using trial-like (‘true’) and real-world-like (‘mismeasured’) outcome measures in a validation sample, and then calibrating parameter estimates in the full study according to the estimated bias in Weibull parameters. We evaluate performance of SRC under varying degrees of existing measurement error bias via simulation, and then illustrate how SRC can address measurement error when estimating median progression-free survival (mPFS) in newly diagnosed multiple myeloma RWD. Results When measurement error exists between trial and real-world mPFS, SRC can effectively account for its resulting bias. SRC yields greater reduction in measurement error bias than standard regression calibration methods, due to its suitability for time-to-event outcomes. Conclusions Outcome measurement error is important to address when combining trials and RWD, as it may lead to biased results. Our SRC method helps mitigate such bias, improving comparability between real-world and trial endpoints and strengthening evidence of treatment efficacy.