Evaluating artificial intelligence (AI) models in clinical medicine requires more than conventional metrics such as accuracy, Area Under the Receiver Operating Characteristic (AUROC), or F1-score, which often overlook key considerations such as fairness, reliability, and real-world utility. We introduce CUES as a multiplicative composite score for clinical prediction models; it is defined as CUES=(C⋅U⋅E⋅S)1/4, where C represents calibration, U integrated clinical utility, E equity across patient subpopulations, and S sampling stability. We formally establish boundedness, monotonicity, and differentiability on the domain (0,1]4, derive first-order sensitivity relations, and provide asymptotic approximations for its sampling distribution via the delta method. To facilitate inference, we propose bootstrap procedures for constructing confidence intervals and for comparative model evaluation. Analytic examples illustrate how CUES can diverge from traditional metrics, capturing dimensions of predictive performance that are essential for clinical reliability but often missed by AUROC or F1-score alone. By integrating multiple facets of clinical utility and robustness, CUES provides a comprehensive tool for model evaluation, comparison, and selection in real-world medical applications.

BackgroundSedentary behavior is common in older adulthood and is associated with poor health outcomes. Less is known about how sedentary behavior relates to cognition in older adulthood and how it relates to increased risk for cognitive decline associated with Alzheimer's disease (AD).ObjectiveWe sought to examine these associations in a large, population-based cohort of community-dwelling older adults residing in a Rust Belt region of the United States.MethodsA subset of the population-based Monongahela-Youghiogheny Healthy Aging Team (MYHAT) participants (n = 193) completed 7 days of wrist-accelerometry following comprehensive neuropsychological assessment. Cross-sectional linear regression models related sedentary time to domains of cognition. Models were adjusted by age, sex, education, and APOE4 carrier status and moderate to vigorous physical activity (MVPA). The interaction between sedentary behavior and APOE4 genotype on cognition was also examined.ResultsGreater sedentary behavior was associated with worse executive function (β = -0.06, p = 0.01) and memory (β = -0.06, p = 0.05) performance. These results were attenuated when adjusting for MVPA. No significant interactions between sedentary time and APOE4 carrier status were observed, although estimation results applying the delta method on regression coefficients suggested the associations were stronger in APOE4 non-carriers when compared to APOE4 carriers.ConclusionsHigher levels of sedentary behavior were associated with worse performance in cognitive domains implicated in AD. Public health initiatives and precision-based medicine approaches to reduce sedentary behavior in a population-based cohort of older adults may be important AD prevention measures. Results support the importance of reducing sedentary time.

Standardized coefficients - including factor loadings, correlations, and indirect effects - are fundamental to interpreting structural equation modeling (SEM) results in psychology. However, they often exhibit skewed sampling distributions in finite samples, which are not captured by conventional symmetric confidence intervals (CIs). Methods such as bootstrap CI that do not impose symmetry are more appropriate for these coefficients. Despite its popularity, the widely used R package lavaan (version 0.6-19 or earlier) provides limited bootstrap support for standardized coefficients. Specifically, its function standardizedSolution() uses the delta method for CIs and lacks bootstrap pvalues. It provides a flexible and powerful function, bootstrapLavaan(), for bootstrapping, and it can be used to form bootstrap CIs for the standardized coefficients. However, this function requires a certain level of R coding skills. Moreover, no built-in functions are available to inspect bootstrap distributions, which are recommended for assessing the stability of the bootstrap estimates. To address these limitations, we developed the semboottools R package, which provides a simple workflow in SEM to form bootstrap confidence intervals for unstandardized and standardized estimates of model and user-defined parameters. It allows researchers to generate percentile or bias-corrected bootstrap CIs, standard errors, asymmetric pvalues, compare the bootstrap CIs with other CI methods (e.g., delta method), and visualize the distributions of bootstrap estimates - with minimal coding effort. We believe the tool can facilitate researchers in easily forming bootstrap CIs, comparing different CI methods to assess the need for bootstrapping, and examining the distribution of bootstrap estimates to assess their stability.

The global increase in the intake of ultra-processed food (UPF) parallels rising rates of early-onset colorectal cancer (CRC), raising concern about possible causal links. Although observational studies suggest that UPFs contribute to gastrointestinal inflammation, it remains unclear whether CRC risk is mediated through inflammatory pathways such as inflammatory bowel disease (IBD). In this review we sought to evaluate, using a 2-stage mediation meta-analysis, the association between UPF consumption and CRC risk and to examine whether IBD mediates this relationship. We searched PubMed, Embase, Scopus, and Web of Science through September 2025. Two reviewers independently extracted data using a standardized form, including study characteristics, UPF assessment method, exposure categories, follow-up, covariates, and adjusted effect estimates (hazard ratio [HR], relative risk [RR], odds ratio [OR], standardized incidence ratios [SIRs]). For UPF-CRC and UPF-IBD, the primary contrast was highest vs lowest UPF category, with per-10% increments recorded when reported. For IBD-CRC, adjusted RRs were abstracted similarly. No individual-level data were obtained. Study-specific effect estimates were log transformed and pooled using random-effects models (REMLs). Heterogeneity was assessed via I2 and Cochran's Q. Associations of UPF-IBD and IBD-CRC were meta-analyzed separately and combined to estimate the indirect UPF-CRC effect via a 2-stage product-of-coefficients method, with SEs derived using the delta method. Sixteen cohort studies including over 2 million participants met inclusion criteria. High UPF intake was modestly associated with increased CRC risk (RR 1.13, 95% CI, 1.06-1.20) and incident IBD (RR 1.33, 95% CI, 1.15-1.55), with stronger effects for Crohn disease. The IBD-CRC association was positive but heterogeneous (RR 1.36, 95% CI, 1.14-1.62). A 2-stage mediation model suggested a small indirect UPF to CRC effect via IBD (approximate RR 1.07). Higher UPF consumption is therefore associated with modestly increased risks of IBD and CRC, although the indirect effect through IBD appears limited. PROSPERO registration No. CRD420251035864.

Abstract This study employed the Weather Research and Forecasting Model to dynamically downscale outputs from the HadGEM2-ES global climate model for the Caribbean at resolutions of 40km and 8km. Simulations were conducted for a historical period (1980-1990) and two future periods corresponding to global warming limits of 1.5 °C (2024-2034) and 2 °C (2038-2048) derived from the Representative Concentration Pathway (RCP) 4.5 projection. The future projections were from the RCP4.5 scenario and the Solar Radiation Modification (SRM) G4 scenario from the Geoengineering Model Intercomparison Project (GeoMIP), focusing on variables relevant to wind and solar energy assessments. Three bias-correction methods were independently applied to the downscaled outputs to evaluate their effectiveness in reducing bias while preserving projected climate change signals. The Quantile Delta Mapping and Delta method produced the best outputs and were subsequently used to assess the potential influence of SRM on solar and wind energy resources at the island scale. Results indicate that wind speeds under the G4 scenario generally decrease across much of the Caribbean, with parts of southern Jamaica and Hispaniola seeing the most notable increases. Changes in solar irradiance appear minimal; however, this finding remains inconclusive due to limitations in validating the more variable historical distribution of the WRF-derived outputs. These findings demonstrate the feasibility of conducting sub-regional and local-scale wind energy assessments in the Caribbean while underscoring the need for improved observational datasets to enhance solar resource validation.

Assessment of climate change impacts in pavement design and analysis is not a widespread practice among practitioners, and there is a lack of consensus on approaches for preparing the outputs of future climate projections into mechanistic-empirical analysis inputs. The research question was: is there a difference in projected pavement temperatures using an average ensemble and individual model selection approach for climate models? This was assessed by computing performance grade binder classifications and subsurface temperature profiles, the latter of which has not been well studied. The asynchronous regional regression model and delta method were used to create impact-relevant hourly projections of air temperature for a future target year, 45 years after a base temporal year. The enhanced integrated climatic model was used to produce subsurface temperatures for a site in Minnesota within the long-term pavement performance InfoPave database seasonal monitoring program. Coupled Model Intercomparison Project Phase 5 (CMIP5) projections from the Downscaled CMIP3 and CMIP5 Climate and Hydrology Projections archive were processed using the United States Department of Transportation CMIP5 tool. Variable preparation was completed for an average ensemble and individual model selection approach with 20 representative concentration pathway 8.5 models. A bias toward warmer minimum and maximum temperatures for the average ensemble approach compared with the individual model approach was discovered and attributed to the sophisticated averaging approach in the asynchronous regional regression model. The resultant impacts on subsurface temperature variation and performance grade binder classifications underscore the need for further investigation for improving guidance for climate model selection.

ABSTRACT Clinical trials with continuous endpoints evaluate efficacy by comparing the difference in mean changes from baseline between groups. However, clinicians often interpret results in terms of a proportional reduction rather than an absolute difference. An alternative approach is to reparametrize this difference as a proportional treatment effect (PTE), calculated by dividing the difference by the placebo mean change. PTE is not a new metric per se, but a specific reparameterization gaining traction in certain clinical contexts. We demonstrate that, in theory, PTE can be more powerful than the simple difference in means while still controlling the type I error rate. This is achieved using the delta method, as implemented in well-established computational tools like the R package ‘msm’ and the SAS procedure ‘NLMIXED’. By analyzing data from phase III trials, we illustrate how a PTE connects treatment outcomes across various endpoints and different presentation formats. The availability of these well-established statistical tools for estimating proportional treatment effects, combined with this theoretical demonstration, suggests an alternative test statistic for clinical trials with continuous endpoints.

In the competing risks setting, the -year absolute risk for a specific time (e.g., 2 years), also called the cumulative incidence function at time , is often interesting to estimate. It is routinely estimated using the nonparametric Aalen-Johansen estimator. This estimator handles right-censored data and has desirable large sample properties, as it is the nonparametric maximum likelihood estimator (NPMLE). Inference for comparing absolute risks, via either a risk difference or a risk ratio, can therefore be done via usual asymptotic normal approximations and the delta method. However, the small sample performances of this approach are not fully satisfactory. Especially, (i) coverage of confidence intervals may be inaccurate and (ii) comparisons made using a risk ratio and a risk difference can lead to inconsistent conclusions, in terms of statistical significance. We, therefore, introduce an alternative empirical likelihood approach. One advantage of this approach is that it always leads to consistent conclusions when comparing absolute risks via a risk ratio and a risk difference, in terms of significance. Simulation results also suggest that small sample inference using this approach can be more accurate. We present the computation of confidence intervals and p-values using this approach and the asymptotic properties that justify them. We provide formulas and algorithms to compute constrained NPMLE, from which empirical likelihood ratios and inference procedures are derived. The novel approach has been implemented in the timeEL package for R, and some of its advantages are demonstrated via reproducible analyses of bone marrow transplantdata.

Performance of blood biomarkers in internal jugular vein for Alzheimer's disease pathologies: the Delta Method study.

Assessing the insulation condition of power transformers is crucial for maintaining the reliability of electrical power systems. This research aims to predict the remaining life of the transformer at PLTU Suralaya Unit 6 by integrating the measurement of the dissipation factor (tan δ) using Dielectric Frequency Response (DFR) testing at ultra-low frequency (1 mHz = 0.001 Hz) and estimating the Degree of Polymerization (DP) through empirical correlation. The DFR measurements were performed with the OMICRON DIRANA device (frequency range 0.1 mHz–1 kHz) and validated against tan δ measurements at 50 Hz using OMICRON CPTD equipment. The dissipation factor at 1 mHz was extracted and converted to an estimated DP value through a validated regression model. Results show a DP value of approximately 302, indicating advanced degradation of the cellulose insulation. This corresponds to an estimated remaining life percentage of 29.68%, equivalent to an operational lifespan of roughly 11.87 years before reaching the end-of-life threshold. The study confirms that ultra-low-frequency DFR testing combined with DP estimation provides a non-destructive and effective approach for transformer remaining life prediction. It is recommended to implement condition-based monitoring and supplement with oil chemical analysis (e.g., furan compounds) and other diagnostic methods to enhance prediction accuracy and support proactive asset management.

ABSTRACTBackgroundObservational studies suggest an association between social isolation and cannabis use disorder (CUD), but causality remains unclear. This study employs Mendelian randomization (MR) to assess the potential causal effect of social isolation on CUD and explore the mediating role of anxiety disorders and depression.MethodsGWAS summary statistics for social isolation, CUD, anxiety disorders, and depression were obtained from public GWAS repositories. Inverse variance weighted (IVW) was the primary MR method, supplemented by MR‐Egger, weighted median, and maximum likelihood approaches to evaluate: (i) The causal effect of social isolation on CUD; (ii) its effect on anxiety disorders and depression; (iii) the effect of anxiety disorders and depression on CUD. Sensitivity analyses included Cochran's Q test for heterogeneity, MR‐Egger intercept and MR‐PRESSO for pleiotropy, and leave‐one‐out analysis for robustness. The mediation effect was quantified using the delta method.ResultsIVW analysis revealed a significant positive correlation between social isolation and increased CUD risk (OR = 4.29, 95% CI: 1.35–13.64, p = 0.014), with supplementary MR methods yielding consistent results (OR > 1). Sensitivity analyses confirmed the robustness of findings. In addition, the mediation MR analysis revealed that depression significantly mediated the causal effect of social isolation on CUD. Specifically, social isolation showed a significant positive association with depression risk (OR = 3.70, 95% CI: 2.32–5.89, p = 3.67E‐08), and depression, in turn, was positively associated with an increased risk of CUD (OR = 1.27, 95% CI: 1.08–1.50, p = 0.003). The delta method indicated that depression mediated 21.8% of the effect of social isolation on CUD risk.ConclusionsSocial isolation is potentially associated with an increased risk of CUD, with depression as a key mediator. The findings should be considered in light of limitations including potential recall bias, European ancestry samples, and the inability to assess exposure‐mediator interactions using summary‐level data.

This study implements Bayesian along with non-Bayesian approaches to estimate the parameters of the three-parameter quadratic hazard rate distribution using hybrid Type-II censoring. The model expands upon linear hazard rate, exponential, and Rayleigh distributions. In the non-Bayesian framework, point estimates and survival and hazard functions are calculated using maximum likelihood estimation (MLE). Asymptotic confidence intervals are derived, with a focus on the delta method. By applying independent normal and gamma priors, Bayesian inference produces point estimates and credible intervals using different symmetric and asymmetric loss functions. The analytical intractability of posterior distributions makes Markov chain Monte Carlo (MCMC) methods necessary for sampling purposes. The evaluation of point and interval estimates depends on root mean squared error (RMSE) in combination with mean relative absolute bias (MRAB), average confidence interval length (AL), and coverage probability (CP). The performance evaluation through different sample sizes and censoring schemes is conducted by simulation studies, while real-world data from COVID-19 mortality demonstrates the practical implementation of methods. Graphical and numerical analyses confirm the existence and uniqueness of the estimates. Results indicate that Bayesian methods deliver superior accuracy and more robust estimates than their non-Bayesian counterparts for survival analysis purposes in clinical and medical research.

Introduction: Aortic aneurysms (AAs), including thoracic (TAA) and abdominal (AAA) types, are associated with a high risk of dissection and rupture, with no pharmacological therapies are available to slow or prevent progression. Multi-omics strategies offer promise for discovering therapeutic targets. While prior studies based on genomic and transcriptomic data have identified lipoprotein(a) and PCSK9 as potential targets, proteomic and metabolomic analyses remain limited. Methods: We employed two-sample Mendelian randomization (MR), summary-data-based MR (SMR) with false discovery rate correction, and Bayesian colocalization analysis with HEIDI testing to evaluate the association between plasma proteins and AA. Proteins significant in two out of three analyses were considered potential drug targets, while those significant in all three were defined as core therapeutic targets. Potential side effects of core targets were evaluated using phenome-wide association studies (PheWAS). Additional MR analyses identified AA-related metabolites, and mediation analysis via the delta method was used to assess causal pathways linking proteins and metabolites. Results: We identified five proteins as potential therapeutic targets: LTBP4 (positive association with AA, TAA), IL6R (negative association with AA, AAA), SMPD1 and ACAT2 (positive association with AA), and PCSK9 (positive association with AAA). SMPD1 emerged as a core therapeutic target for AAA, with significant associations in MR (OR = 1.39, 95% CI: 1.21–1.60, P = 2.04E-6), SMR (OR = 1.42, 95% CI: 1.21–1.67, P = 1.94E-5), and colocalization (PPH4 = 98.76%), and no adverse phenotypes detected in PheWAS. Metabolite MR further identified lignoceroyl sphingomyelin, N-palmitoyl-sphinganine, and N-palmitoyl-sphingosine as associated with AA; oleoyl-linoleoyl-glycerol, N-palmitoyl-sphinganine, and N-palmitoyl-sphingosine with AAA. Mediation analysis showed that N-palmitoyl-sphingosine significantly mediated the effect of SMPD1 on AA (effect proportion: 23.1%, 95% CI: 3.3%–93.6%) and AAA (34.4%, 95% CI: 2.7%–66.0%). Conclusion: This study identifies five plasma proteins and four metabolites as potential therapeutic targets for AA. To our knowledge, this is the first study to highlight SMPD1 as a core therapeutic target for AAA, likely acting through ceramide metabolism involving N-palmitoyl-sphingosine. These findings offer novel mechanistic insights into AAA and suggest promising directions for drug development.

The potency of propofol is measured by its Cp50 value, which is the plasma concentration required to suppress a motor response in 50% of patients during surgical incisions. This Cp50 value can be affected by the concurrent use of other drugs, including opioids, benzodiazepines, or lidocaine. Pregabalin, a medication commonly administered as preoperative premedication, provides mild sedative and anxiolytic effects. Although pregabalin has the potential to reduce the minimum alveolar concentration (MAC) of sevoflurane, its effects on propofol-based anesthesia have not been conclusively studied. Thus, we designed a placebo-controlled, double-blind clinical trial to evaluate the impact of pregabalin on the Cp50 of propofol. Eighty female patients who underwent breast surgery participated in this study. They received either a placebo or 300 mg of pregabalin 2 hours before anesthesia induction. Propofol was administered as the sole anesthetic agent, delivered continuously via a target-controlled infusion (TCI) pump using the Schnider model, without the addition of opioids or other analgesics. Patients in both groups were administered different target effect-site propofol concentrations, and their motor responses to standardized skin incisions were determined. The Cp50 value of propofol was estimated using a logistic regression model, and the results were re-evaluated using bootstrap methods. A significant difference in propofol Cp50 values was found between the placebo and pregabalin groups. Using the delta method, the Cp50 value of propofol was estimated to be 16.9 μg/mL (95% confidence interval [CI], 15.1-18.8) in the placebo group and 9.4 μg/mL (95% CI, 4.46-14.3) in the pregabalin group. Secondary outcome measures revealed significantly decreased opioid consumption and pain levels in the recovery area in the pregabalin group compared to the placebo group. This study demonstrated that pretreatment with 300 mg pregabalin significantly reduced the Cp50 value of propofol by 44%, as calculated using the delta method. When 300 mg of pregabalin is administered before anesthesia and propofol is used for maintenance via TCI, a lower target effect-site concentration might be sufficient. Additionally, pregabalin premedication has the potential to decrease postoperative pain and opioid consumption.

ABSTRACTOften probabilities of nonstandard time‐to‐event endpoints are of interest, which are more complex than overall survival. One such probability is chronic graft‐versus‐host disease (GvHD‐) and relapse‐free survival, the probability of being alive, in remission, and not suffering from chronic GvHD after stem cell transplantation, with chronic GvHD being a recurrent event. Because the probabilities for endpoints with recurrent events may not fall monotonically, one should not use the Kaplan–Meier estimator for estimation, but the Aalen–Johansen estimator. The Aalen–Johansen is a consistent estimator even in non‐Markov scenarios if state occupation probabilities are being estimated and censoring is random. In some multistate models, it is also possible to use linear combinations of Kaplan–Meier estimators, which do not depend on the Markov assumption but can estimate probabilities to be out of bounds. For these linear combinations, we propose a wild bootstrap procedure for inference and compare it with the wild bootstrap for the Aalen–Johansen estimator in non‐Markov scenarios. In the proposed procedure, the limiting distribution of the Nelson–Aalen estimator is approximated using the wild bootstrap and transformed via the functional delta method. This approach is adaptable to different multistate models. Using real data, confidence bands are generated using the wild bootstrap for chronic GvHD‐ and relapse‐free survival. Additionally, coverage probabilities of confidence intervals and confidence bands generated by Efron's bootstrap and the wild bootstrap are examined with simulations.

BackgroundPhysical activity is linked to mental health, yet the dose–response shape remains debated.MethodsIn a cross-sectional sample of Chinese university students, 820 participants (mean age 21.5 years; 51.8% women) wore wrist accelerometers for 7 days. Subjective well-being (SWB) was measured with the WHO-5 (0–100). Restricted cubic spline models adjusted for age, sex, sleep quality, perceived stress, and socioeconomic status. Sensitivity analyses included quadratic and segmented models, trimming/winsorization, and E-value assessment. Peaks/plateaus were estimated via the delta method and bootstrap-BCa confidence intervals.ResultsThe steps–SWB association was non-linear (overall p<0.05). SWB rose steeply up to ~8,650 steps/day and then leveled off, with a statistical plateau near ~19,300 steps/day (bootstrap-BCa 95% CI: 7,997–17,896; delta-method 95% CI: 9,394–14,462). No contrast versus 4,000 steps/day exceeded the prespecified minimal clinically important difference (MCID=10 points). Findings were consistent across specifications; right-tail precision was limited due to few very high step counts.ConclusionAmong university students, higher daily steps are associated with better SWB up to ~8,000–12,000 steps/day, beyond which benefits plateau with diminishing returns rather than harm. Results support range-based, progressive step guidance for student mental health. Please replace the current abstract with the structured IMRaD version provided above.

In health care providers' performance assessment, standardized incidence ratios are essential tools used to assess whether observed event rates deviate from expected values. Accurate estimation of variance in these ratios is crucial as it affects decision-making regarding providers' performance. There is little data on how the choice of these variance estimation methods affects decision-making. In this study, we compared 3 methods (the delta method, bootstrapping method, and Bayesian approach) to estimate the variance of the logarithm of the standardized incidence ratio. Using patient-level data from the Australia and New Zealand Dialysis and Transplant Registry for 2012-2023, we used a random effects model to predict treatment at home 1 year after starting treatment. We compared the 3 approaches (with more than 5000 iterations for bootstrapping and Markov chain Monte Carlo sampling) using bias, variance, and mean squared error (MSE) as performance measures. Using the 3 methods, funnel plots were used to compare the hospitals' performance in treating Indigenous and non-Indigenous patients close to home, as a service-level measure of equity. The bias values across all methods were similar, with the Bayesian method narrowly having the lowest bias (0.01922), followed by the delta method (0.01927) and bootstrap method (0.02567). In addition, the Bayesian method exhibited the lowest variance (0.00005), indicating more stable and less dispersed estimates. The delta method had a higher variance (0.00016), while the bootstrap method had the highest variance (0.00027), meaning it introduced more uncertainty. Finally, the Bayesian method had the lowest MSE (0.00042), indicating better overall accuracy, while the bootstrap method had the highest MSE (0.00094), showing it was the least reliable method. We demonstrated that these methods can be used to measure equity for patient-centered outcomes, both within and between service providers simultaneously. The choice of variance estimation method is critical and heavily affects the interpretation of the performance of health service providers. We favor the Bayesian Markov chain Monte Carlo method as it was found to be a better approach.

Mediation modeling using longitudinal data is an exciting field that captures the interrelations in dynamic changes, such as mediated changes, over time. Even though discrete-time vector autoregressive approaches are commonly used to estimate indirect effects in longitudinal data, they have known limitations due to the dependency of inferential results on the time intervals between successive occasions and the assumption of regular spacing between measurements. Continuous-time vector autoregressive models have been proposed as an alternative to address these issues. Previous work in the area (e.g., Deboeck & Preacher, 2015; Ryan & Hamaker, 2021) has shown how the direct, indirect, and total effects, for a range of time-interval values, can be calculated using parameters estimated from continuous-time vector autoregressive models for causal inferential purposes. However, both standardized effects size measures and methods for calculating the uncertainty around the direct, indirect, and total effects in continuous-time mediation have yet to be explored. Drawing from the mediation model literature, we present and compare results using the delta, Monte Carlo, and parametric bootstrap methods to calculate SEs and confidence intervals for the direct, indirect, and total effects in continuous-time mediation for inferential purposes. Options to automate these inferential procedures and facilitate interpretations are available in the cTMed R package. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Abstract Background Smoking is linked to lower body weight, and concerns about weigh gain may decrease motivation to smoking cessation. Since the long-term impact of smoking on BMI changes is still unclear, we examined how smoking status relates to BMI changes at different life stages. Data and methods Data pooled from 13 longitudinal twin cohorts comprising 91,357 individual twins (45% females) were used. BMI changes were estimated using the delta method if only two measures were available or linear mixed-effects (LME) models if three or more measures were available. Smoking status was categorized as never smokers, current smokers, and former smokers. We first assessed the overall associations between smoking status and BMI changes and then examined these associations in different life stages. Results Over the total life course, BMI changes were smaller in current smokers than in never smokers in men (β = -4.70e-03 kg/m2 per year). When considering different life stages, in men, former smokers had greater BMI changes in late middle age and old age compared to never smokers (β = 6.12e-03 kg/m2 per year and β = 5.48e-03 kg/m2 per year, respectively) and current smokers (β = 0.01 kg/m2 per year and β = 0.02 kg/m2 per year, respectively). In women, current smokers had lower BMI changes in late middle age and old age compared to never smokers (β = -0.01 kg/m2 per year in late middle age and β = -0.02 kg/m2 per year in old age) and former smokers (β = 0.02 kg/m2 per year in both stages). Conclusions The associations between smoking status and BMI change can vary depending on life stage and sex. Former smokers tend to gain more weight, particularly in later life, underscoring the importance of targeted interventions following smoking cessation. Key messages • Over the total life course, only currentsmokers showed lower BMI changes compared to never smokers. • When considering different life stages, the number of associations increase, conveying that the associations between smoking status and BMI change can vary depending on life stage and sex.

To estimate the reliability of two outcome quality measures in Veterans Health Administration (VHA) data using three different methods. We created two cohorts of VHA patients meeting criteria for two measures: (1) risk-standardized complication rates following elective primary total hip arthroplasty and/or total knee arthroplasty (THA/TKA), and (2) risk-standardized mortality rates following acute myocardial infarction hospitalization (AMI). We fit hierarchical logistic regression models and calculated facility-level risk-standardized rates. We estimated entity-level reliability using three commonly applied methods: (1) delta method approximation; (2) latent scale model; (3) split-sample method. For each measure, we extracted risk adjustment and outcome data from the VHA Corporate Data Warehouse for patients meeting eligibility criteria in fiscal years 2021 and 2022. Most facilities had complication rates following total hip and/or knee arthroplasty and mortality rates following hospitalization for acute myocardial infarction that, statistically, were no different from the national average. Reliability estimates based on delta method approximation (0.14 for THA/TKA; 0.12 for AMI) and the split-sample method (0.12 for THA/TKA; 0.19 for AMI) were very low for both measures. As we varied the sample sizes, we found that much higher sample sizes would be needed to reliably differentiate quality of care across facilities. On the other hand, reliability estimates based on the latent scale model were substantially higher than the other two methods (0.64 for THA/TKA; 0.41 for AMI), suggesting that there is substantially more between-facility variation in latent quality than manifests in observed outcomes. Reliability estimates based on the latent scale approach are not numerically or conceptually interchangeable with estimates based on the other two approaches. Given that health outcomes are generally reported using observed outcomes, reliability estimation based on the latent scale approach should not be used without a strong rationale.