Prediction Intervals Research Articles

Challenges of COVID-19 Case Forecasting in the US, 2020-2021.

During the COVID-19 pandemic, forecasting COVID-19 trends to support planning and response was a priority for scientists and decision makers alike. In the United States, COVID-19 forecasting was coordinated by a large group of universities, companies, and government entities led by the Centers for Disease Control and Prevention and the US COVID-19 Forecast Hub (https://covid19forecasthub.org). We evaluated approximately 9.7 million forecasts of weekly state-level COVID-19 cases for predictions 1-4 weeks into the future submitted by 24 teams from August 2020 to December 2021. We assessed coverage of central prediction intervals and weighted interval scores (WIS), adjusting for missing forecasts relative to a baseline forecast, and used a Gaussian generalized estimating equation (GEE) model to evaluate differences in skill across epidemic phases that were defined by the effective reproduction number. Overall, we found high variation in skill across individual models, with ensemble-based forecasts outperforming other approaches. Forecast skill relative to the baseline was generally higher for larger jurisdictions (e.g., states compared to counties). Over time, forecasts generally performed worst in periods of rapid changes in reported cases (either in increasing or decreasing epidemic phases) with 95% prediction interval coverage dropping below 50% during the growth phases of the winter 2020, Delta, and Omicron waves. Ideally, case forecasts could serve as a leading indicator of changes in transmission dynamics. However, while most COVID-19 case forecasts outperformed a naïve baseline model, even the most accurate case forecasts were unreliable in key phases. Further research could improve forecasts of leading indicators, like COVID-19 cases, by leveraging additional real-time data, addressing performance across phases, improving the characterization of forecast confidence, and ensuring that forecasts were coherent across spatial scales. In the meantime, it is critical for forecast users to appreciate current limitations and use a broad set of indicators to inform pandemic-related decision making.

Change in clinical parameters after subgingival instrumentation for the treatment of periodontitis and timing of periodontal re-evaluation: A systematic review and meta-analysis.

To evaluate the changes in periodontal parameters (reduction in probing pocket depth [PPD], gain in clinical attachment level [CAL] and reduction in full-mouth bleeding on probing [BoP]) after subgingival instrumentation of periodontal pockets at different time points in systemically healthy patients suffering from periodontitis. Four databases were searched for RCTs that carried out subgingival instrumentation in periodontal pockets and evaluated PPD at a minimum of two consecutive time points other than baseline. The analysis was conducted for both all pocket depths and stratified for initially shallow (4-5 mm) and deep (≥6 mm) pockets and data were extracted for various time points, 1-2, 3-4 and 5-6 months. Weighted mean effects (WMEs) were calculated with 95% confidence interval (CI) and predictive intervals were calculated. Twenty-nine RCTs were identified, and all of them were included in the meta-analysis. The results showed that for both shallow and deep pockets there was a small though clinically meaningful change between 1- to 2-month and 3- to 4-month time points and between these and 5-6 months. In systemically healthy patients, the greater part of reduction in PPD and gain in CAL occurs within the first 1-2 months after subgingival instrumentation. However, additional benefits in terms of pocket depth reduction occur beyond these early time points.

Application of machine learning methods for spent fuel characterization based on gamma spectrometry measurements

Machine learning models have been developed to predict properties of spent nuclear fuel assemblies from Paks NPP, such as burnup, cooling time, initial enrichment, and Pu-239 content. Measured gamma spectra are processed, and activity ratios of fission products are calculated to serve as input features for Support Vector Regression, Random Forest, and Multi-Layer Perceptron models. Data uncertainty is considered during inference to produce prediction intervals, and input features are ranked using the Gini importance of Random Forest models. A deep learning approach using Convolutional Neural Networks has also been developed to predict the spent fuel parameters from the measured spectra directly. The new models can predict spent fuel parameters with great precision, outperforming earlier approaches that rely on nonlinear regression using a single feature to predict burnup and cooling time and can estimate initial enrichment and Pu-239 content.

No client left behind: A meta-analysis of premature termination from psychotherapy in U.S. service members and veterans.

Dropout has been identified as a significant problem among military populations seeking psychotherapy (Goetter et al., 2015; Hoge et al., 2014), yet an overall estimate of its exact prevalence and predictors does not exist. The aims of the current meta-analysis were to estimate outpatient psychotherapy dropout rates for this population and evaluate potential moderators of this event. In total, 283 articles-comprising data from 719,465 U.S. service members and veterans-met all inclusion criteria and were included in the meta-analysis. The average weighted dropout rate for all outpatient therapies was 25.6%, 95% CI [22.4%, 29.2%], and prediction interval [1.9%, 85.9%]. Furthermore, dropout was 27.0% for cognitive behavioral therapies (CBTs), 25.3% for trauma treatments, 27.6% for the Department of Veterans Affairs (VA), 28.9% for individual therapies, and 9.8% for intensive outpatient settings. Findings from metaregression analyses using mixed-effects models indicated that higher dropout was linked with the following after accounting for other moderators: younger age, CBTs, nonmanualized approaches, VA versus Department of Defense settings, individual versus group therapies, and weekly versus intensive outpatient formats. Dropout was not linked with other client, therapist, treatment, and research variables. Taken together, dropout estimates were obtained for a range of military populations and treatment characteristics, including theoretical orientation, presenting concern, setting, and therapy formats. These estimates may provide potential benchmarks for therapists, administrators, and policymakers serving military populations. Leveraging dropout prevention strategies with at-risk groups highlighted in this study may enhance mental health care outcomes for this high-need population. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Prevalence of perinatal post-traumatic stress disorder (PTSD) in low-income and middle-income countries: a systematic review and meta-analysis

ObjectivesTo systematically synthesise the evidence on prevalence of perinatal post-traumatic stress disorder (PTSD) in low-income and middle-income countries (LMICs).DesignSystematic review and meta-analysis.Data sourcesMEDLINE, Embase, PsycINFO, Scopus, Web of Science, Global...

Externally validated prediction models for pre-eclampsia: systematic review and meta-analysis.

This systematic review and meta-analysis aimed to evaluate the performance of existing externally validated prediction models for pre-eclampsia (PE) (specifically, any-onset, early-onset, late-onset and pretermPE). A systematic search was conducted in five databases (MEDLINE, EMBASE, Emcare, CINAHL and Maternity & Infant Care Database) and using Google Scholar/reference search to identify studies based on the Population, Index prediction model, Comparator, Outcome, Timing and Setting (PICOTS) approach until 20 May 2023. We extracted data using the CHARMS checklist and appraised the risk of bias using the PROBAST tool. A meta-analysis of discrimination and calibration performance was conducted when appropriate. Twenty-three studies reported 52 externally validated prediction models for PE (one preterm, 20 any-onset, 17 early-onset and 14 late-onset PE models). No model had the same set of predictors. Fifteen any-onset PE models were validated externally once, two were validated twice and three were validated three times, while the Fetal Medicine Foundation (FMF) competing-risks model for preterm PE prediction was validated widely in 16 different settings. The most common predictors were maternal characteristics (prepregnancy body mass index, prior PE, family history of PE, chronic medical conditions and ethnicity) and biomarkers (uterine artery pulsatility index and pregnancy-associated plasma protein-A). The FMF model for preterm PE (triple test plus maternal factors) had the best performance, with a pooled area under the receiver-operating-characteristics curve (AUC) of 0.90 (95% prediction interval (PI), 0.76-0.96), and was well calibrated. The other models generally had poor-to-good discrimination performance (median AUC, 0.66 (range, 0.53-0.77)) and were overfitted on external validation. Apart from the FMF model, only two models that were validated multiple times for any-onset PE prediction, which were based on maternal characteristics only, produced reasonable pooled AUCs of 0.71 (95% PI, 0.66-0.76) and 0.73 (95% PI, 0.55-0.86). Existing externally validated prediction models for any-, early- and late-onset PE have limited discrimination and calibration performance, and include inconsistent input variables. The triple-test FMF model had outstanding discrimination performance in predicting preterm PE in numerous settings, but the inclusion of specialized biomarkers may limit feasibility and implementation outside of high-resource settings. © 2023 The Authors. Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of International Society of Ultrasound in Obstetrics and Gynecology.

APOE4 homozygozity represents a distinct genetic form of Alzheimer's disease.

This study aimed to evaluate the impact of APOE4 homozygosity on Alzheimer's disease (AD) by examining its clinical, pathological and biomarker changes to see whether APOE4 homozygotes constitute a distinct, genetically determined form of AD. Data from the National Alzheimer's Coordinating Center and five large cohorts with AD biomarkers were analyzed. The analysis included 3,297 individuals for the pathological study and 10,039 for the clinical study. Findings revealed that almost all APOE4 homozygotes exhibited AD pathology and had significantly higher levels of AD biomarkers from age 55 compared to APOE3 homozygotes. By age 65, nearly all had abnormal amyloid levels in cerebrospinal fluid, and 75% had positive amyloid scans, with the prevalence of these markers increasing with age, indicating near-full penetrance of AD biology in APOE4 homozygotes. The age of symptom onset was earlier in APOE4 homozygotes at 65.1, with a narrower 95% prediction interval than APOE3 homozygotes. The predictability of symptom onset and the sequence of biomarker changes in APOE4 homozygotes mirrored those in autosomal dominant AD and Down syndrome. However, in the dementia stage, there were no differences in amyloid or tau positron emission tomography across haplotypes, despite earlier clinical and biomarker changes. The study concludes that APOE4 homozygotes represent a genetic form of AD, suggesting the need for individualized prevention strategies, clinical trials and treatments.

Reprint of: Out-of-sample tests for conditional quantile coverage: An application to Growth-at-Risk

This paper proposes tests for out-of-sample comparisons of interval forecasts based on parametric conditional quantile models. The tests rank the distance between actual and nominal conditional coverage with respect to the set of conditioning variables from all models, for a given loss function. We propose a pairwise test to compare two models for a single predictive interval. The set-up is then extended to a comparison across multiple models and/or intervals. The limiting distribution varies depending on whether models are strictly non-nested or overlapping. In the latter case, degeneracy may occur. We establish the asymptotic validity of wild bootstrap based critical values across all cases. An empirical application to Growth-at-Risk (GaR) uncovers situations in which a richer set of financial indicators are found to outperform a commonly-used benchmark model when predicting downside risk to economic activity.

An updated evidence synthesis on the Risk-Need-Responsivity (RNR) model: Umbrella review and commentary

PurposeTo conduct an umbrella review of Risk-Need-Responsivity (RNR) principles by synthesizing and appraising the consistency and quality of the underlying evidence base of RNR. MethodsFollowing PRISMA guidelines, we searched three bibliographic databases, the Cochrane Library, and grey literature from 2002 to 2022 for systematic reviews and meta-analysis on RNR principles. We summarized effect sizes, including as odds ratios and Area Under the Curve (AUC) statistic. We evaluated the quality of review evidence by examining risk of bias, excess statistical significance, between-study heterogeneity, and calculated prediction intervals for reported effect sizes. ResultsWe identified 26 unique meta-anlayses that examined RNR principles. These meta-analyses indicate inconsistent statistical support for the individual components of RNR. For the risk principle, there were links with recidivism (OR = 1.6, 95% CI [1.1, 2.3]). For the need principle, although there were associations between adherence to intervention programs and recidivism, risk assessment tools reflecting this principle had low predictive accuracy (AUCs 0.62–0.64). The general and specific responsivity principles received some support. However, the overall quality of the evidence was poor as indicated by potential authorship bias, lack of transparency, substandard primary research, limited subgroup analyses, and conflation of prediction with causality. ConclusionThe prevalent poor quality evidence and identified biases suggests that higher quality research is needed to determine whether current RNR claims of being evidence-based are justified.

Using neural ordinary differential equations to predict complex ecological dynamics from population density data.

Simple models have been used to describe ecological processes for over a century. However, the complexity of ecological systems makes simple models subject to modelling bias due to simplifying assumptions or unaccounted factors, limiting their predictive power. Neural ordinary differential equations (NODEs) have surged as a machine-learning algorithm that preserves the dynamic nature of the data (Chen et al. 2018 Adv. Neural Inf. Process. Syst.). Although preserving the dynamics in the data is an advantage, the question of how NODEs perform as a forecasting tool of ecological communities is unanswered. Here, we explore this question using simulated time series of competing species in a time-varying environment. We find that NODEs provide more precise forecasts than autoregressive integrated moving average (ARIMA) models. We also find that untuned NODEs have a similar forecasting accuracy to untuned long-short term memory neural networks and both are outperformed in accuracy and precision by empirical dynamical modelling . However, we also find NODEs generally outperform all other methods when evaluating with the interval score, which evaluates precision and accuracy in terms of prediction intervals rather than pointwise accuracy. We also discuss ways to improve the forecasting performance of NODEs. The power of a forecasting tool such as NODEs is that it can provide insights into population dynamics and should thus broaden the approaches to studying time series of ecological communities.

Allometric exponents for scaling running economy in human samples: A systematic review and meta-analysis

Ratio-scaled VO2 is the widely used method for quantifying running economy (RE). However, this method should be criticized due to its theoretical defect and curvilinear relationship indicated by the allometric scaling, although no consensus has been achieved on the generally accepted exponent b value of body weight. Therefore, this study aimed to provide a quantitative synthesis of the reported exponents used to scale VO2 to body weight. Six electronic databases were searched based on related terms. Inclusion criteria involved human cardiopulmonary testing data, derived exponents, and reported precision statistics. The random-effects model was applied to statistically analyze exponent b. Subgroup and meta-regression analyses were conducted to explore the potential factors contributing to variation in b values. The probability of the true exponent being below 1 in future studies was calculated. The estimated b values were all below 1 and aligned with the 3/4 power law, except for the 95 % prediction interval of the estimated fat-free body weight exponent b. A publication bias and a slightly greater I2 and τ statistic were also observed in the fat-free body weight study cohort. The estimated probabilities of the true body weight exponent, full body weight exponent, and fat-free body weight exponent being lower than 1 were 93.8 % (likely), 95.1 % (very likely), and 94.5 % (likely) respectively. ‘Sex difference’, ‘age category’, ‘sporting background’, and ‘testing modality’ were four potential but critical variables that impacted exponent b. Overall, allometric-scaled RE should be measured by full body weight with exponent b raised to 3/4.

Interval evaluation of wind power prediction based on skew-slash t distribution

Wind resources have characteristics of stochastic volatility, resulting in wind power forecast errors greatly. The short and medium-term wind power forecast error distribution of the actual wind farm operating system is analyzed, and a sharp peak and thick tail, with heavy tail and skewness characteristics, are presented. A skew-slash t distribution (SST distribution) is proposed to describe the error distribution of short-term wind power prediction, and the parameter estimation is carried out by probability density curve fitting. The fitting results of the wind power forecast error historical data of the Wind power plant based on SST distribution, t distribution, and t Location-slash distribution (TLS distribution) are obtained, and the fitting goodness and prediction accuracy are compared. The results show that the SST distribution can more effectively estimate the wind power prediction interval.

Exercise-based interventions targeting balance and falls in people with COPD: a systematic review and meta-analysis.

This review quantifies the mean treatment effect of exercise-based interventions on balance and falls risk in people with COPD. A structured search strategy (2000-2023) was applied to eight databases to identify studies evaluating the impact of exercise-based interventions (≥14 days in duration) on balance or falls in people with COPD. Pooled mean treatment effects (95% confidence intervals (CIs), 95% prediction intervals (PIs)) were calculated for outcomes reported in five or more studies. Inter-individual response variance and the promise of behaviour change techniques (BCTs) were explored. 34 studies (n=1712) were included. There were greater improvements in balance post intervention compared to controls for the Berg Balance Scale (BBS) (mean 2.51, 95% CI 0.22-4.80, 95% PI -4.60-9.63), Timed Up and Go (TUG) test (mean -1.12 s, 95% CI -1.69- -0.55 s, 95% PI -2.78-0.54 s), Single-Leg Stance (SLS) test (mean 3.25 s, 95% CI 2.72-3.77 s, 95% PI 2.64-3.86 s) and Activities-specific Balance Confidence (ABC) scale (mean 8.50%, 95% CI 2.41-14.58%, 95% PI -8.92-25.92%). Effect on falls remains unknown. Treatment effects were larger in male versus mixed-sex groups for the ABC scale and SLS test, and in balance training versus other exercise-based interventions for the BBS and TUG test. Falls history was not associated with changes in balance. Meta-analysis of individual response variance was not possible and study-level results were inconclusive. Eleven promising BCTs were identified (promise ratio ≥2). Evidence for the effect of exercise-based interventions eliciting clinically important improvements in balance for people with COPD is weak, but targeted balance training produces the greatest benefits. Future exercise interventions may benefit from inclusion of the identified promising BCTs.

Statistical Verification using Surrogate Models and Conformal Inference and a Comparison with Risk-Aware Verification

Uncertainty in safety-critical cyber-physical systems can be modeled using a finite number of parameters or parameterized input signals. Given a system specification in Signal Temporal Logic (STL), we would like to verify that for all (infinite) values of the model parameters/input signals, the system satisfies its specification. Unfortunately, this problem is undecidable in general. Statistical model checking (SMC) offers a solution by providing guarantees on the correctness of CPS models by statistically reasoning on model simulations. We propose a new approach for statistical verification of CPS models for user-provided distribution on the model parameters. Our technique uses model simulations to learn surrogate models , and uses conformal inference to provide probabilistic guarantees on the satisfaction of a given STL property. Additionally, we can provide prediction intervals containing the quantitative satisfaction values of the given STL property for any user-specified confidence level. We compare this prediction interval with the interval we get using risk estimation procedures. We also propose a refinement procedure based on Gaussian Process (GP)-based surrogate models for obtaining fine-grained probabilistic guarantees over sub-regions in the parameter space. This in turn enables the CPS designer to choose assured validity domains in the parameter space for safety-critical applications. Finally, we demonstrate the efficacy of our technique on several CPS models.

Effects of SGLT2 inhibitors on right ventricular function in heart failure patients: Updated meta-analysis of the current literature.

There is some discrepancy in current studies concerning the effect of sodium-glucose cotransporter type 2 inhibitors (SGLT2i) on right ventricular (RV) functions in heart failure (HF) patients. Hence, this meta-analysis was focused on determining the impact of SGLT2i on RV functions in such individuals. Two independent investigators searched PubMed, Google Scholar, and the Cochrane Library for articles of interest. To analyze heterogeneity, Higgins' I2 as well as prediction intervals and Egger's test were used to assess heterogeneity. The Newcastle-Ottawa standard ratings approach was used to assess the quality of observational studies. The ROBINS-I risk of bias algorithm was used to assess bias risks of randomized studies. This meta-analysis evaluated 8 studies in total. Over the follow-up time frame, patients who used SGLT2i had substantially lower systolic pulmonary artery pressure and higher tricuspid annular plane systolic excursion values (mean difference [MD] = -5.23 [-7.81; -2.66] and, MD = 1.47 [1.01; 1.93]; P <0.01, respectively). There was no significant difference in RVS' values between follow-up and baseline (MD = 1.54 [-0.19; 3.26]; P = 0.08). However, as compared to the baseline period, fractional area contraction values were substantially larger at the end of the follow-up (MD = 5.52 [4.23; 6.82]; P <0.01). To the best of our knowledge, this is the first meta-analysis assessing the impact of SGLT2i on RV function in HF patients. Our findings suggest that SGLT2i may improve RV performance in HF patients.

날씨 변수를 고려한 전력 수요량 예측구간 시계열 분석 연구

Annual electricity demand is steadily increasing and the importance of forecasting the electricity demand is emerging since the dependence on domestic electricity is also increasing. The purpose of this study is analysis of the electricity demand considering seasonality and weather variables, for which we study time series modelling and forecasting analysis. ARIMA, SARIMA, ARIMAX, SARIMAX models are handled with optimally selected orders. Out-of-sample forecasting analysis is carried out to evaluate predicted values and their errors such as RMSE, MAE, MAPE and MSLE. The errors by four models are compared. As the optimal model, SARIMAX(2,1,1) (2,1,2,12) model with CDD, HDD and insolation has been chosen. For strict statistical analysis of prediction intervals, normal distribution, laplace distribution and bootstrap method are adopted to construct 80%, 95% prediction intervals. Coverage probability (CP), average length (AL) and mean interval score (MIS) of the prediction intervals by three approximations are evaluated. This study contributes with novelty in that it provides three approaches of prediction intervals along with their comparison. The results of this study are expected to be of practical help in the efficient operation of electricity supply system.

Prediction of Individual Disease Progression Including Parameter Uncertainty in Rare Neurodegenerative Diseases: The Example of Autosomal-Recessive Spastic Ataxia Charlevoix Saguenay (ARSACS)

The aim of this study was to develop a model to predict individual subject disease trajectories including parameter uncertainty and accounting for missing data in rare neurological diseases, showcased by the ultra-rare disease Autosomal-Recessive Spastic Ataxia Charlevoix Saguenay (ARSACS). We modelled the change in SARA (Scale for Assessment and Rating of Ataxia) score versus Time Since Onset of symptoms using non-linear mixed effect models for a population of 173 patients with ARSACS included in the prospective real-world multicenter Autosomal Recessive Cerebellar Ataxia (ARCA) registry. We used the Multivariate Imputation Chained Equation (MICE) algorithm to impute missing covariates, and a covariate selection procedure with a pooled p-value to account for the multiply imputed data sets. We then investigated the impact of covariates and population parameter uncertainty on the prediction of the individual trajectories up to 5 years after their last visit. A four-parameter logistic function was selected. Men were estimated to have a 25% lower SARA score at disease onset and a moderately higher maximum SARA score, and time to progression (T50) was estimated to be 35% lower in patients with age of onset over 15 years. The population disease progression rate started slowly at 0.1 points per year peaking to a maximum of 0.8 points per year (at 36.8 years since onset of symptoms). The prediction intervals for SARA scores 5 years after the last visit were large (median 7.4 points, Q1-Q3: 6.4–8.5); their size was mostly driven by individual parameter uncertainty and individual disease progression rate at that time.Graphical

Multi-objective optimization and uncertainty quantification for inductors based on neural network

PurposeThe prolonged training time of the neural network (NN) has sparked considerable debate regarding their application in the field of optimization. The purpose of this paper is to explore the beneficial assistance of NN-based alternative models in inductance design, with a particular focus on multi-objective optimization and uncertainty analysis processes.Design/methodology/approachUnder Gaussian-distributed manufacturing errors, this study predicts error intervals for Pareto points and select robust solutions with minimal error margins. Furthermore, this study establishes correlations between manufacturing errors and inductance value discrepancies, offering a practical means of determining permissible manufacturing errors tailored to varying accuracy requirements.FindingsThe NN-assisted methods are demonstrated to offer a substantial time advantage in multi-objective optimization compared to conventional approaches, particularly in scenarios where the trained NN is repeatedly used. Also, NN models allow for extensive data-driven uncertainty quantification, which is challenging for traditional methods.Originality/valueThree objectives including saturation current are considered in the multi-optimization, and the time advantages of the NN are thoroughly discussed by comparing scenarios involving single optimization, multiple optimizations, bi-objective optimization and tri-objective optimization. This study proposes direct error interval prediction on the Pareto front, using extensive data to predict the response of the Pareto front to random errors following a Gaussian distribution. This approach circumvents the compromises inherent in constrained robust optimization for inductance design and allows for a direct assessment of robustness that can be applied to account for manufacturing errors with complex distributions.

Trends in medication use after the onset of the COVID-19 pandemic in the Republic of Ireland: an interrupted time series study

Abstract Introduction The COVID-19 pandemic had a substantial impact on a range of health services, particularly in primary care. Research from Ireland suggests while community pharmacies remained open, restrictions for in-person healthcare appointments impacted patients.[1] Although there is evidence that the onset of the pandemic affected medicines utilisation internationally,[2] it is unclear how prescribing in Ireland changed following March 2020. Aim To evaluate how dispensing of medications in primary care in Ireland changed following the onset of the COVID-19 pandemic compared to expected trends. Methods This was an interrupted time series study, and the protocol was pre-registered (doi.org/10.17605/OSF.IO/WNQHR). It used publicly available data from the Health Service Executive Primary Care Reimbursement Services for each month between January 2016 and July 2022. Data covered dispensing on the General Medical Services (i.e. medical card) scheme for all medication therapeutic subgroups and commonly dispensed medications (based on the top 100 individual medications per month). Pre-pandemic data (January 2016-November 2019) was used to forecast expected trends from December 2019 onwards for each subgroup and medication with 99% prediction intervals. The Holt-Winters method was used, which decomposes time series data into seasonal, trend, and irregular components. Three months of observed data unaffected by the pandemic (December 2019-February 2020, validation period) were compared to the forecast to validate accuracy of predictions. Observed data were compared to forecasts in March 2020 (as the first month of pandemic restrictions in Ireland) and over the remainder of the study period from April 2020-July 2022. Statistical significance was defined as observed data outside the 99% prediction interval (p&amp;lt;0.01). Results The overall number of dispensings was 7.6% (99%CI 2.5% to 13.2%) higher than forecast in March 2020. Many (31/77) therapeutic subgroups had dispensing significantly different from forecast in March 2020. Drugs for obstructive airway disease had the largest difference, with dispensing 26.2% (99%CI 19.5%-33.6%) higher than forecasted. Other subgroups with dispensing significantly higher than forecasted included minerals, analgesics, thyroid therapy, serum lipid-reducing agents and diuretics. Dispensing was significantly lower than forecasted for other gynaecologicals (17.7% lower, 99%CI 6.3%-26.6%) and dressings (11.6%, 99%CI 9.4%-41.6%). Similarly, many individual medications had significantly higher dispensing in March 2020. Notably, dispensing of amoxicillin (with/without clavulanic acid) and oral prednisolone were lower than forecasted in the months following the onset of the pandemic, particularly during winter 2020/2021. Conclusion There was a peak in dispensing for many long-term medications in March 2020 suggesting patients obtained additional supplies of their regular medicines as pandemic restrictions were introduced. Exceptions were dispensing of two therapeutic subgroups (dressings/intrauterine devices) linked to in-person healthcare consultations, illustrating the disruption to service delivery. Lower than expected dispensing of antimicrobials and reduced seasonal peaks may be partly due to reduced infection transmission generally. Although we were limited by lacking data on the number of people dispensed each medication, this is the first study to examine changes in medication use during the COVID-19 pandemic in Ireland, considering all therapeutic areas. This study provides evidence to inform planning for medication demand and supply for future major health events.

The Distribution of Risk Across Healthcare Providers and Reducing Misclassification

Four linear multilevel mixed-risk models were compared using model assumption tests and predictions. Models varied by the number of random intercepts from 1 to 4, producing 2-level through 5-level models of the same measure, operative time. Normality of the dependent variable and residuals, variance homoscedasticity, level-1, and level-2 exogeneity were tested using the robust test of the level-1 residuals variance by surgeon, estimates of density, skew, and the Hausman test. Measure (operative time by hospital and surgeon) aberrancy and risk classification were evaluated using traditional methods and used to assess distribution measures. The dependent variable and the level-1 residuals required transformation for linearity and variance stabilization, respectively. Normality criteria were met for both level-1 and level-2 residuals and standardized residuals. The likelihood ratio comparing the four models was significantly larger for the 5-level (1016.1; P&amp;lt;0.00005) model than the likelihood ratio for the four-level and other models. Shrinkage was greatest for the 2-level model (0.039; P&amp;lt;0.00005) and least for the 5-level model (0.028; P&amp;lt;0.00005). Level-1 variance homoscedasticity was confirmed by the robust variance test across all models (P&amp;gt;F=1). Aberrant value detection did not require the exclusion of any observations, while prediction intervals revealed low or high risk for 54.2% of surgeons for the 2-level model and 8.6% for the 5-level model. The traditional (c2 = -11.01; P=1) and instrumental variable (c2 = 21.06; P=1) Hausman tests show that the null hypothesis cannot be rejected for level-1 or level-2 exogeneity. Once level-1 and level-2 exogeneity was confirmed, and since deconfounding was a model consideration, causal inferential capacity was assumed. The likelihood ratio, residual variance, shrinkage, and predictions show that the 5-level model is preferred to the other models.