Establishing causal inference in observational studies has always been a challenge. One of the most well-known biases is unmeasured confounding, which occurs when an unmeasured variable influences both the exposure and outcome. One method for quantifying the potential impact of this bias is through the E-value, which provides the strength a confounder needs to have to explain away a proposed causal association. However, the E-value is typically only derived when the exposure, confounder and outcome do not vary over time. Therefore the E-value is not applicable to longitudinal designs, as it does not handle the complexities of multiple measures of the outcome when analysed simultaneously. In this paper we will apply a recent extension of the E-value for interrupted time series to a two-arm longitudinal study design, concerning the willingness to compete hurt and the use of analgesics in youth elite athletes. In the example, we explain how the interpretation of this extension differs from the interrupted time series design. Moreover, we compare the extension with the original E-value in terms of interpretability and assumptions regarding the confounder. In the example, we demonstrate that the original E-value suggest our association is less robust to confounding than the longitudinal extension, and we explain the practical implications of this discrepancy. Overall this paper highlights the importance of considering the temporal ordering of the average treatment effect when evaluating unmeasured confounding.
Accurate estimation of population means is an important objective in survey sampling, as it provides reliable information for decision-making and policy formulation. To improve estimation efficiency, this study proposes a new estimator for the population mean in stratified random sampling by incorporating two auxiliary variables along with their covariance structure. The proposed estimator is developed using a nonlinear approach, and its statistical properties are derived using first-order approximation techniques. The optimum values of the unknown parameters are obtained through Cramer’s Rule. The efficiency of the proposed estimator is assessed using mean squared error (MSE) and percentage relative efficiency (PRE) and compared with several existing estimators. Both theoretical and empirical results show that the proposed estimator consistently outperforms the competing estimators by producing lower MSE and higher PRE values. To further examine its stability, simulation studies and sensitivity analyses are conducted under different correlation structures, including both negative and positive correlations. The findings demonstrate that the proposed estimator remains robust and efficient across varying conditions. Overall, the study highlights that the effective use of auxiliary information can substantially improve the accuracy and reliability of population mean estimation in stratified random sampling.
Difference-in-differences designs require specifying a reference period for estimating differential changes between treatment and comparison units. In this study, we demonstrate the distinct role of random group-specific temporary shocks when they occur during the reference period versus other periods. We first show that when such shocks occur during any period other than the reference period, they only affect that period’s difference-in-differences estimate; by contrast, when they occur during the reference period, they affect all difference-in-differences estimates, and in the same direction. As a result, random shocks during the reference period can create the appearance of positive or negative treatment effects during the post-exposure period or non-parallel trends during the pre-exposure period even when outcomes move in parallel, and averaging estimates across multiple periods does not mitigate this issue. In Monte Carlo simulations, we further show that type-I error rates of average pre- and post-intervention estimates and type-II error rates of average post-intervention estimates are much more sensitive to the magnitude of random, group-specific shocks when they occur during the reference period compared to other periods. Researchers should be aware of the distinctive role of group-specific shocks when they occur during the reference period and differentially affect either the treatment or comparison groups, and we provide guidance on identifying and addressing this issue.
Empirical research using claims data has found that continuity of care (COC) is associated with a number of important health economic and medication appropriateness-related outcomes (MARO), such as polypharmacy and potentially inappropriate medications (PIM). However, there is no consensus in the literature on whether claims-based COC analyses should control for the number of visits and the number of providers. In this paper, we investigate how controlling for the number of visits impacts regression model performance and estimates. We also perform additional exploratory analyses to investigate the presence of an interaction between COC and the number of visits and of nonlinear effects of COC and the number of visits. In our main analysis, we used multivariate logistic regression models on a dataset of over 30,000 elderly individuals in Germany, based on claims data from statutory health insurance providers, with extreme polypharmacy (10+ distinct medications) as the outcome and the Herfindahl–Hirschman Index (HHI) as the key predictor, controlling for age, sex and morbidity. We reported regression coefficients, standard errors and p-values and used the Akaike Information Criterion (AIC), Tjur’s R^2 , area under the receiver operating characteristic (ROC) curve, cross-validation (accuracy/correct classification rate and Brier’s score) as well as a residual analysis to compare models. In robustness checks, we excluded outliers with a high number of visits, used the Bice-Boxerman Continuity of Care Index (BBCOCI) as the key predictor and used PIM as the outcome. In exploratory analyses, we included interaction terms and nonlinear (quadratic) terms for the number of visits and the HHI/BBCOCI. In the main analysis and all robustness checks, models including the number of visits performed better than models excluding the number of visits. Failing to include the number of visits led to inflated estimates of the association between the HHI/BBCOCI and MARO. The exploratory analyses revealed significant interaction terms and nonlinearities. Based on our findings, we recommend that researchers control for the number of visits in claims-based COC analyses, at least when investigating informational/management continuity. Furthermore, where possible, researchers should consider investigating the interaction between the number of visits and the HHI/BBCOCI and allowing for nonlinearity for these variables.
The COVID-19 pandemic exposed critical shortfalls in ventilator and ICU capacity worldwide, which highlights the need for proactive, data-driven resource planning. We present a population-based forecasting framework that integrates a SARIMA-ANN hybrid model with principled missing-data imputation (K-Nearest Neighbors as the primary method, with clustering as an exploratory comparison) to generate country-level ventilator demand forecasts from openly available sources: Our World in Data, Johns Hopkins CSSE, the Oxford COVID-19 Government Response Tracker, and real-time reproduction-rate estimates. Performance is evaluated through case studies in the United States and India. Over an 83-day out-of-sample window for the United States (October-December 2021), the hybrid approach substantially outperformed standard baselines (MSE: 79.5 vs. 124.9 for a 3-day moving average and 172.7 for first-order autoregression). For India, a 30-day planning window showed stable forecasts averaging approximately 13,437 ventilators in the final week (April 24-30, 2022). A key empirical finding is that severity indicators, particularly new deaths per million, were substantially more informative for ICU burden than transmissibility alone; the reproduction rate showed a weak negative association with ICU occupancy and produced unreliable predictions during rising-reproduction-rate periods. Our framework is scalable to settings with heterogeneous ICU reporting and supports evidence-based preparedness planning. We also discuss limitations during de-escalation phases and identify directions for probabilistic and supply-constrained extensions.
