Model-based Variance Research Articles

Retraction: The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives.

Retraction: The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives.

On variance estimation of target population created by inverse probability weighting

ABSTRACT Inverse probability weighting (IPW) is frequently used to reduce or minimize the observed confounding in observational studies. IPW creates a pseudo-sample by weighting each individual by the inverse of the conditional probability of receiving the treatment level that he/she has actually received. In the pseudo-sample there is no variation among the multiple individuals generated by weighting the same individual in the original sample. This would reduce the variability of the data and therefore bias the variance estimate in the target population. Conventional variance estimation methods for IPW estimators generally ignore this underestimation and tend to produce biased estimates of variance. We here propose a more reasonable method that incorporates this source of variability by using parametric bootstrapping based on intra-stratum variability estimates. This approach firstly uses propensity score stratification and intra-stratum standard deviation to approximate the variability among multiple individuals generated based on a single individual whose propensity score falls within the corresponding stratum. The parametric bootstrapping is then used to incorporate the target variability by re-generating outcomes after adding a random error term to the original data. The performance of the proposed method is compared with three existing methods including the naïve model-based variance estimator, the nonparametric bootstrap variance estimator, and the robust variance estimator in the simulation section. An example of patients with sarcopenia is used to illustrate the implementation of the proposed approach. According to the results, the proposed approach has desirable statistical properties and can be easily implemented using the provided R code.

Power Approximations for Overall Average Effects in Meta-Analysis With Dependent Effect Sizes

Meta-analytic models for dependent effect sizes have grown increasingly sophisticated over the last few decades, which has created challenges for a priori power calculations. We introduce power approximations for tests of average effect sizes based upon several common approaches for handling dependent effect sizes. In a Monte Carlo simulation, we show that the new power formulas can accurately approximate the true power of meta-analytic models for dependent effect sizes. Lastly, we investigate the Type I error rate and power for several common models, finding that tests using robust variance estimation provide better Type I error calibration than tests with model-based variance estimation. We consider implications for practice with respect to selecting a working model and an inferential approach.

A general method for calculating power for GEE analysis of complete and incomplete stepped wedge cluster randomized trials.

Stepped wedge designs have uni-directional crossovers at randomly assigned time points (steps) where clusters switch from control to intervention condition. Incomplete stepped wedge designs are increasingly used in cluster randomized trials of health care interventions and have periods without data collection due to logistical, resource and patient-centered considerations. The development of sample size formulae for stepped wedge trials has primarily focused on complete designs and continuous responses. Addressing this gap, a general, fast, non-simulation based power procedure is proposed for generalized estimating equations analysis of complete and incomplete stepped wedge designs and its predicted power is compared to simulated power for binary and continuous responses. An extensive set of simulations for six and twelve clusters is based upon the Connect-Home trial with an incomplete stepped wedge design. Results show that empirical test size is well controlled using a t-test with bias-corrected sandwich variance estimator for as few as six clusters. Analytical power agrees well with a simulated power in scenarios with twelve clusters. For six clusters, analytical power is similar to simulated power with estimation using the correctly specified model-based variance estimator. To explore the impact of study design choice on power, the proposed fast GEE power method is applied to the Connect-Home trial design, four alternative incomplete stepped wedge designs and one complete design.

Regression analysis for covariate-adaptive randomization: Arobust and efficient inference perspective.

Linear regression is arguably the most fundamental statistical model; however, the validity of its use in randomized clinical trials, despite being common practice, has never been crystal clear, particularly when stratified or covariate-adaptive randomization is used. In this article, we investigate several of the most intuitive and commonly used regression models for estimating and inferring the treatment effect in randomized clinical trials. By allowing the regression model to be arbitrarily misspecified, we demonstrate that all these regression-based estimators robustly estimate the treatment effect, albeit with possibly different efficiency. We also propose consistent non-parametric variance estimators and compare their performances to those of the model-based variance estimators that are readily available in standard statistical software. Based on the results and taking into account both theoretical efficiency and practical feasibility, we make recommendations for the effective use of regression under various scenarios. For equal allocation, it suffices to use the regression adjustment for the stratum covariates and additional baseline covariates, if available, with the usual ordinary-least-squares variance estimator. For unequal allocation, regression with treatment-by-covariate interactions should be used, together with our proposed variance estimators. These recommendations apply to simple and stratified randomization, and minimization, among others. We hope this work helps to clarify and promote the usage of regression in randomized clinical trials.

Analysis of odds, probability, and hazard ratios: From 2 by 2 tables to two-sample survival data

Analysis of 2 by 2 tables and two-sample survival data has been widely used. Exact calculation is computational intractable for conditional likelihood inference in odds ratio models with large marginals in 2 by 2 tables, or partial likelihood inference in Cox’s proportional hazards models with considerable tied event times. Approximate methods are often employed, but their statistical properties have not been formally studied while taking into account the approximation involved. We develop new methods and theory by constructing suitable estimating functions while leveraging knowledge from conditional or partial likelihood inference. We propose a weighted Mantel–Haenszel estimator in an odds ratio model such as Cox’s discrete-time proportional hazards model. Moreover, we consider a probability ratio model, and derive as a consistent estimator the Breslow–Peto estimator, which has been regarded as an approximation to partial likelihood estimation in the odds ratio model. We study both model-based and model-robust variance estimation. For the Breslow–Peto estimator, our new model-based variance estimator is no greater than the commonly reported variance estimator. We present numerical studies which support the theoretical findings.

Random effect misspecification in stepped wedge designs.

Stepped wedge cluster randomized trials are often analysed using linear mixed effects models that may include random effects for cluster, time and/or treatment. We investigate the impact of misspecification of the random effects structure of the model. Specifically, we considered two cases of misspecification of the random effects in a cross-sectional stepped wedge cluster randomized trials model - fit a linear mixed effects model with random time effects but the true model includes random treatment effects (case 1) or fit a linear mixed effects model with random treatment effect but the true model includes random time effects (case 2) - and derived the variance of the estimated treatment effect under misspecification. We defined two measures of the effect of misspecification: validity and efficiency. Validity is the ratio of the model-based variance of the treatment effect from the mis-specified model divided by the true variance of the treatment effect from the mis-specified model (based on a sandwich estimate of the variance). Efficiency is the ratio of the model-based variance of the treatment effect from the correctly specified model divided by the true variance of the treatment effect from the mis-specified model. We found that validity is less than 1.0 (anti-conservative) in almost all situations investigated with the exception of case 1 with two sequences, when validity could be greater than 1.0. Efficiency is less than 1 in all cases and depends on the intracluster correlation coefficient, the relative magnitude of the variance of the misclassified variance component, and the number of sequences. In general, there is no universal recommendation as to the most robust approach except for the case of a classic stepped wedge cluster randomized trial with only 2 sequences, where fitting a random time model is less likely to lead to anti-conservative inference compared with fitting a random intervention model.

Power considerations for generalized estimating equations analyses of four-level cluster randomized trials.

In this article, we develop methods for sample size and power calculations in four-level intervention studies when intervention assignment is carried out at any level, with a particular focus on cluster randomized trials (CRTs). CRTs involving four levels are becoming popular in healthcare research, where the effects are measured, for example, from evaluations (level 1) within participants (level 2) in divisions (level 3) that are nested in clusters (level 4). In such multilevel CRTs, we consider three types of intraclass correlations between different evaluations to account for such clustering: that of the same participant, that of different participants from the same division, and that of different participants from different divisions in the same cluster. Assuming arbitrary link and variance functions, with the proposed correlation structure as the true correlation structure, closed-form sample size formulas for randomization carried out at any level (including individually randomized trials within a four-level clustered structure) are derived based on the generalized estimating equations approach using the model-based variance and using the sandwich variance with an independence working correlation matrix. We demonstrate that empirical power corresponds well with that predicted by the proposed method for as few as eight clusters, when data are analyzed using the matrix-adjusted estimating equations for the correlation parameters with a bias-corrected sandwich variance estimator, under both balanced and unbalanceddesigns.

Power calculation for analyses of cross-sectional stepped-wedge cluster randomized trials with binary outcomes via generalized estimating equations.

Power calculation for stepped-wedge cluster randomized trials (SW-CRTs) presents unique challenges, beyond those of standard parallel cluster randomized trials, due to the need to consider temporal within cluster correlations and background period effects. To date, power calculation methods specific to SW-CRTs have primarily been developed under a linear model. When the outcome is binary, the use of a linear model corresponds to assessing a prevalence difference; yet trial analysis often employs a nonlinear link function. We propose power calculation methods for cross-sectional SW-CRTs under a logistic model fitted by generalized estimating equations. Firstly, under an exchangeable correlation structure, we show the power based on a logistic model is lower than that from assuming a linear model in the absence of period effects. We then evaluate the impact of background prevalence changes over time on power. To allow the correlation among outcomes in the same cluster to change over time and with treatment status, we generalize the methods to more complex correlation structures. Our simulation studies demonstrate that the proposed power calculation methods perform well with the model-based variance under the true correlation structure and reveal that a working independence structure can result in substantial efficiency loss, while a working exchangeable structure performs well even when the underlying correlation structure deviates from exchangeable. An extension to our methods accounts for variable cluster sizes and reveals that unequal cluster sizes have a modest impact on power. We illustrate the approaches by application to a quality of care improvement trial for acute coronary syndrome.

Effect of Occupational Health and Safety, and Work Environment on Employee Performance with Working Satisfaction as Mediation Variable

Objective - This study aims to determine and analyze the influence of Occupational Health and Safety, and the Working Environment on Employee Performance with Job Satisfaction as a mediating variable in PT. Kereta Api Indonesia (Persero) with sample on DAOP I Jakarta. Methodology/Technique - The study population numbered 292 employees and 75 respondents be adopted as a sample of the study. Techniques of analysis using a statistical test structural equation model-based variance (SmartPLS). Findings – The results showed that, (1) Occupational Health and Safety had no effect on Job Satisfaction and Employee Performance, (2) the Work Environment had a positive and significant effect on Job Satisfaction and Employee Performance (3) Job Satisfaction has a positive and significant effect on Employee Performance, (4) Occupational Health and Safety has no effect on Employee Performance even though through Job Satisfaction mediation, (5) the Work Environment has a positive and significant effect on Employee Performance through mediation of Job Satisfaction, (6) Occupational Health and Safety, and the Work Environment simultaneously have a positive and significant effect on Job Satisfaction with the coefficient of determination, which is equal to 0,533, (7) Occupational Health and Safety, Work Environment, and Job Satisfaction simultaneously have a positive effect and significant to Employee Performance with coefficient of determination, which is equal to 0,890. Novelty - The company is expected to provide adequate rest periods, maintain the nutritional intake of its employees by providing healthy food, provide educational scholarships for further levels for employees, safeguard the work environment from chemical hazards and other hazards, and give positive motivation to the employees. Type of Paper: Empirical. JEL Classification: J20, J24, J28. Keywords: Occupational Health and Safety, Work Environment, Job Satisfaction, Employee Performance Reference to this paper should be made as follows: Dwi, L.S; Putri, N; Yuwono; Amir, I. (2021). Effect of Occupational Health and Safety, and Work Environment on Employee Performance with Working Satisfaction as Mediation Variable, Journal of Management and Marketing Review, 6(2) 117 – 124. https://doi.org/10.35609/jmmr.2021.6.2(3)

Does the variance of surface EMG signals during isometric contractions follow an inverse gamma distribution?

In this paper, the validity of the stochastic model-based variance distribution of surface electromyogram (EMG) signals during isometric contraction is investigated. In the model, the EMG variance is considered as a random variable following an inverse gamma distribution, thereby allowing the representation of variations in the variance. This inverse gamma-based model for the EMG variance is experimentally validated through comparison with the empirical distribution of variances. The difference between the model distribution and the empirical distribution is quantified using the Kullback- Leibler divergence. Additionally, regression analysis is conducted between the model parameters and the statistics calculated from the empirical distribution of EMG variances. Experimental results showed that the inverse gamma-based model is potentially suitable and that its parameters can be used to evaluate the stochastic properties of the EMG variance.

The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives.

The purpose of the study is to reduce the error in the pricing process of financial derivatives, as well as to obtain more accurate product values, thereby reducing transaction costs, accelerating transaction speed, establishing a larger investment scale, and enabling investors to obtain excellent returns under market conditions as much as possible. Based on the variance reduction technology, a Monte Carlo model that can effectively analyze financial prices is added to analyze price fluctuations and find the optimal holding time for users of financial derivatives, thereby reducing the risk of holding the financial derivatives. The results show that the Monte Carlo model-based variance reduction technology can significantly improve the simulation efficiency of financial derivatives pricing. In addition, the importance sampling method is used to optimize the selection, thereby making it closer to the theoretical values. The proposed method is easy to implement and has higher computational efficiency, which can ensure the financial benefits of users holding financial derivatives during the holding period. It can be seen that the Monte Carlo model-based variance reduction technology has high application value in the pricing of financial derivatives, and it is of great significance for the pricing of other products.

Robustness of ANCOVA in randomized trials with unequal randomization.

Randomized trials with continuous outcomes are often analyzed using analysis of covariance (ANCOVA), with adjustment for prognostic baseline covariates. The ANCOVA estimator of the treatment effect is consistent under arbitrary model misspecification. In an article recently published in the journal, Wang et al proved the model-based variance estimator for the treatment effect is also consistent under outcome model misspecification, assuming the probability of randomization to each treatment is 1/2. In this reader reaction, we derive explicit expressions which show that when randomization is unequal, the model-based variance estimator can be biased upwards or downwards. In contrast, robust sandwich variance estimators can provide asymptotically valid inferences under arbitrary misspecification, even when randomization probabilities are notequal.

A classical regression framework for mediation analysis: fitting one model to estimate mediation effects.

SUMMARYMediation analysis explores the degree to which an exposure’s effect on an outcome is diverted through a mediating variable. We describe a classical regression framework for conducting mediation analyses in which estimates of causal mediation effects and their variance are obtained from the fit of a single regression model. The vector of changes in exposure pathway coefficients, which we named the essential mediation components (EMCs), is used to estimate standard causal mediation effects. Because these effects are often simple functions of the EMCs, an analytical expression for their model-based variance follows directly. Given this formula, it is instructive to revisit the performance of routinely used variance approximations (e.g., delta method and resampling methods). Requiring the fit of only one model reduces the computation time required for complex mediation analyses and permits the use of a rich suite of regression tools that are not easily implemented on a system of three equations, as would be required in the Baron–Kenny framework. Using data from the BRAIN-ICU study, we provide examples to illustrate the advantages of this framework and compare it with the existing approaches.

Model-based variance estimation in two-dimensional systematic sampling

A variance estimator for the mean of a systematic sample in two dimensions is proposed and analyzed. The estimation strategy relies on a super-population model which follows a spatial auto-regressive structure and allows for the presence of covariates. The small sample properties of the proposed procedure are analyzed by simulations: the model-based estimation strategy shows an excellent performance in a variety of situations which are common in real situations.

Multilevel Hierarchical Bayesian Versus State Space Approach in time Series Small Area Estimation: the Dutch Travel Survey

Summary This study compares state space models (estimated with the Kalman filter with a frequentist approach to hyperparameter estimation) with multilevel time series models (based on the hierarchical Bayesian framework). The application chosen is the Dutch Travel Survey featuring small sample sizes and discontinuities caused by the survey redesigns. Both modelling approaches deliver similar point and variance estimates. Slight differences in model-based variance estimates appear mostly in small-scaled domains and are due to neglecting uncertainty around the hyperparameter estimates in the state space models, and to a lesser extent to skewness in the posterior distributions of the parameters of interest. The results suggest that the reduction in design-based standard errors with the hierarchical Bayesian approach is over 50% at the provincial level, and over 30% at the national level.

Comparing Empirical and Semi-Empirical Approaches to Forest Biomass Modelling in Different Biomes Using Airborne Laser Scanner Data

Airborne laser scanner (ALS) data are used operationally to support field inventories and enhance the accuracy of forest biomass estimates. Modelling the relationship between ALS and field data is a fundamental step of such applications and the quality of the model is essential for the final accuracy of the estimates. Different modelling approaches and variable transformations have been advocated in the existing literature, but comparisons are few or non-existent. In the present study, two main approaches to modelling were compared: the empirical and semi-empirical approaches. Evaluation of model performance was conducted using a conventional evaluation criterion, i.e., the mean square deviation (MSD). In addition, a novel evaluation criterion, the model error (ME), was proposed. The ME was constructed by combining a MSD expression and a model-based variance estimate. For the empirical approach, multiple regression models were developed with two alternative transformation strategies: square root transformation of the response, and natural logarithmic transformation of both response and predictors. For the semi-empirical approach, a nonlinear regression of a power model form was chosen. Two alternative predictor variables, mean canopy height and top canopy height, were used separately. Results showed that the semi-empirical approach resulted in the smallest MSD in three of five study sites. The empirical approach resulted in smaller ME in the temperate and boreal biomes, while the semi-empirical approach resulted in smaller ME in the tropical biomes.

Robust Inference from Conditional Logistic Regression Applied to Movement and Habitat Selection Analysis.

Conditional logistic regression (CLR) is widely used to analyze habitat selection and movement of animals when resource availability changes over space and time. Observations used for these analyses are typically autocorrelated, which biases model-based variance estimation of CLR parameters. This bias can be corrected using generalized estimating equations (GEE), an approach that requires partitioning the data into independent clusters. Here we establish the link between clustering rules in GEE and their effectiveness to remove statistical biases in variance estimation of CLR parameters.The current lack of guidelines is such that broad variation in clustering rules can be found among studies (e.g., 14–450 clusters) with unknown consequences on the robustness of statistical inference. We simulated datasets reflecting conditions typical of field studies. Longitudinal data were generated based on several parameters of habitat selection with varying strength of autocorrelation and some individuals having more observations than others. We then evaluated how changing the number of clusters impacted the effectiveness of variance estimators. Simulations revealed that 30 clusters were sufficient to get unbiased and relatively precise estimates of variance of parameter estimates. The use of destructive sampling to increase the number of independent clusters was successful at removing statistical bias, but only when observations were temporally autocorrelated and the strength of inter-individual heterogeneity was weak. GEE also provided robust estimates of variance for different magnitudes of unbalanced datasets. Our simulations demonstrate that GEE should be estimated by assigning each individual to a cluster when at least 30 animals are followed, or by using destructive sampling for studies with fewer individuals having intermediate level of behavioural plasticity in selection and temporally autocorrelated observations. The simulations provide valuable information to build reliable habitat selection and movement models that allow for robustness of statistical inference without removing excessive amounts of ecological information.

Abstract 11806: Early, Intensive Atorvastatin Treatment Reduces First and Recurrent Hard Cardiovascular Events After Acute Coronary Syndrome

Background: Early, intensive statin treatment is standard of care after acute coronary syndrome (ACS), but only one placebo (PBO)-controlled trial has demonstrated an early benefit of such treatment. In the Myocardial Ischemia Reduction with Aggressive Cholesterol Lowering (MIRACL) trial, the primary outcome of time to first occurrence of death, MI, resuscitated cardiac arrest, or hospitalization for unstable angina (UA) was reduced with atorvastatin (ATV) 80 mg/day, compared with PBO. However, this result was borderline significant (HR 0.84, 95% CI 0.70-1.00, p=0.048) and driven largely by reduced UA, leading some to argue that early intensive statin treatment does not modify early “hard” events after ACS. On the other hand, the efficacy of an intervention after ACS is only partially accounted for by time to first event because patients may experience multiple events of similar importance, especially when competing risk for death is relatively low. Objective: In a post-hoc analysis of MIRACL, we evaluated the efficacy of ATV to reduce total (first and recurrent) hard cardiovascular events after ACS. Hard events were defined as death, MI, stroke, and resuscitated cardiac arrest. Methods: 3086 patients were randomly assigned to treatment with ATV or PBO, beginning 1-4 days after ACS and continuing for 16 weeks. Time to first event was assessed by Cox regression. Total events were analyzed by Cox regression with model-based variance estimation to determine correlation between events within a subject. Results: ATV did not significantly reduce time to first hard event (HR 0.89, 95% CI 0.72-1.11, P=0.27), but did significantly reduce total hard events ( Table ). To prevent 1 hard event, only 10.6 patient-years of treatment with ATV were required. The HR for total events was minimally affected by inclusion or exclusion of UA. Conclusion: Intensive treatment with ATV reduces total hard events over 16 weeks following ACS, and is an efficient secondary prevention intervention.

Model-based variance estimation in non-measurable spatial designs

Two-dimensional systematic sampling and maximal stratification are frequently used in spatial surveys, because of their ease of implementation and design efficiency. An important drawback of these designs, however, is that no direct estimator of the design variance is available. In this paper estimation of the sampling variance of a total in a model-based context is considered.The estimation strategy is based on the use of the sample variogram which can be either a non-parametric or a parametric one. Consistency of the estimators is discussed; simulations and an application to real data show the good performance of the proposed procedure in practice.