Model-based Variance Estimation Research Articles

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.

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.

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.

Inference of Haplotype Effects in Case‐Control Studies Using Unphased Genotype and Environmental Data

A retrospective likelihood-based approach was proposed to test and estimate the effect of haplotype on disease risk using unphased genotype data with adjustment for environmental covariates. The proposed method was also extended to handle the data in which the haplotype and environmental covariates are not independent. Likelihood ratio tests were constructed to test the effects of haplotype and gene-environment interaction. The model parameters such as haplotype effect size was estimated using an Expectation Conditional-Maximization (ECM) algorithm developed by Meng and Rubin (1993). Model-based variance estimates were derived using the observed information matrix. Simulation studies were conducted for three different genetic effect models, including dominant effect, recessive effect, and additive effect. The results showed that the proposed method generated unbiased parameter estimates, proper type I error, and true beta coverage probabilities. The model performed well with small or large sample sizes, as well as short or long haplotypes.

Model-based variance estimation under unequal probability sampling

This paper deals with a model-based variance estimation of the Horvitz–Thompson (HT) estimator when auxiliary information is available. A small simulation study is carried out to illustrate and establish some of the findings.

Identifying differentially expressed genes in microarray experiments with model-based variance estimation

Statistical tests have been employed to identify genes differentially expressed under different conditions using data from microarray experiments. The variance of gene expression levels is often required in various statistical tests; however, due to the small number of replicates, the variance estimated from the sample variance is not accurate, which causes large false positive and negative errors. More accurate and robust variance estimation is thus highly desirable to improve the performance of statistical tests. In this paper, cluster analysis was performed on the microarray data using a model-based clustering method. The variance for each gene was then estimated from cluster variances. Since cluster variances are estimated from multiple genes whose microarray data have similar variance, the proposed estimation method pools the relevant genes together; this effectively increases the number of samples in variance estimation, thereby improving variance estimation. Using simulated data, it is shown that with the novel variance estimation, the performance of the t-test, regularized t-test, and a variant of SAM test, which is called the S-test here, can be improved. Using colon microarray data of Alon et al., it is demonstrated that the proposed method offers better or comparable performance compared with other gene pooling methods. Using the IHF microarray data of Arfin et al., it is shown that the proposed novel variance estimation decreases the significance of those genes having a small fold change but a high significant score assigned by the t-test using the sample variance, which potentially reduces false positive probability.

A note on design-based versus model-based variance estimation in stereology

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

A note on design-based versus model-based variance estimation in stereology

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

Local time estimation for the slotted correlation function of randomly sampled LDA data

The task of autocorrelation and power spectral density estimation from velocity data sampled irregularly in time by a laser-Doppler anemometer (LDA) is addressed in this article. A new method based on the slotting technique was found to be a very reliable estimator. This article describes specific improvements of the slotting technique, the model-based variance estimation and the spectral transform leading to more accurate estimates of the autocorrelation function and the power spectral density. Furthermore, the new method yields more information especially at short time lags of the autocorrelation function, which can be used to derive improved estimates of the Taylor time scale.

Use of passive integrated transponder tags to estimate survival of migrant juvenile salmonids in the Snake and Columbia rivers

Single-release and modified single-release statistical models were evaluated as means to generate reliable survival estimates from release-recapture studies of migrant salmonid smolts in the Snake and Columbia rivers of the northwestern United States. Monte Carlo simulation studies were used to assess robustness of estimation methods to violations of model assumptions. To field test model assumptions, passive integrated transponder tagged chinook salmon (Oncorhynchus tshawytscha) smolts were released on seven consecutive days in 1993 above Lower Granite Dam on the Snake River. These releases were used to estimate sampling variability of survival estimates for comparison with model-based variance estimates and to assess mixing of detected and nondetected individuals. Field results satisfied model assumptions. The average survival estimate from point of release to the tailrace of Lower Granite Dam (31 km) was 0.902 ± 0.004 (mean ± SE). From the tailrace of Lower Granite Dam to the tailrace of Little Goose Dam (60 km) the average survival estimate was 0.859 ± 0.013.

Iterative Weighted Least Squares Estimation in Heteroscedastic Linear Models

This article addresses the problem of choosing weights for iterative weighted least squares estimation in heteroscedastic linear models. An asymptotically optimal method for determining weights at each iteration is derived under a Bayesian model for the variances. The method uses a compromise between model-based and model-free variance estimates. Consider a heteroscedastic linear regression model in which responses are grouped so that the variance is constant within each group. Let β denote the vector of regression parameters and let θ denote a vector of parameters determining a prior distribution for the variances. Iterative weighted least squares estimators are defined as follows. Given estimates and , calculate a weight for the ith group as a function of , the values in the ith group of the predictor variables, and the average of the squared residuals from the estimated mean responses in the ith group. Given weights, calculate the weighted least squares estimate and a new estimate . Continue until conv...