Quantifying uncertainty in method of moments estimates of the heterogeneity variance in random effects meta-analysis.

The between-study variance or heterogeneity variance is an important parameter in random effects meta-analysis. This paper uses an M-estimation framework to introduce and discuss variance estimators for quantifying the uncertainty in estimates of the heterogeneity variance using the noniterative generalized method of moments estimator and some related method of moments estimators. An example is used to further illustrate the variance estimators, and simulation results are presented for assessing the empirical properties of the proposed variance estimators.

A note on the empirical Bayes heterogeneity variance estimator in meta-analysis.

This paper focuses on the empirical Bayes (EB) or Mandel-Paule estimator of the heterogeneity variance in meta-analysis, which was discussed by Morris and proposed in earlier publications by Mandel and Paule in an inter-laboratory context. The relationship of the EB estimator to other heterogeneity variance estimators typically used in meta-analysis is explored, and approximate variance estimators for the EB estimate of the heterogeneity variance are proposed based on the M-estimation method. Statistical inference for the overall treatment effect using the EB estimator and the proposed standard errors is discussed using two example data sets from meta-analysis applications.

A comparison of the variance estimation methods for heteroscedastic nonlinear models.

Heteroscedasticity is commonly encountered when fitting nonlinear regression models in practice. We discuss eight different variance estimation methods for nonlinear regression models with heterogeneous response variances, and present a simulation study to compare the performance of the eight methods in terms of estimating the standard errors of the fitted model parameters. The simulation study suggests that when the true variance is a function of the mean model, the power of the mean variance function estimation method and the transform-both-sides method are the best choices for estimating the standard errors of the estimated model parameters. In general, the wild bootstrap estimator and two modified versions of the standard sandwich variance estimator are reasonably accurate with relatively small bias, especially when the heterogeneity is nonsystematic across values of the covariate. Furthermore, we note that the two modified sandwich estimators are appealing choices in practice, considering the computational advantage of these two estimation methods relative to the variance function estimation method and the transform-both-sides approach. Copyright © 2016 John Wiley & Sons, Ltd.

Testing for parallelism in the heteroscedastic four-parameter logistic model.

For bioassay data in drug discovery and development, it is often important to test for parallelism of the mean response curves for two preparations, such as a test sample and a reference sample in determining the potency of the test preparation relative to the reference standard. For assessing parallelism under a four-parameter logistic model, tests of the parallelism hypothesis may be conducted based on the equivalence t-test or the traditional F-test. However, bioassay data often have heterogeneous variance across dose levels. Specifically, the variance of the response may be a function of the mean, frequently modeled as a power of the mean. Therefore, in this article we discuss estimation and tests for parallelism under the power variance function. Two examples are considered to illustrate the estimation and testing approaches described. A simulation study is also presented to compare the empirical properties of the tests under the power variance function in comparison to the results from ordinary least squares fits, which ignore the non-constant variance pattern.

A neural network model to translate brain developmental events across mammalian species.

Translating the timing of brain developmental events across mammalian species using suitable models has provided unprecedented insights into neural development and evolution. More importantly, these models can prove to be useful abstractions and predict unknown events across species from known empirical event timing data retrieved from published literature. Such predictions can be especially useful since the distribution of the event timing data is skewed with a majority of events documented only across a few selected species. The present study investigates the choice of single hidden layer feed-forward neural networks (FFNN) for predicting the unknown events from the empirical data. A leave-one-out cross-validation approach is used to determine the optimal number of units in the hidden layer and the decay parameter for the FFNN. It is shown that unlike the present Finlay-Darlington (FD) model, FFNN does not impose any constraints on the functional form of the model and falls under the class of semiparametric regression models that can approximate any continuous function. The results from FFNN as well as FD model also indicate that a majority of events with large absolute prediction errors correspond to those of primates and late events comprising the tail of event timing data distribution with minimal representation in the empirical data. These results also indicate that accurate prediction of primate events may be challenging.

Adolescent gambling: a review of an emerging field of research.

PURPOSE: The purpose of this review was to summarize the research on adolescent gambling with implications for research and prevention or intervention. METHOD: The methodology involved a comprehensive and systematic search of "adolescent or youth gambling" in three diverse electronic databases (MedlineAdvanced, PsycINFO, and Sociological Abstracts) and three peer-reviewed journals (International Journal of Gambling Studies, International Journal of Mental Health and Addiction, and Journal of Gambling Issues). RESULTS: The search resulted in 137 articles (1985-2010) focusing on gambling among youth aged between 9 and 21 years: 103 quantitative, 8 qualitative, and 26 non-empirical. The study of adolescent gambling can be summarized as follows: (a) it is conducted by a relatively small group of researchers in Britain, Canada, and the United States; (b) it is primarily prevalence-focused, quantitative, descriptive, school-based, and atheoretical; (c) it has most often been published in the Journal of Gambling Studies; (d) it is most often examined in relation to alcohol use; (e) it has relatively few valid and reliable screening instruments that are developmentally appropriate for adolescents, and (f) it lacks racially diverse samples. CONCLUSION: Four recommendations are presented for both research and prevention or intervention which are as follows: (1) to provide greater attention to the development and validation of survey instruments or diagnostic criteria to assess adolescent problem gambling; (2) to begin to develop and test more gambling prevention or intervention strategies; (3) to not only examine the co-morbidity of gambling and alcohol abuse, but also include other behaviors such as sexual activity; and (4) to pay greater attention to racial and ethnic differences in the study of adolescent gambling.

Equivalence testing for parallelism in the four-parameter logistic model.

For assay or dose-response data in drug discovery, it is often important to test for parallelism of the response curves for two preparations, such as a test drug and a standard drug, in order to determine the potency of the test preparation relative to the standard preparation. A typical approach is to perform a three-degree of freedom approximate F test of the null hypothesis that the relevant parameters are equal for the two preparations. We argue that this problem may be more appropriately viewed as a practical equivalence testing problem, and present an alternative method for testing parallelism in the four-parameter logistic response curve, based on the theory of intersection-union tests. The approach is intuitively appealing and simple to implement using commonly available software, and may provide more appropriate inference for the problem of interest. Two examples are discussed to illustrate the testing approach outlined in this article, and to compare it with the typical approach to testing parallelism. A simulation study is also presented to compare the empirical properties of the two different testing approaches for a set of cases based approximately on one of the examples.

Emerging adult versus adult status among college students: examination of explanatory variables.

The first purpose of this study was to report how many college students, 18 to 25 years of age, are classified as "emerging adults," "undecideds" or "adults." The second purpose was to determine the relationships between emerging adults versus adults and (a) background characteristics, (b) risk-taking behaviors; (c) sensation-seeking scores, and (d) income. A survey was administered to a total of 450 students enrolled in psychology classes in a southern state. Based on responses to four questions, 186 (41%) were emerging adults, 148 (33%) undecided, and 116 (26%) adults. Adult status was not significantly associated with gender or parenthood. Adults were more likely to be African-American and low income and were less likely to consume alcohol, binge drink, smoke cigarettes, and gamble. In addition, adults had significantly lower disinhibition scores than emerging adults.

A comparison of heterogeneity variance estimators in combining results of studies.

For random effects meta-analysis, seven different estimators of the heterogeneity variance are compared and assessed using a simulation study. The seven estimators are the variance component type estimator (VC), the method of moments estimator (MM), the maximum likelihood estimator (ML), the restricted maximum likelihood estimator (REML), the empirical Bayes estimator (EB), the model error variance type estimator (MV), and a variation of the MV estimator (MVvc). The performance of the estimators is compared in terms of both bias and mean squared error, using Monte Carlo simulation. The results show that the REML and especially the ML and MM estimators are not accurate, having large biases unless the true heterogeneity variance is small. The VC estimator tends to overestimate the heterogeneity variance in general, but is quite accurate when the number of studies is large. The MV estimator is not a good estimator when the heterogeneity variance is small to moderate, but it is reasonably accurate when the heterogeneity variance is large. The MVvc estimator is an improved estimator compared to the MV estimator, especially for small to moderate values of the heterogeneity variance. The two estimators MVvc and EB are found to be the most accurate in general, particularly when the heterogeneity variance is moderate to large.

Disordered gambling among college students: a meta-analytic synthesis.

The purpose of this study was to use a meta-analytic procedure to synthesize the rates of disordered gambling for college students that have been reported in the research literature. In order to identify all possible studies that met stringent inclusion criteria, Medline, PsychINFO, and SocioIndex databases were searched with the terms "gambling," and "college student". This process resulted in 15 studies concerning gambling among college students that were published through July 2005. To synthesize the 15 studies, a random effects model for meta-analysis was applied. The estimated proportion of disordered gamblers among college students was 7.89%. This estimate is noteworthy because it is higher than that reported for adolescents, college students or adults in a previous study using meta-analytic procedures with studies conducted prior to 1997.

A note on variance estimation in random effects meta-regression.

For random effects meta-regression inference, variance estimation for the parameter estimates is discussed. Because estimated weights are used for meta-regression analysis in practice, the assumed or estimated covariance matrix used in meta-regression is not strictly correct, due to possible errors in estimating the weights. Therefore, this note investigates the use of a robust variance estimation approach for obtaining variances of the parameter estimates in random effects meta-regression inference. This method treats the assumed covariance matrix of the effect measure variables as a working covariance matrix. Using an example of meta-analysis data from clinical trials of a vaccine, the robust variance estimation approach is illustrated in comparison with two other methods of variance estimation. A simulation study is presented, comparing the three methods of variance estimation in terms of bias and coverage probability. We find that, despite the seeming suitability of the robust estimator for random effects meta-regression, the improved variance estimator of Knapp and Hartung (2003) yields the best performance among the three estimators, and thus may provide the best protection against errors in the estimated weights.

Practice variation and length of stay in alcohol and drug detoxification centers.

Admissions to 20 publicly funded alcohol and drug detoxification centers in Massachusetts were examined to identify program and patient variables that influenced length of stay. The last admission during fiscal year 1996 was abstracted for patients 18 years of age and older seeking alcohol, cocaine, or heroin detoxification (n=21,311; 29% women). A hierarchical generalized linear model examined the effects of patient and program characteristics on variation in length of stay and tested case-mix adjustments. Program size had the most influence on mean adjusted length of stay; stays were more than 40% longer in detoxification centers with 35 or more beds (7.69 days) than in centers with less than 35 beds (5.42 days). The study highlights the contribution of program size to treatment processes and suggests the need for more attention to program attributes in studies of patient outcomes and treatment processes.

A simple confidence interval for meta-analysis.

In the context of a random effects model for meta-analysis, a number of methods are available to estimate confidence limits for the overall mean effect. A simple and commonly used method is the DerSimonian and Laird approach. This paper discusses an alternative simple approach for constructing the confidence interval, based on the t-distribution. This approach has improved coverage probability compared to the DerSimonian and Laird method. Moreover, it is easy to calculate, and unlike some methods suggested in the statistical literature, no iterative computation is required.