Least-squares tests of time-series,invention effects with and without autocorrelations

Gottman's version of the Mann and Wald asymptotic test for intervention effects in time-series data is presented as a useful small sample procedure. A Monte Carlo simulaltion is conducted to evaluate the procedure for controlling Type I errors with varying values of autoregressive coefficients. Results indicate the procedure works better than Gottman's work originally indicated. However, in some cases error rates can be unacceptably high. Procedures for evaluating changes in level in the presence of autocorrelation and slope are suggested and evaluated.     

A method for screening active effects in supersaturated designs

A supersaturated design (SSD) is a design whose run size is not enough for estimating all the main effects. The goal in conducting such a design is to identify, presumably only a few, relatively dominant active effects with a cost as low as possible. However, data analysis of such designs remains primitive: traditional approaches are not appropriate in such a situation and several methods which were proposed in the literature in recent years are effective when used to analyze two-level SSDs. In this paper, we introduce a variable selection procedure, called the PLSVS method, to screen active effects in mixed-level SSDs based on the variable importance in projection which is an important concept in the partial least-squares regression. Simulation studies show that this procedure is effective.     

Controlling Bayes directional false discovery rate in random effects model

Starting with a decision theoretic formulation of simultaneous testing of null hypotheses against two-sided alternatives, a procedure controlling the Bayesian directional false discovery rate (BDFDR) is developed through controlling the posterior directional false discovery rate (PDFDR). This is an alternative to Lewis and Thayer [2004. A loss function related to the FDR for random effects multiple comparison. J. Statist. Plann. Inference 125, 49–58.] with a better control of the BDFDR. Moreover, it is optimum in the sense of being the non-randomized part of the procedure maximizing the posterior expectation of the directional per-comparison power rate given the data, while controlling the PDFDR. A corresponding empirical Bayes method is proposed in the context of one-way random effects model. Simulation study shows that the proposed Bayes and empirical Bayes methods perform much better from a Bayesian perspective than the procedures available in the literature.     

Simultaneous confidence intervals by iteratively adjusted alpha for relative effects in the one-way layout

A bootstrap based method to construct 1−α simultaneous confidence intervals for relative effects in the one-way layout is presented. This procedure takes the stochastic correlation between the test statistics into account and results in narrower simultaneous confidence intervals than the application of the Bonferroni correction. Instead of using the bootstrap distribution of a maximum statistic, the coverage of the confidence intervals for the individual comparisons are adjusted iteratively until the overall confidence level is reached. Empirical coverage and power estimates of the introduced procedure for many-to-one comparisons are presented and compared with asymptotic procedures based on the multivariate normal distribution.     

Nonparametric estimation in one-way random effects models

We present a rank based method for obtaining point and interval estimates of a scale version of the intraclass correlation coefficient in a one-way random effects model. When compared to the method of Arvesen and Schmitz (1970), the new method is not only applicable to a broader class of situations, but also much easier to implement. Results of a simulation study indicate that the new procedure compares favorably with the Arvesen-Schmitz procedure and the classical normal theory procedure especially If the random components have heavy tailed distributions.     

Random effects in generalized linear models and the em algoritham

Nelder and Wedderburn (1972) gave a practical fitting procedure that encompassed a more gencral family of data distributions than the Gaussian distribution and provided an easily understood conceptual framework. In extending the framework to more than one error structure the technical difficulties of the fitting procedure have tended to cloud the concepts. Here we show that a simple extension to the fitting procedure is possible and thus pave the way for a fuller examimtion of mixed effects models in generalized linear model distributions. It is clear that we should not, and do not have to, confine ourselves to fitting random effects using the Gaussian distribiition. In addition, in, some quite general mixing distribution problems the application of the EM algorithm to the complete data likelihood leads to iterative schemes that maximize the marginal likelihood of the observed data variable.     

Monitoring long-term clinical trials for beneeficial and adverse treatment effects

When the data from a long-term clinical trial are reviewed continually over time for evidence of adverse or beneficial treatment effects, the classical significance tests are not appropriate. A simulation procedure is described which provides the correct critical regions corresponding to specified frequencies of data reviews over the course of the trial. Several different types of critical boundaries (e.g., horizontal, sloping,stepped, and asymmetric) are compared with respect to statistical power and closeness to the classical critical values at the final data review.     

A two-stage estimation for panel data models with grouped fixed effects

ABSTRACT

This paper considers panel data models with fixed effects which have grouped patterns with unknown group membership. A two-stage estimation (TSE) procedure is developed to improve the properties of the GFE estimators of common parameters when the time span is small. Firstly, the common parameters are estimated. Subsequently, the optimal group assignment and the estimators of group effects are obtained by the K-means algorithm. Monte Carlo results reveal that the TSE estimator has a much smaller bias than the GFE estimator when the values of difference between effects are moderately small or at high variance of the idiosyncratic error.     

A general joint model for longitudinal measurements and competing risks survival data with heterogeneous random effects

This article studies a general joint model for longitudinal measurements and competing risks survival data. The model consists of a linear mixed effects sub-model for the longitudinal outcome, a proportional cause-specific hazards frailty sub-model for the competing risks survival data, and a regression sub-model for the variance–covariance matrix of the multivariate latent random effects based on a modified Cholesky decomposition. The model provides a useful approach to adjust for non-ignorable missing data due to dropout for the longitudinal outcome, enables analysis of the survival outcome with informative censoring and intermittently measured time-dependent covariates, as well as joint analysis of the longitudinal and survival outcomes. Unlike previously studied joint models, our model allows for heterogeneous random covariance matrices. It also offers a framework to assess the homogeneous covariance assumption of existing joint models. A Bayesian MCMC procedure is developed for parameter estimation and inference. Its performances and frequentist properties are investigated using simulations. A real data example is used to illustrate the usefulness of the approach.     

Landmark estimation of survival and treatment effects in observational studies

Clinical studies aimed at identifying effective treatments to reduce the risk of disease or death often require long term follow-up of participants in order to observe a sufficient number of events to precisely estimate the treatment effect. In such studies, observing the outcome of interest during follow-up may be difficult and high rates of censoring may be observed which often leads to reduced power when applying straightforward statistical methods developed for time-to-event data. Alternative methods have been proposed to take advantage of auxiliary information that may potentially improve efficiency when estimating marginal survival and improve power when testing for a treatment effect. Recently, Parast et al. (J Am Stat Assoc 109(505):384–394, 2014) proposed a landmark estimation procedure for the estimation of survival and treatment effects in a randomized clinical trial setting and demonstrated that significant gains in efficiency and power could be obtained by incorporating intermediate event information as well as baseline covariates. However, the procedure requires the assumption that the potential outcomes for each individual under treatment and control are independent of treatment group assignment which is unlikely to hold in an observational study setting. In this paper we develop the landmark estimation procedure for use in an observational setting. In particular, we incorporate inverse probability of treatment weights (IPTW) in the landmark estimation procedure to account for selection bias on observed baseline (pretreatment) covariates. We demonstrate that consistent estimates of survival and treatment effects can be obtained by using IPTW and that there is improved efficiency by using auxiliary intermediate event and baseline information. We compare our proposed estimates to those obtained using the Kaplan–Meier estimator, the original landmark estimation procedure, and the IPTW Kaplan–Meier estimator. We illustrate our resulting reduction in bias and gains in efficiency through a simulation study and apply our procedure to an AIDS dataset to examine the effect of previous antiretroviral therapy on survival.     

Bayesian analysis of longitudinal ordered data with flexible random effects using McMC: application to diabetic macular Edema data

In the analysis of correlated ordered data, mixed-effect models are frequently used to control the subject heterogeneity effects. A common assumption in fitting these models is the normality of random effects. In many cases, this is unrealistic, making the estimation results unreliable. This paper considers several flexible models for random effects and investigates their properties in the model fitting. We adopt a proportional odds logistic regression model and incorporate the skewed version of the normal, Student's t and slash distributions for the effects. Stochastic representations for various flexible distributions are proposed afterwards based on the mixing strategy approach. This reduces the computational burden being performed by the McMC technique. Furthermore, this paper addresses the identifiability restrictions and suggests a procedure to handle this issue. We analyze a real data set taken from an ophthalmic clinical trial. Model selection is performed by suitable Bayesian model selection criteria.     

Sensitivity analysis of the unconfoundedness assumption with an application to an evaluation of college choice effects on earnings

We evaluate the effects of college choice on earnings using Swedish register databases. This case study is used to motivate the introduction of a novel procedure to analyse the sensitivity of such an observational study to the assumption made that there are no unobserved confounders – variables affecting both college choice and earnings. This assumption is not testable without further information, and should be considered an approximation of reality. To perform a sensitivity analysis, we measure the departure from the unconfoundedness assumption with the correlation between college choice and earnings when conditioning on observed covariates. The use of a correlation as a measure of dependence allows us to propose a standardised procedure by advocating the use of a fixed value for the correlation, typically 1% or 5%, when checking the sensitivity of an evaluation study. A correlation coefficient is, moreover, intuitive to most empirical scientists, which makes the results of our sensitivity analysis easier to communicate than those of previously proposed methods. In our evaluation of the effects of college choice on earnings, the significantly positive effect obtained could not be questioned by a sensitivity analysis allowing for unobserved confounders inducing at most 5% correlation between college choice and earnings.     

Response prediction in mixed effects models

Although prediction in mixed effects models usually concerns the random effects, in this paper we deal with the problem of prediction of a future, or yet unobserved, response random variable, belonging to a given cluster. In particular, the aim is to define computationally tractable prediction intervals, with conditional and unconditional coverage probability close to the target nominal value. This solution involves the conditional density of the future response random variable given the observed data, or a suitable high-order approximation based on the Laplace method. We prove that, unless the amount of data is very limited, the estimative or naive predictive procedure gives a relatively simple, feasible solution for response prediction. An application to generalized linear mixed models is presented.     

One-sided tolerance limits for unbalanced one-way random effects models: a generalized Mee and Owen procedure

This article proposes a new procedure for obtaining one-sided tolerance limits in unbalanced random effects models. The procedure is a generalization of that proposed by Mee and Owen for the balanced situation, and can be easily implemented, because it only needs a non-central-t table. Two simulation studies are carried out to assess the performance of the new procedure and to compare it with one of the other procedures laid out in previous statistical literature. The article findings show that the new procedure is much simpler to compute and performs better than the previous ones, having inferior values of the gamma bias in a wide range of situations, representative of many actual industrial applications, and behaving also reasonably well in more extreme sampling situations. The use of the new limits is illustrated by an application to an actual example from the steel industry.     

Inference on treatment effects for targeted clinical trials under enrichment design

After completion of a human genome project, the disease targets at molecular level can be identified. As a result, treatment modality for molecular targets can be developed. In practice, targeted clinical trials are usually conducted for evaluation of the possibility and feasibility of the individualized treatment of patients. However, the accuracy of diagnostic devices for identification of such molecular targets is usually not perfect. Therefore, some of the patients enrolled in targeted clinical trials with a positive result by the diagnostic device might not have the specific molecular targets and hence the treatment effects of the targeted drugs estimated from targeted clinical trials could be biased for the patient population truly with the molecular targets. Under an enrichment design for targeted clinical trials, we propose to use the EM algorithm and bootstrap method for obtaining the inference of the treatment effects of the targeted drugs in the patient population truly with molecular targets. A simulation study was conducted to empirically investigate the bias and variability of the proposed estimator and the size and power of the proposed testing method. Simulation results demonstrate that the proposed estimator is unbiased with adequate precision and the confidence interval can provide satisfactory coverage probability. In addition, the proposed testing procedure can adequately control the size with sufficient power. A practical example illustrates the utility of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust designs for linear mixed effects models

Summary.  In health sciences, medicine and social sciences linear mixed effects models are often used to analyse time-structured data. The search for optimal designs for these models is often hampered by two problems. The first problem is that these designs are only locally optimal. The second problem is that an optimal design for one model may not be optimal for other models. In this paper the maximin principle is adopted to handle both problems, simultaneously. The maximin criterion is formulated by means of a relative efficiency measure, which gives an indication of how much efficiency is lost when the uncertainty about the models over a prior domain of parameters is taken into account. The procedure is illustrated by means of three growth studies. Results are presented for a vocabulary growth study from education, a bone gain study from medical research and an epidemiological decline in height study. It is shown that, for the mixed effects polynomial models that are applied to these studies, the maximin designs remain highly efficient for different sets of models and combinations of parameter values.     

Taylor linearization sampling errors and design effects for poverty measures and other complex statistics

A systematic procedure for the derivation of linearized variables for the estimation of sampling errors of complex nonlinear statistics involved in the analysis of poverty and income inequality is developed. The linearized variable extends the use of standard variance estimation formulae, developed for linear statistics such as sample aggregates, to nonlinear statistics. The context is that of cross-sectional samples of complex design and reasonably large size, as typically used in population-based surveys. Results of application of the procedure to a wide range of poverty and inequality measures are presented. A standardized software for the purpose has been developed and can be provided to interested users on request. Procedures are provided for the estimation of the design effect and its decomposition into the contribution of unequal sample weights and of other design complexities such as clustering and stratification. The consequence of treating a complex statistic as a simple ratio in estimating its sampling error is also quantified. The second theme of the paper is to compare the linearization approach with an alternative approach based on the concept of replication, namely the Jackknife repeated replication (JRR) method. The basis and application of the JRR method is described, the exposition paralleling that of the linearization method but in somewhat less detail. Based on data from an actual national survey, estimates of standard errors and design effects from the two methods are analysed and compared. The numerical results confirm that the two alternative approaches generally give very similar results, though notable differences can exist for certain statistics. Relative advantages and limitations of the approaches are identified.     

Modelling method effects as individual causal effects

Summary.  Method effects often occur when different methods are used for measuring the same construct. We present a new approach for modelling this kind of phenomenon, consisting of a definition of method effects and a first model, the method effect model , that can be used for data analysis. This model may be applied to multitrait–multimethod data or to longitudinal data where the same construct is measured with at least two methods at all occasions. In this new approach, the definition of the method effects is based on the theory of individual causal effects by Neyman and Rubin. Method effects are accordingly conceptualized as the individual effects of applying measurement method j instead of k . They are modelled as latent difference scores in structural equation models. A reference method needs to be chosen against which all other methods are compared. The model fit is invariant to the choice of the reference method. The model allows the estimation of the average of the individual method effects, their variance, their correlation with the traits (and other latent variables) and the correlation of different method effects among each other. Furthermore, since the definition of the method effects is in line with the theory of causality, the method effects may (under certain conditions) be interpreted as causal effects of the method. The method effect model is compared with traditional multitrait–multimethod models. An example illustrates the application of the model to longitudinal data analysing the effect of negatively (such as 'feel bad') as compared with positively formulated items (such as 'feel good') measuring mood states.     

Estimating individual-level interaction effects in multilevel models: a Monte Carlo simulation study with application*

Moderated multiple regression provides a useful framework for understanding moderator variables. These variables can also be examined within multilevel datasets, although the literature is not clear on the best way to assess data for significant moderating effects, particularly within a multilevel modeling framework. This study explores potential ways to test moderation at the individual level (level one) within a 2-level multilevel modeling framework, with varying effect sizes, cluster sizes, and numbers of clusters. The study examines five potential methods for testing interaction effects: the Wald test, F-test, likelihood ratio test, Bayesian information criterion (BIC), and Akaike information criterion (AIC). For each method, the simulation study examines Type I error rates and power. Following the simulation study, an applied study uses real data to assess interaction effects using the same five methods. Results indicate that the Wald test, F-test, and likelihood ratio test all perform similarly in terms of Type I error rates and power. Type I error rates for the AIC are more liberal, and for the BIC typically more conservative. A four-step procedure for applied researchers interested in examining interaction effects in multi-level models is provided.     

Exploring changes in treatment effects across design stages in adaptive trials

The recently published Committee for Medicinal Products for Human Use reflection paper on flexible designs highlights a controversial issue regarding the interpretation of adaptive trials. The guideline suggests that a test for heterogeneity should be preplanned and if treatment effect estimates differ significantly between design stages then data collected before and after the interim analysis might not be combined in a formal analysis. In this paper we investigate error rates for such a procedure in the presence of calendar-time effects. Furthermore, we present an alternative testing strategy based on change point methods. In a simulation study we demonstrate that our procedure performs well in comparison to that suggested by the guideline.