Testing for qualitative interaction of multiple sources of informative dropout in longitudinal data

Longitudinal studies suffer from patient dropout. The dropout process may be informative if there exists an association between dropout patterns and the rate of change in the response over time. Multiple patterns are plausible in that different causes of dropout might contribute to different patterns. These multiple patterns can be dichotomized into two groups: quantitative and qualitative interaction. Quantitative interaction indicates that each of the multiple sources is biasing the estimate of the rate of change in the same direction, although with differing magnitudes. Alternatively, qualitative interaction results in the multiple sources biasing the estimate of the rate of change in opposing directions. Qualitative interaction is of special concern, since it is less likely to be detected by conventional methods and can lead to highly misleading slope estimates. We explore a test for qualitative interaction based on simultaneous confidence intervals. The test accommodates the realistic situation where reasons for dropout are not fully understood, or even entirely unknown. It allows for an additional level of clustering among participating subjects. We apply these methods to a study exploring tumor growth rates in mice as well as a longitudinal study exploring rates of change in cognitive functioning for Alzheimer's patients.     

Borrowing Information across Populations in Estimating Positive and Negative Predictive Values

A marker's capacity to predict risk of a disease depends on disease prevalence in the target population and its classification accuracy, i.e. its ability to discriminate diseased subjects from non-diseased subjects. The latter is often considered an intrinsic property of the marker; it is independent of disease prevalence and hence more likely to be similar across populations than risk prediction measures. In this paper, we are interested in evaluating the population-specific performance of a risk prediction marker in terms of positive predictive value (PPV) and negative predictive value (NPV) at given thresholds, when samples are available from the target population as well as from another population. A default strategy is to estimate PPV and NPV using samples from the target population only. However, when the marker's classification accuracy as characterized by a specific point on the receiver operating characteristics (ROC) curve is similar across populations, borrowing information across populations allows increased efficiency in estimating PPV and NPV. We develop estimators that optimally combine information across populations. We apply this methodology to a cross-sectional study where we evaluate PCA3 as a risk prediction marker for prostate cancer among subjects with or without previous negative biopsy.     

Longitudinal dynamic analyses of cognition in the health and retirement study panel

The purpose of this paper is to highlight some classic issues in the measurement of change and to show how contemporary solutions can be used to deal with some of these issues. Five classic issues will be raised here: (1) Separating individual changes from group differences; (2) options for incomplete longitudinal data over time, (3) options for nonlinear changes over time; (4) measurement invariance in studies of changes over time; and (5) new opportunities for modeling dynamic changes. For each issue we will describe the problem, and then review some contemporary solutions to these problems base on Structural Equation Models (SEM). We will fit these SEM to using existing panel data from the Health & Retirement Study (HRS) cognitive variables. This is not intended as an overly technical treatment, so only a few basic equations are presented, examples will be displayed graphically, and more complete references to the contemporary solutions will be given throughout.     

Vendor Selection with Bundling: A Comment*

In a recent article by Rosenthal, Zydiak, and Chaudhry (1995), a mixed integer linear programming model was introduced to solve the vendor selection problem for the case in which the vendor can sell items individually or as part of a bundle. Each vendor offered only one type of bundle, and the buyer could purchase at most one bundle per vendor. The model employed n(m+ 1) binary variables, where n is the number of vendors and m is the number of products they sell. The existing model can lead to a purchasing paradox: it may force the buyer to pay more to receive less. We suggest a reformulation of the same problem that (i) eliminates this paradox and reveals a more cost-effective purchasing strategy; (ii) uses only n integer variables and significantly reduces the computational workload; and (iii) permits the buyer to purchase more than one bundle per vendor.     

Designing Lateral Organizations: An Analysis of the Benefits,Costs, and Enablers of Nonhierarchical Organizational Forms*

Twenty-first century organizations will require designs that enable them to cope with turbulent environments. Organizations have experimented with lateral organizational designs for this purpose, but research evidence concerning these forms is sparse. We analyzed data obtained from 512 employees within eight diverse organizations implementing flexible lateral organizations. Using a sequence comparison methodology, we were able to identify and categorize the major costs, benefits, and enablers associated with implementing these forms of complex organizations. Propositions for effectively managing lateral relations were tested and managerial implications were explored.     

Bias and precision of measures of survival gain from right‐censored data

In cost‐effectiveness analyses of drugs or health technologies, estimates of life years saved or quality‐adjusted life years saved are required. Randomised controlled trials can provide an estimate of the average treatment effect; for survival data, the treatment effect is the difference in mean survival. However, typically not all patients will have reached the endpoint of interest at the close‐out of a trial, making it difficult to estimate the difference in mean survival. In this situation, it is common to report the more readily estimable difference in median survival. Alternative approaches to estimating the mean have also been proposed. We conducted a simulation study to investigate the bias and precision of the three most commonly used sample measures of absolute survival gain – difference in median, restricted mean and extended mean survival – when used as estimates of the true mean difference, under different censoring proportions, while assuming a range of survival patterns, represented by Weibull survival distributions with constant, increasing and decreasing hazards. Our study showed that the three commonly used methods tended to underestimate the true treatment effect; consequently, the incremental cost‐effectiveness ratio (ICER) would be overestimated. Of the three methods, the least biased is the extended mean survival, which perhaps should be used as the point estimate of the treatment effect to be inputted into the ICER, while the other two approaches could be used in sensitivity analyses. More work on the trade‐offs between simple extrapolation using the exponential distribution and more complicated extrapolation using other methods would be valuable. Copyright © 2015 John Wiley & Sons, Ltd.     

The impact of place? A reassessment of the importance of the South in affecting beliefs about racial inequality

Research shows that individuals living in the southern part of the United States express more negative racial attitudes than those living outside the South. Using data from The American National Election Study (NES), the purpose of this paper is to assess whether key factors often associated with the Southern attitude distinction are indeed more potent in the South than elsewhere. Drawing data from the 1980s, 1990s, and 2000s, we further assess whether the impact of the South has increased or decreased over time. Results indicate that the impact of the South is negligible at best. Findings do show that place does matter for conservatives. However, in this case, non-South location matters more than the South. Relative to their liberal counterparts, conservatives in the non-South espouse more individualistic beliefs than do their Southern counterparts. These findings are discussed within the dominant theoretical framework in this area.     

Prosecuting the prosecutor: The makings of the Michael Morton Act

Prosecutorial misconduct is not a rare event, but it often goes undetected, unreported, or no action is taken by the criminal justice system. However, when one Texas prosecutor, Ken Anderson, served jail time for wrongfully prosecuting an innocent man, Michael Morton, for murdering his wife, he made history. Anderson withheld exculpatory evidence leading to Morton wrongfully serving 25 years before being released with new DNA evidence. However, Anderson only served a five-day sentence and $500 fine. We discuss the case in the context of inequality and legal realism in the criminal justice system. Also, we look at the implications and new legal action taken by the state of Texas to try and combat this problem, along with looking at these secretive occupational subcultures.     

On Variational Bayes Estimation and Variational Information Criteria for Linear Regression Models

Variational Bayes (VB) estimation is a fast alternative to Markov Chain Monte Carlo for performing approximate Baesian inference. This procedure can be an efficient and effective means of analyzing large datasets. However, VB estimation is often criticised, typically on empirical grounds, for being unable to produce valid statistical inferences. In this article we refute this criticism for one of the simplest models where Bayesian inference is not analytically tractable, that is, the Bayesian linear model (for a particular choice of priors). We prove that under mild regularity conditions, VB based estimators enjoy some desirable frequentist properties such as consistency and can be used to obtain asymptotically valid standard errors. In addition to these results we introduce two VB information criteria: the variational Akaike information criterion and the variational Bayesian information criterion. We show that variational Akaike information criterion is asymptotically equivalent to the frequentist Akaike information criterion and that the variational Bayesian information criterion is first order equivalent to the Bayesian information criterion in linear regression. These results motivate the potential use of the variational information criteria for more complex models. We support our theoretical results with numerical examples.     

Covariate Decomposition Methods for Longitudinal Missing‐at‐Random Data and Predictors Associated with Subject‐Specific Effects

Investigators often gather longitudinal data to assess changes in responses over time within subjects and to relate these changes to within‐subject changes in predictors. Missing data are common in such studies and predictors can be correlated with subject‐specific effects. Maximum likelihood methods for generalized linear mixed models provide consistent estimates when the data are ‘missing at random’ (MAR) but can produce inconsistent estimates in settings where the random effects are correlated with one of the predictors. On the other hand, conditional maximum likelihood methods (and closely related maximum likelihood methods that partition covariates into between‐ and within‐cluster components) provide consistent estimation when random effects are correlated with predictors but can produce inconsistent covariate effect estimates when data are MAR. Using theory, simulation studies, and fits to example data this paper shows that decomposition methods using complete covariate information produce consistent estimates. In some practical cases these methods, that ostensibly require complete covariate information, actually only involve the observed covariates. These results offer an easy‐to‐use approach to simultaneously protect against bias from both cluster‐level confounding and MAR missingness in assessments of change.