Diagnostics for Joint Longitudinal and Dropout Time ModelingDobson, Angela; Henderson, Robin
doi: 10.1111/j.0006-341x.2003.00087.xpmid: N/A
Summary. We present a variety of informal graphical procedures for diagnostic assessment of joint models for longitudinal and dropout time data. A random effects approach for Gaussian responses and proportional hazards dropout time is assumed. We consider preliminary assessment of dropout classification categories based on residuals following a standard longitudinal data analysis with no allowance for informative dropout. Residual properties conditional upon dropout information are discussed and case influence is considered. The proposed methods do not require computationally intensive methods over and above those used to fit the proposed model. A longitudinal trial into the treatment of schizophrenia is used to illustrate the suggestions.
Testing for Spatial Correlation in Nonstationary Binary Data, with Application to Aberrant Crypt Foci in Colon CarcinogenesisApanasovich, Tatiyana V.; Sheather, Simon; Lupton, Joanne R.; Popovic, Natasa; Turner, Nancy D.; Chapkin, Robert S.; Braby, Leslie A.; Carroll, Raymond J.
doi: 10.1111/j.0006-341x.2003.00088.xpmid: N/A
Summary. In an experiment to understand colon carcinogenesis, all animals were exposed to a carcinogen, with half the animals also being exposed to radiation. Spatially, we measured the existence of what are referred to as aberrant crypt foci (ACF), namely, morphologically changed colonic crypts that are known to be precursors of colon cancer development. The biological question of interest is whether the locations of these ACFs are spatially correlated: if so, this indicates that damage to the colon due to carcinogens and radiation is localized. Statistically, the data take the form of binary outcomes (corresponding to the existence of an ACF) on a regular grid. We develop score‐type methods based upon the Matern and conditionally autoregressive (CAR) correlation models to test for the spatial correlation in such data, while allowing for nonstationarity. Because of a technical peculiarity of the score‐type test, we also develop robust versions of the method. The methods are compared to a generalization of Moran's test for continuous outcomes, and are shown via simulation to have the potential for increased power. When applied to our data, the methods indicate the existence of spatial correlation, and hence indicate localization of damage.
Random Effects Selection in Linear Mixed ModelsChen, Zhen; Dunson, David B.
doi: 10.1111/j.0006-341x.2003.00089.xpmid: N/A
Summary. We address the important practical problem of how to select the random effects component in a linear mixed model. A hierarchical Bayesian model is used to identify any random effect with zero variance. The proposed approach reparameterizes the mixed model so that functions of the covariance parameters of the random effects distribution are incorporated as regression coefficients on standard normal latent variables. We allow random effects to effectively drop out of the model by choosing mixture priors with point mass at zero for the random effects variances. Due to the reparameterization, the model enjoys a conditionally linear structure that facilitates the use of normal conjugate priors. We demonstrate that posterior computation can proceed via a simple and efficient Markov chain Monte Carlo algorithm. The methods are illustrated using simulated data and real data from a study relating prenatal exposure to polychlorinated biphenyls and psychomotor development of children.
Flexible Implementations of Group Sequential Stopping Rules Using Constrained BoundariesBurington, Bart E.; Emerson, Scott S.
doi: 10.1111/j.0006-341x.2003.00090.xpmid: N/A
Summary. Group sequential stopping rules are often used during the conduct of clinical trials in order to attain more ethical treatment of patients and to better address efficiency concerns. Because the use of such stopping rules materially affects the frequentist operating characteristics of the hypothesis test, it is necessary to choose an appropriate stopping rule during the planning of the study. It is often the case, however, that the number and timing of interim analyses are not precisely known at the time of trial design, and thus the implementation of a particular stopping rule must allow for flexible determination of the schedule of interim analyses. In this article, we consider the use of constrained stopping boundaries in the implementation of stopping rules. We compare this approach when used on various scales for the test statistic. When implemented on the scale of boundary crossing probabilities, this approach is identical to the error spending function approach of Lan and DeMets (1983).
Demographic Analysis from Summaries of an Age‐Structured PopulationLink, William A.; Royle, J. Andrew; Hatfield, Jeff S.
doi: 10.1111/j.0006-341x.2003.00091.xpmid: N/A
Summary. Demographic analyses of age‐structured populations typically rely on life history data for individuals, or when individual animals are not identified, on information about the numbers of individuals in each age class through time. While it is usually difficult to determine the age class of a randomly encountered individual, it is often the case that the individual can be readily and reliably assigned to one of a set of age classes. For example, it is often possible to distinguish first‐year from older birds. In such cases, the population age structure can be regarded as a latent variable governed by a process prior, and the data as summaries of this latent structure. In this article, we consider the problem of uncovering the latent structure and estimating process parameters from summaries of age class information. We present a demographic analysis for the critically endangered migratory population of whooping cranes (Grus americana), based only on counts of first‐year birds and of older birds. We estimate age and year‐specific survival rates. We address the controversial issue of whether management action on the breeding grounds has influenced recruitment, relating recruitment rates to the number of seventh‐year and older birds, and examining the pattern of variation through time in this rate.
Open Capture‐Recapture Models with Heterogeneity: I. Cormack‐Jolly‐Seber ModelPledger, Shirley; Pollock, Kenneth H.; Norris, James L.
doi: 10.1111/j.0006-341x.2003.00092.xpmid: N/A
Summary. In open population capture‐recapture studies, it is usually assumed that similar animals (e.g., of the same sex and age group) have similar survival rates and capture probabilities. These assumptions are generally perceived to be an oversimplification, and they can lead to incorrect model selection and biased parameter estimates. Allowing for individual variability in survival and capture probabilities among apparently similar animals is now becoming possible, due to advances in closed population models and improved computing power. This article presents a flexible framework of likelihood‐based models which allow for individual heterogeneity in survival and capture rates. Heterogeneity is modeled using finite mixtures, which have enough flexibility of distribution shape to accommodate a wide variety of different patterns of individual variation. The models condition on the first capture of each animal, and include as a special case the Cormack‐Jolly‐Seber model. Model selection is done either using Akaike's information criterion or by likelihood ratio tests, making available checks of different influences on survival rates. Bias in parameter estimates is reduced by including individual heterogeneity. Model selection and bias reduction are important in population studies and for making informed management decisions.
Joint Regression and Association Modeling of Longitudinal Ordinal DataEkholm, Anders; Jokinen, Jukka; McDonald, John W.; Smith, Peter W. F.
doi: 10.1111/j.0006-341x.2003.00093.xpmid: N/A
Summary. We propose models for longitudinal, or otherwise clustered, ordinal data. The association between subunit responses is characterized by dependence ratios (Ekholm, Smith, and McDonald, 1995, Biometrika82, 847–854), which are extended from the binary to the multicategory case. The joint probabilities of the subunit responses are expressed as explicit functions of the marginal means and the dependence ratios of all orders, obtaining a computational advantage for likelihood‐based inference. Equal emphasis is put on finding regression models for the univariate cumulative probabilities, and on deriving the dependence ratios from meaningful association‐generating mechanisms. A data set on the effects of treatment with Fluvoxamine, which has been analyzed in parts before (Molenberghs, Kenward, and Lesaffre, 1997, Biometrika84, 33–44), is analyzed in its entirety. Selection models are used for studying the sensitivity of the results to drop‐out.
Shape‐Invariant Modeling of Circadian Rhythms with Random Effects and Smoothing Spline ANOVA DecompositionsWang, Yuedong; Ke, Chunlei; Brown, Morton B.
doi: 10.1111/j.0006-341x.2003.00094.xpmid: 14969458
Summary. Medical studies often collect physiological and/or psychological measurements over time from multiple subjects, to study dynamics such as circadian rhythms. Under the assumption that the expected response functions of all subjects are the same after shift and scale transformations, shape‐ invariant models have been applied to analyze this kind of data. The shift and scale parameters provide efficient and interpretable data summaries, while the common shape function is usually modeled nonparametrically, to provide flexibility. However, due to the deterministic nature of the shift and scale parameters, potential correlations within a subject are ignored. Furthermore, the shape of the common function may depend on other factors, such as disease. In this article, we propose shape‐invariant mixed effects models. A second‐stage model with fixed and random effects is used to model individual shift and scale parameters. A second‐stage smoothing spline ANOVA model is used to study potential covariate effects on the common shape function. We apply our methods to a real data set to investigate disease effects on circadian rhythms of cortisol, a hormone that is affected by stress. We find that patients with Cushing's syndrome lost circadian rhythms and their 24‐hour means were elevated to very high levels. Patients with major depression had the same circadian shape and phases as normal subjects. However, their 24‐hour mean levels were elevated and amplitudes were dampened for some patients.