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PubMed2003

A Bayesian change-point analysis of electromyographic data: detecting muscle activation patterns and associated applications.

Many facets of neuromuscular activation patterns and control can be assessed via electromyography and are important for understanding the control of locomotion. After spinal cord injury, muscle activation patterns can affect locomotor recovery. We present a novel application of reversible jump Markov chain Monte Carlo simulation to estimate activation patterns from electromyographic data. We assume the data to be a zero-mean, heteroscedastic process. The variance is explicitly modeled using a step function. The number and location of points of discontinuity, or change-points, in the step function, the inter-change-point variances, and the overall mean are jointly modeled along with the mean and variance from baseline data. The number of change-points is considered a nuisance parameter and is integrated out of the posterior distribution. Whereas current methods of detecting activation patterns are deterministic or provide only point estimates, ours provides distributional estimates of muscle activation. These estimates, in turn, are used to estimate physiologically relevant quantities such as muscle coactivity, total integrated energy, and average burst duration and to draw valid statistical inferences about these quantities.

Bayes Theorem↗
PubMed1988

Estimation of sample sizes in case-control studies with multiple controls per case: dichotomous data.

In planning case-control studies with matched sets, the calculation of exact sample sizes is difficult, because this calculation depends on some nuisance parameters that are usually unknown in practice. Using the Pitman efficiency of Miettinen's test relative to McNemar's test, Schlesselman and Stolley (Case-control studies: design, conduct, analysis. Oxford: Oxford University Press, 1982:144-70) derived an approximate sample size formula which requires the assumption that the difference in exposure rates between cases and controls is small. Furthermore, on the basis of an assumption similar to that used in Schlesselman and Stolley's approach, Taylor (Stat Med 1986;5:29-36) proposed another approximation formula. In this paper, an alternative and explicit formula that does not require the exposure difference to be small between case and control groups has been derived. Monte Carlo studies are given for comparing the accuracy of these three procedures. The results indicate that when odds ratios of exposure between cases and controls are small (less than or equal to 4) and there is more than one matched control per case, the formula derived in this paper seems to be the best. When odds ratios are large (greater than or equal to 5), however, Taylor's more conservative estimate is recommended, unless the exposure prevalence in the general population is large (0.9).

Epidemiologic Methods↗
PubMed2003

Sequential conditional probability ratio tests for normalized test statistic on information time.

Sequential conditional probability ratio tests (SCPRTs) provide monitoring procedures with a unique property that a decision reached at early stopping is unlikely to be reversed should the trial continue to the planned end (Xiong, X., 1995, Journal of the American Statistical Association 90, 1463-1473; Tan, M., Xiong, X., and Kutner, M. H., 1998, Biometrics 54, 682-95). It actually provides a probability statement of a conclusion reversal, should the proposed interim analysis plan be used. To broaden its scope of applications, in this article we develop the SCPRT in terms of Brownian motion, which is applicable to most clinical trials with various endpoints. In addition, we utilize the unique structure of the SCPRT to derive a class of adaptive sequential tests that retain the significance level and power in the presence of a nuisance parameter. We illustrate the proposed methods with examples in clinical trials.

Biometry↗
PubMed1999

Unconditional versions of several tests commonly used in the analysis of contingency tables.

By focusing on a confidence interval for a nuisance parameter, Berger and Boos (1994, Journal of the American Statistical Association 89, 1012-1016) proposed new unconditional tests. In particular, they showed that, for a 2 x 2 table, this procedure generally was more powerful than Fisher's exact test. This paper utilizes and extends their approach to obtain unconditional tests for combining several 2 x 2 tables and testing for trend and homogeneity in a 2 x K table. The unconditional procedures are compared to the conditional ones by reanalyzing some published biomedical data.

Algorithms↗
PubMed1999

A hierarchical Bayesian model for combining multiple 2 x 2 tables using conditional likelihoods.

This paper introduces a hierarchical Bayesian model for combining multiple 2 x 2 tables that allows the flexibility of different odds ratio estimates for different tables and at the same time allows the tables to borrow information from each other. The proposed model, however, is different from a full Bayesian model in that the nuisance parameters are eliminated by conditioning instead of integration. The motivation is a more robust model and a faster and more stable Gibbs algorithm. We work out a Gibbs scheme using the adaptive rejection sampling for log concave density and an algorithm for the mean and variance of the noncentral hypergeometric distribution. The model is applied to a multicenter ulcer clinical trial.

Algorithms↗
PubMed2000

Weighted normality-based estimator in correcting correlation coefficient estimation between incomplete nutrient measurements.

Consider the problem of estimating the correlation between two nutrient measurements, such as the percent energy from fat obtained from a food frequency questionnaire (FFQ) and that from repeated food records or 24-hour recalls. Under a classical additive model for repeated food records, it is known that there is an attenuation effect on the correlation estimation if the sample average of repeated food records for each subject is used to estimate the underlying long-term average. This paper considers the case in which the selection probability of a subject for participation in the calibration study, in which repeated food records are measured, depends on the corresponding FFQ value, and the repeated longitudinal measurement errors have an autoregressive structure. This paper investigates a normality-based estimator and compares it with a simple method of moments. Both methods are consistent if the first two moments of nutrient measurements exist. Furthermore, joint estimating equations are applied to estimate the correlation coefficient and related nuisance parameters simultaneously. This approach provides a simple sandwich formula for the covariance estimation of the estimator. Finite sample performance is examined via a simulation study, and the proposed weighted normality-based estimator performs well under various distributional assumptions. The methods are applied to real data from a dietary assessment study.

Biometry↗
PubMed2000

Conditional and unconditional categorical regression models with missing covariates.

We consider methods for analyzing categorical regression models when some covariates (Z) are completely observed but other covariates (X) are missing for some subjects. When data on X are missing at random (i.e., when the probability that X is observed does not depend on the value of X itself), we present a likelihood approach for the observed data that allows the same nuisance parameters to be eliminated in a conditional analysis as when data are complete. An example of a matched case-control study is used to demonstrate our approach.

Biometry↗
PubMed2001

Unbiased confidence intervals for the odds ratio of two independent binomial samples with application to case-control data.

The problem of confidence interval construction for the odds ratio of two independent binomial samples is considered. Two methods of eliminating the nuisance parameter from the exact likelihood, conditioning and maximization, are described. A conditionally exact tail method exists by putting together upper and lower bounds. A shorter interval can be obtained by simultaneous consideration of both tails. We present here new methods that extend the tail and simultaneous approaches to the maximized likelihood. The methods are unbiased and applicable to case-control data, for which the odds ratio is important. The confidence interval procedures are compared unconditionally for small sample sizes in terms of their expected length and coverage probability. A Bayesian confidence interval method and a large-sample chi2 procedure are included in the comparisons.

Case-Control Studies↗
PubMed2001

Synthesis of evidence from epidemiological studies with interval-censored exposure due to grouping.

We describe a method for assessing dose-response effects from a series of case-control and cohort studies in which the exposure information is interval censored. The interval censoring of the exposure variable is dealt with through the use of retrospective models in which the exposure is treated as a multinomial response and disease status as a binary covariate. Polychotomous logistic regression models are adopted in which the dose-response relationship between exposure and disease may be modeled in a discrete or continuous fashion. Partial conditioning is possible to eliminate some of the nuisance parameters. The methods are applied to the motivating study of the relationship between chorionic villus sampling and the occurrence of terminal transverse limb reduction.

Biometry↗
PubMed2002

Estimation in the cox proportional hazards model with left-truncated and interval-censored data.

We show that the nonparametric maximum likelihood estimate (NPMLE) of the regression coefficient from the joint likelihood (of the regression coefficient and the baseline survival) works well for the Cox proportional hazards model with left-truncated and interval-censored data, but the NPMLE may underestimate the baseline survival. Two alternatives are also considered: first, the marginal likelihood approach by extending Satten (1996, Biometrika 83, 355-370) to truncated data, where the baseline distribution is eliminated as a nuisance parameter; and second, the monotone maximum likelihood estimate that maximizes the joint likelihood by assuming that the baseline distribution has a nondecreasing hazard function, which was originally proposed to overcome the underestimation of the survival from the NPMLE for left-truncated data without covariates (Tsai, 1988, Biometrika 75, 319-324). The bootstrap is proposed to draw inference. Simulations were conducted to assess their performance. The methods are applied to the Massachusetts Health Care Panel Study data set to compare the probabilities of losing functional independence for male and female seniors.

Activities of Daily Living↗
PubMed2003

Abundance estimation from multiple photo surveys: confidence distributions and reduced likelihoods for bowhead whales off Alaska.

Maximum likelihood estimates of abundance are obtained from repeated photographic surveys of a closed stratified population with naturally marked and unmarked individuals. Capture intensities are assumed log-linear in stratum, year, and season. In the chosen model, an approximate confidence distribution for total abundance of bowhead whales, with an accompanying likelihood reduced of nuisance parameters, is found from a parametric bootstrap experiment. The confidence distribution depends on the assumed study protocol. A confidence distribution that is exact (except for the effect of discreteness) is found by conditioning in the unstratified case without unmarked individuals.

Aging↗
PubMed2003

Homogeneity score test for the intraclass version of the kappa statistics and sample-size determination in multiple or stratified studies.

When the intraclass correlation coefficient or the equivalent version of the kappa agreement coefficient have been estimated from several independent studies or from a stratified study, we have the problem of comparing the kappa statistics and combining the information regarding the kappa statistics in a common kappa when the assumption of homogeneity of kappa coefficients holds. In this article, using the likelihood score theory extended to nuisance parameters (Tarone, 1988, Communications in Statistics-Theory and Methods 17(5), 1549-1556) we present an efficient homogeneity test for comparing several independent kappa statistics and, also, give a modified homogeneity score method using a noniterative and consistent estimator as an alternative. We provide the sample size using the modified homogeneity score method and compare it with that using the goodness-of-fit method (GOF) (Donner, Eliasziw, and Klar, 1996, Biometrics 52, 176-183). A simulation study for small and moderate sample sizes showed that the actual level of the homogeneity score test using the maximum likelihood estimators (MLEs) of parameters is satisfactorily close to the nominal and it is smaller than those of the modified homogeneity score and the goodness-of-fit tests. We investigated statistical properties of several noniterative estimators of a common kappa. The estimator (Donner et al., 1996) is essentially efficient and can be used as an alternative to the iterative MLE. An efficient interval estimation of a common kappa using the likelihood score method is presented.

Alcohol Drinking↗
PubMed2004

Joint analysis of time-to-event and multiple binary indicators of latent classes.

Multiple categorical variables are commonly used in medical and epidemiological research to measure specific aspects of human health and functioning. To analyze such data, models have been developed considering these categorical variables as imperfect indicators of an individual's "true" status of health or functioning. In this article, the latent class regression model is used to model the relationship between covariates, a latent class variable (the unobserved status of health or functioning), and the observed indicators (e.g., variables from a questionnaire). The Cox model is extended to encompass a latent class variable as predictor of time-to-event, while using information about latent class membership available from multiple categorical indicators. The expectation-maximization (EM) algorithm is employed to obtain maximum likelihood estimates, and standard errors are calculated based on the profile likelihood, treating the nonparametric baseline hazard as a nuisance parameter. A sampling-based method for model checking is proposed. It allows for graphical investigation of the assumption of proportional hazards across latent classes. It may also be used for checking other model assumptions, such as no additional effect of the observed indicators given latent class. The usefulness of the model framework and the proposed techniques are illustrated in an analysis of data from the Women's Health and Aging Study concerning the effect of severe mobility disability on time-to-death for elderly women.

Aged↗
PubMed2006

QTL mapping under ascertainment.

Mapping quantitative trait loci (QTL) using ascertained sibships is discussed. It is shown that under the standard normality assumption of variance components analysis the efficient scores are unchanged by ascertainment, and two different schemes of ascertainment correction suggested in the literature are asymptotically equivalent. The use of conditional maximum likelihood estimators derived under the normality assumption to estimate nuisance parameters is shown to result in only a small loss of power compared to the case of known parameters, even when the distribution of phenotypes is non-normal and/or the ascertainment criterion is ill defined.

Chromosome Mapping↗
PubMed1992

Bayesian analysis of stochastic constraints in structural equation models.

Structural equation models are analysed in the presence of stochastic constraints. Based on a Bayesian perspective, a prior distribution on nuisance parameters in the unknown covariance matrix of error measurements with stochastic constraints is considered. An iterative procedure is implemented to produce the various Bayesian estimates with stochastic constraints. A simulation study is conducted to illustrate the accuracy and behaviour of this Bayesian approach. A real-life example is provided to illustrate the theory.

Bayes Theorem↗
PubMed2003

Heterogeneity in IBD allele sharing among covariate-defined subgroups: issues and findings for affected relatives.

OBJECTIVES: Modelling of variation in identical-by-descent (IBD) allele sharing using covariates can increase power to detect linkage, identify covariate-defined subgroups linked to particular marker regions, and improve the design of subsequent studies to localize genes and characterize their effects. In this report, we highlight issues that arise in studies of families with affected relatives. METHODS: Mirea et al. [Genet Epidemiol 2003, in press] extended linear and exponential linkage likelihood models [Kong and Cox, Am J Hum Genet 1997;61: 1179-1188] to model variation in NPL scores among covariate-defined groups of families, and proposed likelihood ratio (LR) and t statistics to detect differences in allele sharing between groups defined by a binary covariate. Here we evaluate factors affecting the power of these tests analytically and by example, as well as effects of constraints, nuisance parameters, and incomplete data on test validity by simulation of locus heterogeneity in families with affected siblings or affected cousins. RESULTS: Provided constraints on the parameters are avoided, these tests are particularly useful when one subgroup has less than expected IBD sharing. The distribution of the LR statistic depends on the extent of linkage, particularly in the presence of constraints. The t statistic may be biased by group differences in information content. CONCLUSIONS: We recommend that constraints be applied cautiously, and covariate effects in IBD allele sharing models interpreted with care.

Alleles↗
PubMedDate not supplied

Intraindividual variability, change, and aging: conceptual and analytical issues.

BACKGROUND: Developmental researchers use a variety of research designs to examine aging-related changes. Most longitudinal studies of aging are based on research designs that feature successive, widely spaced, assessments to estimate changes in cognitive performance. Such designs assume that short-term variations in cognitive performance are small relative to long-term changes or have modeled such phenomena as nuisance parameters. OBJECTIVE: There is now sufficient empirical evidence to establish intraindividual cognitive variability as a systematic source of individual differences and of important predictive value for aging-relevant outcomes. METHODS: After an overview of types of change, potential underlying processes, and adequate analytic designs, we discuss consequences for lifespan aging research. RESULTS: We emphasize that interpretations of both cross-sectional and longitudinal results need to consider and specify theoretical assumptions about short-term and long-term changes. CONCLUSIONS: Above and beyond the analysis of long-term mean changes, short- term changes are an important aspect of aging-related change, and their analysis may help to explain psychological processes of adaptation.

Aging↗
PubMed2005

The posterior probability of linkage allowing for linkage disequilibrium and a new estimate of disequilibrium between a trait and a marker.

The posterior probability of linkage (PPL) statistic has been developed as a method for the rigorous accumulation of evidence for or against linkage allowing for both intra- and inter-sample heterogeneity. To date, the method has assumed linkage equilibrium between alleles at the trait locus and the marker locus. We now generalize the PPL to allow for linkage disequilibrium (LD), by incorporating variable phase probabilities into the underlying linkage likelihood. This enables us to recover the marginal posterior density of the recombination fraction, integrating out nuisance parameters of the trait model, including the locus heterogeneity (admixture) parameter, as well as a vector of LD parameters. The marginal posterior density can then be updated across data subsets or new data as they become available, while allowing parameters of the trait model to vary between data sets. The method applies immediately to general pedigree structures and to markers with multiple alleles. In the case of SNPs, the likelihood is parameterized in terms of the standard single LD parameter D'; and it therefore affords a mechanism for estimation of D' between the marker and the trait, again, without fixing the parameters of the trait model and allowing for updating across data sets. It is even possible to allow for a different associated allele in different populations, while accumulating information regarding the strength of LD. While a computationally efficient implementation for multi-allelic markers is still in progress, we have implemented a version of this new LD-PPL for SNPs and evaluated its performance in nuclear families. Our simulations show that LD-PPLs tend to be larger than PPLs (stronger evidence in favor of linkage/LD) with increased LD level, under a variety of generating models; while in the absence of linkage and LD, LD-PPLs tend to be smaller than PPLs (stronger evidence against linkage). The estimate of D' also behaves well even in relatively small, heterogeneous samples.

Genes, Dominant↗