The issue of joint confidence region and simultaneous confidence interval estimation for ratios of the parameters of a nonlinear mixed-effects model is addressed using a Fieller's theorem approach. The method pres...
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The issue of joint confidence region and simultaneous confidence interval estimation for ratios of the parameters of a nonlinear mixed-effects model is addressed using a Fieller's theorem approach. The method presented is similarly applicable to linear mixed-effects models. In addition, previous work on linear fixed-effects models is demonstrated to be a special case of the present method. The methodology is applied to the ratios of slopes in a study of gestational maturation of placental glucose transfer capacity in sheep.
To study the effect of methadone treatment in reducing multiple drug use, say heroin and benzodiazepines while controlling for their possible interaction, we analyse the results of urine drug screens from patients in ...
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To study the effect of methadone treatment in reducing multiple drug use, say heroin and benzodiazepines while controlling for their possible interaction, we analyse the results of urine drug screens from patients in treatment at a Sydney clinic in 1986. Weekly tests are either positive or negative for each type of drug and a bivariate binary model was developed to analyse such repeated bivariate binary outcomes. It models simultaneously the legit of each type of drug use and their log adds ratio linearly in some covariates. The serial correlation within subject is accounted for by including the 'previous outcome' of both drugs and their interaction as covariates. Our main conclusion is that drug use is reduced over time and the interaction between dose and time effects is not significant. It also suggests that while methadone maintenance is effective in reducing heroin use (CHAN et al., 1995), it does not suppress non-opioid drug use. Concerning the association between the two drugs, it is found that the present strength of their association depends on the previous outcomes only through a measure of concordance. The proposed model has a tractable likelihood function and so a full likelihood analysis is possible. It can be easily extended to incorporate mixture effects. The em algorithm is used for the estimation of parameters in the mixture model and model selection can be based on the Akaike Information Criterion.
McNemar's test is used to compare two marginal positive rates from an independent-sample of paired binary data. When the pairs are not mutually independent, the McNemar's test may not be valid. In this paper, ...
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McNemar's test is used to compare two marginal positive rates from an independent-sample of paired binary data. When the pairs are not mutually independent, the McNemar's test may not be valid. In this paper, we propose a random-effects regression model for comparing two marginal probabilities from nonindependent matched pairs data with covariates. An example of comparing positive rates of two blood culture systems illustrates this method. In this example, there is no external gold standard, the paired data are clustered, the data with negative results from both systems are not available, and one culture-specific covariate is involved. The computing method for the maximum likelihood estimation is efficient.
We present a framework of quasi-Bayes (QB) learning of the parameters of the continuous density hidden Markov model (CDHMM) with Gaussian mixture state observation densities, The QB formulation is based on the theory ...
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We present a framework of quasi-Bayes (QB) learning of the parameters of the continuous density hidden Markov model (CDHMM) with Gaussian mixture state observation densities, The QB formulation is based on the theory of recursive Bayesian inference, The QB algorithm is designed to incrementally update the hyperparameters of the approximate posterior distribution and the CDHMM parameters simultaneously, By further introducing a simple forgetting mechanism to adjust the contribution of previously observed sample utterances, the algorithm is adaptive in nature and capable of performing an online adaptive learning using only the current sample utterance, It can, thus, be used to cope with the time-varying nature of some acoustic and environmental variabilities, including mismatches caused by changing speakers, channels, and transducers. As an example, the QB learning framework is applied to on-line speaker adaptation and its viability is confirmed in a series of comparative experiments using a 26-letter English alphabet vocabulary.
The Cox regression model with a shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times. Estimation in this model when the frailties are assumed to f...
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The Cox regression model with a shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times. Estimation in this model when the frailties are assumed to follow a gamma distribution is reviewed, and we address the problem of obtaining variance estimates for regression coefficients, frailty parameter, and cumulative baseline hazards using the observed nonparametric information matrix. A number of examples are given comparing this approach with fully parametric inference in models with piecewise constant baseline hazards.
In this paper a likelihood-based method for analyzing mixed discrete and continuous regression models is proposed. We focus on marginal regression models, that is, models in which the marginal expectation of the respo...
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In this paper a likelihood-based method for analyzing mixed discrete and continuous regression models is proposed. We focus on marginal regression models, that is, models in which the marginal expectation of the response vector is related to covariates by known link functions. The proposed model is based on an extension of the general location model of Olkin and Tate (1961, Annals of Mathematical Statistics 32, 448-465), and can accommodate missing responses. When there are no missing data, our particular choice of parameterization yields maximum likelihood estimates of the marginal mean parameters that are robust to misspecification of the association between the responses. This robustness property does not, in general, hold for the case of incomplete data. There are a number of potential benefits of a multivariate approach over separate analyses of the distinct responses. First, a multivariate analysis can exploit the correlation structure of the response vector to address intrinsically multivariate questions. Second, multivariate test statistics allow for control over the inflation of the type I error that results when separate analyses of the distinct responses are performed without accounting for multiple comparisons. Third, it is generally possible to obtain more precise parameter estimates by accounting for the association between the responses. Finally, separate analyses of the distinct responses may be difficult to interpret when there is nonresponse because different sets of individuals contribute to each analysis. Furthermore, separate analyses can introduce bias when the missing responses are missing at random (MAR). A multivariate analysis can circumvent both of these problems. The proposed methods are applied to two biomedical datasets.
This paper considers nonparametric estimation of age-and time-specific trends in disease incidence using serial prevalence data collected from multiple cross-sectional samples of a population over time. The methodolog...
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This paper considers nonparametric estimation of age-and time-specific trends in disease incidence using serial prevalence data collected from multiple cross-sectional samples of a population over time. The methodology accounts for differential selection of diseased and undiseased individuals resulting, for example, from differences in mortality. It is shown that when a log-linear incidence odds model is adopted, an Ehl algorithm provides a convenient method for carrying out maximum likelihood estimation, primarily using existing generalized linear models software. The procedure is quite general, allowing a range of age-time incidence models to be fitted under the same framework. Furthermore, by making use of existing software for fitting generalized additive models, the procedure can be generalized with virtually no extra complexity to allow maximization of a penalized likelihood for smooth nonparametric estimation. Automatic choice of smoothing level for the penalized likelihood estimates is discussed, using generalized cross-validation, The method is applied to a data set on serial toxoplasmosis prevalence, which has previously been analyzed under the assumption of nondifferential selection. A variety of age-time incidence models are fitted, and the sensitivity to plausible differential selection patterns is considered. It is found that nonmultiplicative models are unnecessary and that qualitative incidence trends are fairly robust to differential selection.
Latent class analysis has been applied in medical research to assessing the sensitivity and specificity of diagnostic tests/diagnosticians. In these applications, a dichotomous latent variable corresponding to the uno...
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Latent class analysis has been applied in medical research to assessing the sensitivity and specificity of diagnostic tests/diagnosticians. In these applications, a dichotomous latent variable corresponding to the unobserved true disease status of the patients is assumed. Associations among multiple diagnostic tests are attributed to the unobserved heterogeneity induced by the latent variable, and inferences for the sensitivities and specificities of the diagnostic tests are made possible even though the true disease status is unknown. However, a shortcoming of this approach to analyses of diagnostic tests is that the standard assumption of conditional independence among the diagnostic tests given a latent class is contraindicated by the data-in some applications. In the present paper, models incorporating dependence among the diagnostic tests given a latent class are proposed. The models are parameterized so that the sensitivities and specificities of the diagnostic tests are simple functions of model parameters, and the usual latent class model obtains as a special case. Marginal models are used to account for the dependencies within each latent class. An accelerated em gradient algorithm is demonstrated to obtain maximum likelihood estimates of the parameters of interest, as well as estimates of the precision of the estimates.
This paper presents and discusses the estimation of genetic and residual (co-) variance components for conformation traits recorded in different environments using mixed linear models. Testing procedures for genetic p...
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This paper presents and discusses the estimation of genetic and residual (co-) variance components for conformation traits recorded in different environments using mixed linear models. Testing procedures for genetic parameters (genetic correlations between environments constant or equal to one, genetic correlation equal to one and constant intra-class correlations, homogeneity of variance-covariance components) are presented. These hypotheses were described via heteroskedastic univariate sire models taking into account genotype x environment interaction. An expectation-maximization (em) algorithm was proposed for calculating restricted maximum likelihood (RemL) estimates of the residual and genetic components of variances and co-variances. Likelihood ratio tests were suggested to assess hypotheses concerning genetic parameters. The procedures presented in the paper were used to analyze and to detect sources of variation on conformation traits in the Montbeliarde cattle breed using 24 301 progeny records of 528 sires. On all variables analyzed, several sources (stage of lactation, classifiers, type of housing) of heterogeneity of residual and genetic variances were clearly highlighted, but intra-class correlations between environments of type traits remained generally constant.
A model is proposed for longitudinal ordinal data with nonrandom drop-out, which combines the multivariate Dale model for longitudinal ordinal data with a logistic regression model for drop-out. Since response and dro...
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A model is proposed for longitudinal ordinal data with nonrandom drop-out, which combines the multivariate Dale model for longitudinal ordinal data with a logistic regression model for drop-out. Since response and drop-out are modelled as conditionally independent given complete data, the resulting likelihood can be maximised relatively simply, using the em algorithm, which with acceleration is acceptably fast and, with appropriate additions, can produce estimates of precision. The approach is illustrated with an example. Such modelling of nonrandom drop-out requires caution because the interpretation of the fitted models depends on assumptions that are unexaminable in a fundamental sense, and the conclusions cannot be regarded as necessarily robust. The main role of such modelling may be as a component of a sensitivity analysis.
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