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Testing Covariance Structure in Multivariate Models: Application to Family Disease Data

多元模型协方差结构检验及其在家族疾病数据中的应用

Recent interest in modeling multivariate responses for members of groups has emphasized the need for testing goodness of fit. Here we describe a way to test the covariance structure of a multivariate distribution parameterized by a vector θ. The idea is to extend this distribution, the “null” distribution, to a more general distribution that depends on θ, an additional scalar γ, and a specific quadratic function of the response vector chosen to capture features of an…

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Testing Covariance Structure in Multivariate Models: Application to Family Disease Data

多元模型协方差结构的检验及家族疾病数据应用

Recent interest in modeling multivariate responses for members of groups has emphasized the need for testing goodness of fit. Here we describe a way to test the covariance structure of a multivariate distribution parameterized by a vector θ. The idea is to extend this distribution, the “null” distribution, to a more general distribution that depends on θ, an additional scalar γ, and a specific quadratic function of the response vector chosen to capture features of an…

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Multistage Sampling Designs and Estimating Equations

Summary In some applications it is cost efficient to sample data in two or more stages. In the first stage a simple random sample is drawn and then stratified according to some easily measured attribute. In each subsequent stage a random subset of previously selected units is sampled for more detailed and costly observation, with a unit’s sampling probability determined by its attributes as observed in the previous stages. This paper describes multistage sampling designs and…

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Logistic Regression of Family Data from Case-Control Studies

病例对照研究中家庭数据的 Logistic 回归

Multivariate regression models are applied to binary disease data in families identified from case-control studies. Attention is restricted to ‘ marginal’ or reproducible models, i. e. those whose parameters have the same interpretations in the marginal distributions for all subsets of a family, with a logistic specification of each individual's marginal disease probability. For such models, it is shown that the case-control family data can be analysed as if they were…

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Testing Odds-Ratio Equality for Several Diseases

多个疾病的优势比相等性检验

We present a test for the hypothesis that odds-ratios are constant across two or more diseases, using matched case-control data. The test requires less computing than the usual conditional likelihood score test (Prentice, 1979) because it excludes the control covariates. We give a practical algorithm to compute the test statistic and discuss its power.

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Testing odds-ratio equality for several diseases

多种疾病的优势比相等性检验

We present a test for the hypothesis that odds-ratios are constant across two or more diseases, using matched case-control data. The test requires less computing than the usual conditional likelihood score test (Prentice, 1979) because it excludes the control covariates. We give a practical algorithm to compute the test statistic and discuss its power.

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Approximations for Regression with Covariate Measurement Error

协变量测量误差回归的近似修正

The effect of covariate measurement error on maximum likelihood and maximum quasilikelihood estimates (MLE's or MQLE's) of regression parameters is considered. The naive estimates, obtained by ignoring error, are modified to account for it. The modified estimates can be computed explicitly from the naive ones, and have less bias for small error. They are particularly useful for Berkson error models. Examples illustrate their application to linear and nonlinear regression,…

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A Test to Detect Clusters of Disease

检测疾病空间聚集的检验

A test is given to detect clustering in disease incidence or mortality data The test statistic is the mean distance between all pairs of disease cases. Its null mean and variance and its asymptotic normality are derived under assumptions that accommodate differences in population distribution among demographic subgroups at different disease risk. The test is illustrated on 63 cases of anal and rectal squamous cell carcinoma in San Francisco during 1973–1981.

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A test to detect clusters of disease

疾病病例聚集的检测检验

A test is given to detect clustering in disease incidence or mortality data The test statistic is the mean distance between all pairs of disease cases. Its null mean and variance and its asymptotic normality are derived under assumptions that accommodate differences in population distribution among demographic subgroups at different disease risk. The test is illustrated on 63 cases of anal and rectal squamous cell carcinoma in San Francisco during 1973–1981.

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Sample Size for Logistic Regression with Small Response Probability

低响应概率下逻辑回归的样本量计算

The Fisher information matrix for the estimated parameters in a multiple logistic regression can be approximated by the augmented Hessian matrix of the moment-generating function for the covariates. The approximation is valid when the probability of response is small. With its use one can obtain a simple closed-form estimate of the asymptotic covariance matrix of the maximum likelihood parameter estimates, and thus approximate sample sizes needed to test hypotheses about the…

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