Sample size calculations for time-averaged difference of longitudinal binary outcomes

In clinical trials with repeated measurements, the responses from each subject are measured multiple times during the study period. Two approaches have been widely used to assess the treatment effect, one that compares the rate of change between two groups and the other that tests the time-averaged difference (TAD). While sample size calculations based on comparing the rate of change between two groups have been reported by many investigators, the literature has paid relatively little attention to the sample size estimation for time-averaged difference (TAD) in the presence of heterogeneous correlation structure and missing data in repeated measurement studies. In this study, we investigate sample size calculation for the comparison of time-averaged responses between treatment groups in clinical trials with longitudinally observed binary outcomes. The generalized estimating equation (GEE) approach is used to derive a closed-form sample size formula, which is flexible enough to account for arbitrary missing patterns and correlation structures. In particular, we demonstrate that the proposed sample size can accommodate a mixture of missing patterns, which is frequently encountered by practitioners in clinical trials. To our knowledge, this is the first study that considers the mixture of missing patterns in sample size calculation. Our simulation shows that the nominal power and type I error are well preserved over a wide range of design parameters. Sample size calculation is illustrated through an example.     

Identification of longitudinal biomarkers for survival by a score test derived from a joint model of longitudinal and competing risks data

In this paper, we consider joint modelling of repeated measurements and competing risks failure time data. For competing risks time data, a semiparametric mixture model in which proportional hazards model are specified for failure time models conditional on cause and a multinomial model for the marginal distribution of cause conditional on covariates. We also derive a score test based on joint modelling of repeated measurements and competing risks failure time data to identify longitudinal biomarkers or surrogates for a time to event outcome in competing risks data.     

The Rate of Convergence of some Asymptotic Expansions for Distribution Approximations via an Esseen Type Estimate

Some asymptotic expansions not necessarily related to the central limit theorem are studied. We first observe that the smoothing inequality of Esseen implies the proximity, in the Kolmogorov distance sense, of the distributions of the random variables of two random sequences satisfying a sort of general asymptotic relation. We then present several instances of this observation. A first example, partially motivated by the the statistical theory of high precision measurements, is given by a uniform asymptotic approximation to (g(X + μ _n )) _n∈?, where g is some smooth function, X is a random variable and (μ _n ) _n∈? is a sequence going to infinity; a multivariate version is also stated and proved. We finally present a second class of examples given by a randomization of the interesting parameter in some classical asymptotic formulas; namely, a generic Laplace's type integral, randomized by the sequence (μ _n X) _n∈?, X being a Gamma distributed random variable.     

Confidence estimation of a normal mean vector with incomplete data

The problem of confidence estimation of a normal mean vector when data on different subsets of response variables are missing is considered. A simple approximate confidence region is proposed when the data matrix is of monotone pattern. Simultaneous inferential procedures based on Scheffe's method and Bonferroni's method are outlined. Further, applications of the results to a repeated measurements model are given. The results are illustrated using a practical example.     

Effect of measurement error and autocorrelation on the X¯ chart

Measurement error and autocorrelation often exist in quality control applications. Both have an adverse effect on the X¯ chart's performance. To counteract the undesired effect of autocorrelation, we build-up the samples with non-neighbouring items, according to the time they were produced. To counteract the undesired effect of measurement error, we measure the quality characteristic of each item of the sample several times. The chart's performance is assessed when multiple measurements are applied and the samples are built by taking one item from the production line and skipping one, two or more before selecting the next.     

Efficiency of generalized estimating equations for binary responses

Summary.  Using standard correlation bounds, we show that in generalized estimation equations (GEEs) the so-called 'working correlation matrix' R ( α ) for analysing binary data cannot in general be the true correlation matrix of the data. Methods for estimating the correlation param-eter in current GEE software for binary responses disregard these bounds. To show that the GEE applied on binary data has high efficiency, we use a multivariate binary model so that the covariance matrix from estimating equation theory can be compared with the inverse Fisher information matrix. But R ( α ) should be viewed as the weight matrix, and it should not be confused with the correlation matrix of the binary responses. We also do a comparison with more general weighted estimating equations by using a matrix Cauchy–Schwarz inequality. Our analysis leads to simple rules for the choice of α in an exchangeable or autoregressive AR(1) weight matrix R ( α ), based on the strength of dependence between the binary variables. An example is given to illustrate the assessment of dependence and choice of α .     

Analysis of repeated categorical responses from fully and partially cross-classified data

Many follow-up studies involve categorical data measured on the same individual at different times. Frequently, some of the individuals are missing one or more of the measurements. This results in a contingency table with both fully and partially cross-classified data. Two models can be used to analyze data of this type: (i) The multiple-sample model, in which all the study subjects with the same configuration of missing observations are considered a separate sample. (ii) The single-sample model, which assumes that the missing observations are the result of a mechanism causing subjects to lose the informtion from one or some of the measurements. In this work we compare the two approaches and show that under certain conditions, the two models yield the same maximum likelihood estimates of the cell probabilities in the underlying contingency table.     

Repeated measurements,log likelihood ratio tests and small samples

Various models have previously been proposed for data comprising m repeated measurements on each of N subjects. Log likelihood ratio tests may be used to help choose between possible models, but these tests are based on distributions which in theory apply only asymptotically. With small N , the log likelihood ratio approximation is unreliable, tending to reject the simpler of two models more often than it should. This is shown by reference to three datasets and analogous simulated data. For two of the three datasets, subjects fall into two groups. Log likelihood ratio tests confirm that for each of these two datasets group means over time differ. Tests suggest that group covariance structures also differ.     

Modelling Survival Events with Longitudinal Covariates Measured with Error

In survival analysis, time-dependent covariates are usually present as longitudinal data collected periodically and measured with error. The longitudinal data can be assumed to follow a linear mixed effect model and Cox regression models may be used for modelling of survival events. The hazard rate of survival times depends on the underlying time-dependent covariate measured with error, which may be described by random effects. Most existing methods proposed for such models assume a parametric distribution assumption on the random effects and specify a normally distributed error term for the linear mixed effect model. These assumptions may not be always valid in practice. In this article, we propose a new likelihood method for Cox regression models with error-contaminated time-dependent covariates. The proposed method does not require any parametric distribution assumption on random effects and random errors. Asymptotic properties for parameter estimators are provided. Simulation results show that under certain situations the proposed methods are more efficient than the existing methods.     

维生素C(Vit C)、贮藏时间、温度对香肠pH值和酸值(AV值)的影响

通过添加不同水平的VitC和贮藏时间及温度的变化，测定香肠中pH值、酸值（AV值）的大小，研究其各因素之间的影响。结果表明：VitC能使香肠中pH值、AV值降低；贮藏时间越长，AV值将增大，而pH值先减少，第32d后又略有增大；贮藏温度越低，虽能降低香肠中的AV值，但对pH值影响差异不显著（P＞0.05）；pH值与AV值之间的变化无相关性。