Hierarchical likelihood approach to non-Gaussian factor analysis

Factor models, structural equation models (SEMs) and random-effect models share the common feature that they assume latent or unobserved random variables. Factor models and SEMs allow well developed procedures for a rich class of covariance models with many parameters, while random-effect models allow well developed procedures for non-normal models including heavy-tailed distributions for responses and random effects. In this paper, we show how these two developments can be combined to result in an extremely rich class of models, which can be beneficial to both areas. A new fitting procedures for binary factor models and a robust estimation approach for continuous factor models are proposed.     

An additive–multiplicative mean model for panel count data with dependent observation and dropout processes

This paper discusses regression analysis of panel count data with dependent observation and dropout processes. For the problem, a general mean model is presented that can allow both additive and multiplicative effects of covariates on the underlying point process. In addition, the proportional rates model and the accelerated failure time model are employed to describe possible covariate effects on the observation process and the dropout or follow‐up process, respectively. For estimation of regression parameters, some estimating equation‐based procedures are developed and the asymptotic properties of the proposed estimators are established. In addition, a resampling approach is proposed for estimating a covariance matrix of the proposed estimator and a model checking procedure is also provided. Results from an extensive simulation study indicate that the proposed methodology works well for practical situations, and it is applied to a motivating set of real data.     

Rank aggregation using latent-scale distance-based models

Rank aggregation aims at combining rankings of a set of items assigned by a sample of rankers to generate a consensus ranking. A typical solution is to adopt a distance-based approach to minimize the sum of the distances to the observed rankings. However, this simple sum may not be appropriate when the quality of rankers varies. This happens when rankers with different backgrounds may have different cognitive levels of examining the items. In this paper, we develop a new distance-based model by allowing different weights for different rankers. Under this model, the weight associated with a ranker is used to measure his/her cognitive level of ranking of the items, and these weights are unobserved and exponentially distributed. Maximum likelihood method is used for model estimation. Extensions to the cases of incomplete rankings and mixture modeling are also discussed. Empirical applications demonstrate that the proposed model produces better rank aggregation than those generated by Borda and the unweighted distance-based models.

     

Properties of the weighted log‐rank test in the design of confirmatory studies with delayed effects

Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. This assumption not only affects the analysis part but also the sample size calculation. The presence of delayed effects causes a change in the hazard ratio while the trial is ongoing since at the beginning we do not observe any difference between treatment arms, and after some unknown time point, the differences between treatment arms will start to appear. Hence, the proportional hazards assumption no longer holds, and both sample size calculation and analysis methods to be used should be reconsidered. The weighted log‐rank test allows a weighting for early, middle, and late differences through the Fleming and Harrington class of weights and is proven to be more efficient when the proportional hazards assumption does not hold. The Fleming and Harrington class of weights, along with the estimated delay, can be incorporated into the sample size calculation in order to maintain the desired power once the treatment arm differences start to appear. In this article, we explore the impact of delayed effects in group sequential and adaptive group sequential designs and make an empirical evaluation in terms of power and type‐I error rate of the of the weighted log‐rank test in a simulated scenario with fixed values of the Fleming and Harrington class of weights. We also give some practical recommendations regarding which methodology should be used in the presence of delayed effects depending on certain characteristics of the trial.     

Mixture structure analysis using the Akaike Information Criterion and the bootstrap

Given i.i.d. observations x1,x2,x3,...,xn drawn from a mixture of normal terms, one is often interested in determining the number of terms in the mixture and their defining parameters. Although the problem of determining the number of terms is intractable under the most general assumptions, there is hope of elucidating the mixture structure given appropriate caveats on the underlying mixture. This paper examines a new approach to this problem based on the use of Akaike Information Criterion (AIC) based pruning of data driven mixture models which are obtained from resampled data sets. Results of the application of this procedure to artificially generated data sets and a real world data set are provided.     

Csiszar’s ϕ-divergences for testing the order in a Markov chain

x ₁, ..., x _n+r can be treated as the sample values of a Markov chain of order r or less (chain in which the dependence extends over r+1 consecutive variables only), and consider the problem of testing the hypothesis H ₀ that a chain of order r− 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: _ϕ-Divergences. More precisely, if p _{a 1 ....., a r}: _{a r +1} denotes the transition probability for a r ^th order Markov chain, the hypothesis to be tested is H ₀:p _{a 1 ....., a r}: _{a r +1} = p _{a 2 ....., a r}: _{a r +1}, a _i ∈{1, ..., s}, i = 1, ..., r + 1 The tests given in this paper, for the first time, will have as a particular case the likelihood ratio test and the test based on the chi-squared statistic. Received: August 3, 1998; revised version: November 25, 1999     

Latin hypercube sampling with multidimensional uniformity

Complex models can only be realized a limited number of times due to large computational requirements. Methods exist for generating input parameters for model realizations including Monte Carlo simulation (MCS) and Latin hypercube sampling (LHS). Recent algorithms such as maximinLHS seek to maximize the minimum distance between model inputs in the multivariate space. A novel extension of Latin hypercube sampling (LHSMDU) for multivariate models is developed here that increases the multidimensional uniformity of the input parameters through sequential realization elimination. Correlations are considered in the LHSMDU sampling matrix using a Cholesky decomposition of the correlation matrix. Computer code implementing the proposed algorithm supplements this article. A simulation study comparing MCS, LHS, maximinLHS and LHSMDU demonstrates that increased multidimensional uniformity can significantly improve realization efficiency and that LHSMDU is effective for large multivariate problems.     

Confidence intervals for treatment effect from restricted maximum likelihood

An explicit form of confidence intervals for the treatment effect in random effects meta-analysis model obtained from Harville–Jeske–Kenward–Roger approach is given. These restricted likelihood based intervals are compared to alternative procedures commonly used in collaborative studies when the number of participants is small and study-specific variances are heterogeneous. Monte Carlo simulation experiments show that the former intervals have quite conservative coverage probabilities and favor the latter intervals.     

Estimating the frequency of familial dilated cardiomyopathy in the presence of misclassification errors

Dilated cardiomyopathy is a disease of unknown cause characterized by dilation and impaired function of one or both ventricles. Most cases are believed to be sporadic, although familial forms have been detected. The familial form has been estimated to have a relative frequency of about 25%. Since, except for familial history, familial form has no other characteristics that could help in classifying the two diseases, the estimate of the frequency of the familial form should take into account a possible misclassification error. In our study, 100 cases were randomly selected in a prospective series of 350 patients. Out of them, 28 index cases were included in the analysis: 12 were known to be familial, and 88 were believed to be sporadic. After extensive clinical examination of the relatives, 3 patients supposed to have a sporadic form were found to have a familial form. 13 cases had a confirmed sporadic disease. Models in the Log-Linear Product class (LLP) have been used to separate classification errors from underlying patterns of disease incidence. The most conservative crude estimate of the misclassification error is 16.1% (CI 0.22- 23.27%), which leads to a crude estimate of the frequency of the familiar form of about 60%. An estimate of the disease frequency, adjusted for taking into consideration the sampling plan, is 40.93% (CI 32.29-44.17%). The results are consistent with the hypothesis that genetic factors are still underestimated, although they represent a major cause of the disease.