Abstract: Many longitudinal studies generate both the time to some event of interest and repeated measures data. This article is motivated by a study on patients with a renal allograft, in which interest lies in the association between longitudinal proteinuria (a dichotomous variable) measurements and the time to renal graft failure. An interesting feature of the sample at hand is that nearly half of the patients were never tested positive for proteinuria (>1g/day) during follow-up, which introduces a degenerate part in the random-effects density for the longitudinal process. In this article we propose a two-part shared parameter model framework that effectively takes this feature into account, and we investigate sensitivity to the various dependence structures used to describe the association between the longitudinal measurements of proteinuria and the time to renal graft failure.
Abstract: The logistic transformation, originally suggested by Johnson (1949), is applied to analyze responses that are restricted to a finite interval (e.g. (0,1)), so-called bounded outcome scores. Bounded outcome scores often have a non-standard distribution, e.g. J- or U-shaped, precluding classical parametric statistical approaches for analysis. Applying the logistic transformation on a normally distributed random variable, gives rise to a logit-normal (LN) distribution. This distribution can take a variety of shapes on (0,1). Further, the model can be extended to correct for (baseline) covariates. Therefore, the method could be useful for comparative clinical trials. Bounded outcomes can be found in many research areas, e.g. drug compliance research, quality-of-life studies, and pain (and pain relief) studies using visual analog scores, but all these scores can attain the boundary values 0 or 1. A natural extension of the above approach is therefore to assume a latent score on 0,1) having a LN distribution. Two cases are considered: (a) the bounded outcome score is a proportion where the true probabilities have a LN distribution on (0,1) and (b) the bounded outcome score on [0,1] is a coarsened version of a latent score with a LN distribution on (0,1). We also allow the variance (on the transformed scale) to depend on treatment. The usefulness of our approach for comparative clinical trials will be assessed in this paper. It turns out to be important to distinguish the case of equal and unequal variances. For a bounded outcome score of the second type and with equal variances, our approach comes close to ordinal probit (OP) regression. However, ignoring the inequality of variances can lead to highly biased parameter estimates. A simulation study compares the performance of our approach with the two-sample Wilcoxon test and with OP regression. Finally, the different methods are illustrated on two data sets.
Abstract: Until recently, item response models such as the factor analysis model for metric responses, the two-parameter logistic model for binary responses and the multinomial model for nominal responses considered only the main effects of latent variables without allowing for interaction or polynomial latent variable effects. However, nonlinear relationships among the latent variables might be necessary in real applications. Methods for fitting models with nonlinear latent terms have been developed mainly under the structural equation modeling approach. In this paper, we consider a latent variable model framework for mixed responses (metric and categorical) that allows inclusion of both nonlinear latent and covariate effects. The model parameters are estimated using full Maximum Likelihood based on a hybrid integration-maximization algorithm. Finally, a method for obtaining factor scores based on multiple Imputation is proposed here for the non-linear model.
Abstract: We consider power and sample size calculations for randomized trials with a bounded outcome score (BOS) as primary response adjusted for a priori chosen covariates. We define BOS to be a random variable restricted to a finite interval. Typically, a BOS has a J- or U-shaped distribution hindering traditional parametric methods of analysis. When no adjustment for covariates is needed, a non-parametric test could be chosen. However, there is still a problem with calculating the power since the common location-shift alternative does not hold in general for a BOS. In this paper, we consider a parametric approach and assume that the observed BOS is a coarsened version of a true BOS, which has a logit-normal distribution in each treatment group allowing correction for covariates. A two-step procedure is used to calculate the power. Firstly, the power function is defined conditionally on the covariate values. Secondly, the marginal power is obtained by averaging the conditional power with respect to an assumed distribution for the covariates using Monte Carlo integration. A simulation study evaluates the performance of our method which is also applied to the ECASS-1 stroke study.
Abstract: The R package ltm has been developed for the analysis of multivariate dichotomous and polytomous data using latent variable models, under the Item Response Theory approach. For dichotomous data the Rasch, the Two-Parameter Logistic, and Birnbaum’s Three-Parameter models have been implemented, whereas for polytomous data Semejima’s Graded Response model is available. Parameter estimates are obtained under marginal maximum likelihood using the Gauss-Hermite quadrature rule. The capabilities and features of the package are illustrated using two real data examples.
