The validation of surrogate end points by using data from randomized clinical trials: a case-study in advanced colorectal cancer

Summary.  In many therapeutic areas, the identification and validation of surrogate end points is of prime interest to reduce the duration and/or size of clinical trials. Buyse and co-workers and Burzykowski and co-workers have proposed a validation strategy for end points that are either normally distributed or (possibly censored) failure times. In this paper, we address the problem of validating an ordinal categorical or binary end point as a surrogate for a failure time true end point. In particular, we investigate the validity of tumour response as a surrogate for survival time in evaluating fluoropyrimidine-based experimental therapies for advanced colorectal cancer. Our analysis is performed on data from 28 randomized trials in advanced colorectal cancer, which are available through the Meta-Analysis Group in Cancer.     

Homosexualities in the Netherlands

Loving relationships between two men, or between two women, are by no means generally accepted in the Netherlands. Prejudices, mistrust, and aversion on the part of those surrounding them are the daily lot of homosexuals. Young people who are attracted to members of their own sex have understandable difficulties in dealing with this state of affairs. Becoming aware of their own homosexual feelings, looking for contact, building up relationships, developing a measure of self-esteem—all become especially difficult when there is little support, understanding, and no role models for homosexual lifestyles to be found in the immediate environment.In this article we will successively examine the attitudes of the Dutch population toward homosexuality and the living situation of homosexuals in the Netherlands. A more detailed report will be given of a comparative investigation of homosexual and heterosexual boys and girls carried out by the author.     

Marginal correlation from an extended random-effects model for repeated and overdispersed counts

Vangeneugden et al. [15 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C. and Sotto, C. 2007. Marginal correlation in longitudinal binary data based on generalized linear mixed models, Tech. Rep., Hasselt University. submitted for publication [Google Scholar]] derived approximate correlation functions for longitudinal sequences of general data type, Gaussian and non-Gaussian, based on generalized linear mixed-effects models (GLMM). Their focus was on binary sequences, as well as on a combination of binary and Gaussian sequences. Here, we focus on the specific case of repeated count data, important in two respects. First, we employ the model proposed by Molenberghs et al. [13 Molenberghs, G., Verbeke, G. and Demétrio, C. G.B. 2007. An extended random-effects approach to modeling repeated, overdispersed count data. Lifetime Data Anal., 13: 513–531. [Crossref], [PubMed], [Web of Science ®] [Google Scholar]], which generalizes at the same time the Poisson-normal GLMM and the conventional overdispersion models, in particular the negative-binomial model. The model flexibly accommodates data hierarchies, intra-sequence correlation, and overdispersion. Second, means, variances, and joint probabilities can be expressed in closed form, allowing for exact intra-sequence correlation expressions. Next to the general situation, some important special cases such as exchangeable clustered outcomes are considered, producing insightful expressions. The closed-form expressions are contrasted with the generic approximate expressions of Vangeneugden et al. [15 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C. and Sotto, C. 2007. Marginal correlation in longitudinal binary data based on generalized linear mixed models, Tech. Rep., Hasselt University. submitted for publication [Google Scholar]]. Data from an epileptic-seizures trial are analyzed and correlation functions derived. It is shown that the proposed extension strongly outperforms the classical GLMM.     

On the Weibull-Gamma frailty model, its infinite moments, and its connection to generalized log-logistic, logistic, Cauchy, and extreme-value distributions

It is shown that the commonly used Weibull-Gamma frailty model has a finite number of finite moments only and that its marginal distribution generalizes the log-logistic distribution. In some cases there is not even a finite variance, and there are cases without a single finite moment. Upon transformation to the entire real line, generalized logistic and generalized Cauchy distributions are introduced and their connection with the previous ones established, as well as with the extreme-value distribution. Apart from intrinsic and classroom value, the family can be of use when formulating non-informative priors in Bayesian data analysis. Also, gauging the amount of finite moments is important when checking regularity conditions in the Weibull-Gamma model. Our findings are illustrated using data from survival in cancer patients.     

An extended random-effects approach to modeling repeated, overdispersed count data

Non-Gaussian outcomes are often modeled using members of the so-called exponential family. The Poisson model for count data falls within this tradition. The family in general, and the Poisson model in particular, are at the same time convenient since mathematically elegant, but in need of extension since often somewhat restrictive. Two of the main rationales for existing extensions are (1) the occurrence of overdispersion, in the sense that the variability in the data is not adequately captured by the model's prescribed mean-variance link, and (2) the accommodation of data hierarchies owing to, for example, repeatedly measuring the outcome on the same subject, recording information from various members of the same family, etc. There is a variety of overdispersion models for count data, such as, for example, the negative-binomial model. Hierarchies are often accommodated through the inclusion of subject-specific, random effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these issues may occur simultaneously, models accommodating them at once are less than common. This paper proposes a generalized linear model, accommodating overdispersion and clustering through two separate sets of random effects, of gamma and normal type, respectively. This is in line with the proposal by Booth et al. (Stat Model 3:179-181, 2003). The model extends both classical overdispersion models for count data (Breslow, Appl Stat 33:38-44, 1984), in particular the negative binomial model, as well as the generalized linear mixed model (Breslow and Clayton, J Am Stat Assoc 88:9-25, 1993). Apart from model formulation, we briefly discuss several estimation options, and then settle for maximum likelihood estimation with both fully analytic integration as well as hybrid between analytic and numerical integration. The latter is implemented in the SAS procedure NLMIXED. The methodology is applied to data from a study in epileptic seizures.     

Random effects models for estimation of the probability and time to progression of a continuous biomarker

Biomarkers play a key role in the monitoring of disease progression. The time taken for an individual to reach a biomarker exceeding or lower than a meaningful threshold is often of interest. Due to the inherent variability of biomarkers, persistence criteria are sometimes included in the definitions of progression, such that only two consecutive measurements above or below the relevant threshold signal that “true” progression has occurred. In previous work, a novel approach was developed, which allowed estimation of the time to threshold using the parameters from a linear mixed model where the residual variance was assumed to be pure measurement error. In this paper, we extend this methodology so that serial correlation can be accommodated. Assuming that the Markov property holds and applying the chain rule of probabilities, we found that the probability of progression at each timepoint can be expressed simply as the product of conditional probabilities. The methodology is applied to a cohort of HIV positive individuals, where the time to reach a CD4 count threshold is estimated. The second application we present is based on a study on abdominal aortic aneurysms, where the time taken for an individual to reach a diameter exceeding 55 mm is studied. We observed that erroneously ignoring the residual correlation when it is strong may result in substantial overestimation of the time to threshold. The estimated probability of the biomarker reaching a threshold of interest, expected time to threshold, and confidence intervals are presented for selected patients in both applications.     

Two Stochastic Multidimensional Choice Models for Marketing Research

Two recently developed probabilistic multidimensional models for analyzing pairwise choice data are introduced, discussed in terms of their differential properties, and extended in several ways. The first one, the wandering vector model, was originally suggested by Carroll [12] and extended by De Soete and Carroll [30]. The second model, called the wandering ideal point model, is a more recently proposed [32] unfolding analog of the wandering vector model. A general maximum likelihood estimation method for fitting the various models described is mentioned, as well as a statistical test for assessing the goodness of fit. Finally, an application of the models is provided concerning consumer choice for some 14 brands of over-the-counter analgesics to illustrate how such models can be gainfully utilized for marketing decision making concerning product positioning.     

‘I Need Help on Mondays,It’s Not My Day. The Other Days,I’m OK’.—Perspectives of Disabled Children on Inclusive Education

This article examines the experience of inclusive education from the perspective of disabled children. We worked with the observations of, and interviews with, 15 children, aged 5–17 who go to a mainstream school. The study is set in the context of a 3‐year research project exploring the practice of inclusive education in Flanders. Here, we report on the key findings from the children’s accounts, focusing on what they had to say about themselves, what they think about school, friends, support and their future prospects.     

Sensitivity analysis for incomplete contingency tables: the Slovenian plebiscite case

Classical inferential procedures induce conclusions from a set of data to a population of interest, accounting for the imprecision resulting from the stochastic component of the model. Less attention is devoted to the uncertainty arising from (unplanned) incompleteness in the data. Through the choice of an identifiable model for non-ignorable non-response, one narrows the possible data-generating mechanisms to the point where inference only suffers from imprecision. Some proposals have been made for assessing the sensitivity to these modelling assumptions; many are based on fitting several plausible but competing models. For example, we could assume that the missing data are missing at random in one model, and then fit an additional model where non-random missingness is assumed. On the basis of data from a Slovenian plebiscite, conducted in 1991, to prepare for independence, it is shown that such an ad hoc procedure may be misleading. We propose an approach which identifies and incorporates both sources of uncertainty in inference: imprecision due to finite sampling and ignorance due to incompleteness. A simple sensitivity analysis considers a finite set of plausible models. We take this idea one step further by considering more degrees of freedom than the data support. This produces sets of estimates (regions of ignorance) and sets of confidence regions (combined into regions of uncertainty).