Demystifying optimal dynamic treatment regimes

A dynamic regime is a function that takes treatment and covariate history and baseline covariates as inputs and returns a decision to be made. Murphy (2003, Journal of the Royal Statistical Society, Series B 65, 331-366) and Robins (2004, Proceedings of the Second Seattle Symposium on Biostatistics, 189-326) have proposed models and developed semiparametric methods for making inference about the optimal regime in a multi-interval trial that provide clear advantages over traditional parametric approaches. We show that Murphy's model is a special case of Robins's and that the methods are closely related but not equivalent. Interesting features of the methods are highlighted using the Multicenter AIDS Cohort Study and through simulation.     

A Monte Carlo method for Bayesian inference in frailty models

Many analyses in epidemiological and prognostic studies and in studies of event history data require methods that allow for unobserved covariates or "frailties." Clayton and Cuzick (1985, Journal of the Royal Statistical Society, Series A 148, 82-117) proposed a generalization of the proportional hazards model that implemented such random effects, but the proof of the asymptotic properties of the method remains elusive, and practical experience suggests that the likelihoods may be markedly nonquadratic. This paper sets out a Bayesian representation of the model in the spirit of Kalbfleisch (1978, Journal of the Royal Statistical Society, Series B 40, 214-221) and discusses inference using Monte Carlo methods.     

Facial width-to-height ratio in a Turkish population is not sexually dimorphic and is unrelated to aggressive behavior

Recently, Weston et al. (2004; Wide faces or large canines? The attractive versus the aggressive primate. Proceedings of the Royal Society of London, Series B, 271, 416–419) found that facial width-to-height ratio (WHR) is a sexually dimorphic characteristic in humans; males have higher facial WHR than females. Following this study, Carré et al. (2008; In your face: facial metrics predict aggressive behavior in the laboratory and in varsity and professional hockey players. Proceedings of the Royal Society of London, Series B, 275, 2651–2656) found that individual differences in facial WHR accounted for a significant proportion of the variance in aggressive behavior of men, but not women. I tested these two hypotheses in a sample of 470 Turkish university students. Facial WHR was measured from frontal photographs. I also measured the aggressiveness level of 212 individuals using the Buss and Perry aggressiveness questionnaire. The mean facial WHR (and standard deviation) was 1.89±0.12 for males and 1.91±0.11 for females. There was no relationship between facial WHR and the self-reported aggressive behavior for either sex. The facial WHR is not a sexually dimorphic characteristic (at least) for Turkish people, and it does not appear to be associated with self-reported trait aggression.     

Global cross-ratio models for bivariate, discrete, ordered responses

A family of statistical models is presented for bivariate, discrete response to a regressor when both components of the response have ordered categories. Association between components is expressed in terms of global cross-ratios, cross-product ratios of quadrant probabilities, for each double dichotomy of the response table of probabilities into quadrants (Pearson and Heron, 1913, Biometrika 9, 159-315). These models are extensions to the work of Plackett (1965, Journal of the American Statistical Association 60, 516-522) and Mantel and Brown (1973, Biometrics 29, 649-665). The marginal cumulative probabilities may satisfy linear logistic or other generalized linear models (McCullagh, 1980, Journal of the Royal Statistical Society, Series B 42, 109-142). An analysis of patients' postoperative pain level and medication frequency illustrates these methods.     

A Bayesian approach to nonlinear random effects models

Nonlinear random effects models are considered from the Bayesian point of view. The method of analysis follows closely that of Lindley and Smith (1972, Journal of the Royal Statistical Society, Series B 34, 1-42). The numerical method is related to the EM algorithm.     

Book Reviews

Natural Antioxidants in Human Health and Disease Edited by Balz Frei Academic Press, San Diego

In Vitro Toxicology Edited by: Shayne Cox Gad Raven Press Ltd.: New York, 290pp ISBN: 0-88167-974-7

Active Oxygen, Lipid Peroxidation and Antioxidants Edited by Kunio Yagi Japan Scientific Society Press: Tokyo ISBN 4-7622-6738-4, 1993 CRC Press: Boca Raton ISBN 0-8493-7769-2, 1993 x +372 pages Y 13, 000

Free Radicals, Cardiovascular Dysfunction and Protection Strategies R C Kukreja and M L Hess R G Landes Company: Austin, Texas, USA, 1994

Oxygen and Environmental Stress in Plants (Special issue of the Proceedings of the Royal Society of Edinburgh, volume 102 1994) eds R M M Crawford, G A F Hendry and B A Goodman

Mitochondria: DNA, Proteins and Disease Eds. V. Darley Usmar and A.H.V. Schapira Portland Press Research Monograph V, London, 1994

Human Medicinal Agents From Plants Edited by A. Douglas Kinghorn and Manuel F. Balandrin ACS Symposium Series 534 American Chemical Society: Washington DC, 1993, pp. xii + 356. ISBN 08412 2705 5. $89.95.     

The Mizon-Richard encompassing test for the Cox and Aalen additive hazards models.

The Cox hazards model (Cox, 1972, Journal of the Royal Statistical Society, Series B34, 187-220) for survival data is routinely used in many applied fields, sometimes, however, with too little emphasis on the fit of the model. A useful alternative to the Cox model is the Aalen additive hazards model (Aalen, 1980, in Lecture Notes in Statistics-2, 1-25) that can easily accommodate time changing covariate effects. It is of interest to decide which of the two models that are most appropriate to apply in a given application. This is a nontrivial problem as these two classes of models are nonnested except only for special cases. In this article we explore the Mizon-Richard encompassing test for this particular problem. It turns out that it corresponds to fitting of the Aalen model to the martingale residuals obtained from the Cox regression analysis. We also consider a variant of this method, which relates to the proportional excess model (Martinussen and Scheike, 2002, Biometrika 89, 283-298). Large sample properties of the suggested methods under the two rival models are derived. The finite-sample properties of the proposed procedures are assessed through a simulation study. The methods are further applied to the well-known primary biliary cirrhosis data set.     

Survival estimation using splines

A nonparametric maximum likelihood procedure is given for estimating the survivor function from right-censored data. It approximates the hazard rate by a simple function such as a spline, with different approximations yielding different estimators. A special case is that proposed by Nelson (1969, Journal of Quality Technology 1, 27-52) and Altshuler (1970, Mathematical Biosciences 6, 1-11). The estimators are uniformly consistent and have the same asymptotic weak convergence properties as the Kaplan-Meier (1958, Journal of the American Statistical Association 53, 457-481) estimator. However, in small and in heavily censored samples, the simplest spline estimators have uniformly smaller mean squared error than do the Kaplan-Meier and Nelson-Altshuler estimators. The procedure is extended to estimate the baseline hazard rate and regression coefficients in the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model and is illustrated using experimental carcinogenesis data.     

Sensitivity analysis for nonrandom dropout: a local influence approach

Diggle and Kenward (1994, Applied Statistics 43, 49-93) proposed a selection model for continuous longitudinal data subject to nonrandom dropout. It has provoked a large debate about the role for such models. The original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests. Since then, the view has emerged that these models should ideally be made part of a sensitivity analysis. This paper presents a formal and flexible approach to such a sensitivity assessment based on local influence (Cook, 1986, Journal of the Royal Statistical Society, Series B 48, 133-169). The influence of perturbing a missing-at-random dropout model in the direction of nonrandom dropout is explored. The method is applied to data from a randomized experiment on the inhibition of testosterone production in rats.     

Cohort case-control design and analysis for clustered failure-time data

Cohort case-control design is an efficient and economical design to study risk factors for disease incidence or mortality in a large cohort. In the last few decades, a variety of cohort case-control designs have been developed and theoretically justified. These designs have been exclusively applied to the analysis of univariate failure-time data. In this work, a cohort case-control design adapted to multivariate failure-time data is developed. A risk set sampling method is proposed to sample controls from nonfailures in a large cohort for each case matched by failure time. This method leads to a pseudolikelihood approach for the estimation of regression parameters in the marginal proportional hazards model (Cox, 1972, Journal of the Royal Statistical Society, Series B 34, 187-220), where the correlation structure between individuals within a cluster is left unspecified. The performance of the proposed estimator is demonstrated by simulation studies. A bootstrap method is proposed for inferential purposes. This methodology is illustrated by a data example from a child vitamin A supplementation trial in Nepal (Nepal Nutrition Intervention Project-Sarlahi, or NNIPS).     

Immune effector mechanisms in parasitic infections

edited by F.Y. Liew and K. Vickerman, Philosophical Transactions of the Royal Society of London Series B, Vol. 352, No. 1359, 1997. pp 1293-1394, ISSN 0962-8436.     

Introduction to Brain mechanisms of selective perception and action. Proceedings of a Discussion Meeting held at the Royal Society of London on 19 and 20 November 1997.

Introduction to Brain mechanisms of selective perception and action. Proceedings of a Discussion Meeting held at the Royal Society of London on 19 and 20 November 1997. Organized and edited by G. W. Humphreys, J. Duncan and A. Treisman.     

Reviews of publications

Evolution and Extinction. Proceedings of a Joint Symposium of the Royal Society and the Linnean Society held on 9 and 10 November 1989 , organized and edited by W. G. Chaloner and A. Hallam.
On Stress, Disease and Evolution. A Unifying Theory , by Graham W. Boyd.
The Use of Plant Genetic Resources , edited by A. H. D. Brown, O. H. Frankel, D. R. Marshall and J. T. Williams.     

Wavelet thresholding with bayesian false discovery rate control

The false discovery rate (FDR) procedure has become a popular method for handling multiplicity in high-dimensional data. The definition of FDR has a natural Bayesian interpretation; it is the expected proportion of null hypotheses mistakenly rejected given a measure of evidence for their truth. In this article, we propose controlling the positive FDR using a Bayesian approach where the rejection rule is based on the posterior probabilities of the null hypotheses. Correspondence between Bayesian and frequentist measures of evidence in hypothesis testing has been studied in several contexts. Here we extend the comparison to multiple testing with control of the FDR and illustrate the procedure with an application to wavelet thresholding. The problem consists of recovering signal from noisy measurements. This involves extracting wavelet coefficients that result from true signal and can be formulated as a multiple hypotheses-testing problem. We use simulated examples to compare the performance of our approach to the Benjamini and Hochberg (1995, Journal of the Royal Statistical Society, Series B57, 289-300) procedure. We also illustrate the method with nuclear magnetic resonance spectral data from human brain.     

A family of confidence intervals for the ratio of two binomial proportions

The power divergence family of statistics introduced by Cressie and Read (1984, Journal of the Royal Statistical Society, Series B 46, 440-464) is used to obtain approximate confidence intervals for the ratio of two proportions. Intervals based on inverting the Pearson, likelihood-ratio, and Freeman-Tukey statistics are included in this family. Small-sample comparisons of the intervals are presented.     

Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies

This article presents results for the maximum likelihood analysis of several groups of measurements made on the same quantity. Following Cochran (1937, Journal of the Royal Statistical Society 4(Supple), 102-118; 1954, Biometrics 10, 101-129; 1980, in Proceedings of the 25th Conference on the Design of Experiments in Army Research, Development and Testing, 21-33) and others, this problem is formulated as a one-way unbalanced random-effects ANOVA with unequal within-group variances. A reparametrization of the likelihood leads to simplified computations, easier identification and interpretation of multimodality of the likelihood, and (through a non-informative-prior Bayesian approach) approximate confidence regions for the mean and between-group variance.     

Plants for Food and Medicine: Proceedings of the Joint Conference of the Society for Economic Botany and the International Society for Ethnopharmacology

Plants for Food and Medicine: Proceedings of the Joint Conference of the Society for Economic Botany and the International Society for Ethnopharmacology. H. D. V. Prendergast. N. L. Etkin. D. R. Harris. and P. J. Houghton. eds. Kew, Richmond, UK: Scientific Publications Dept., Royal Botanic Gardens, 1998. 438 pp.     

The Mizon–Richard Encompassing Test for the Cox and Aalen Additive Hazards Models

Summary .   The Cox hazards model ( Cox, 1972 , Journal of the Royal Statistical Society, Series B 34, 187–220) for survival data is routinely used in many applied fields, sometimes, however, with too little emphasis on the fit of the model. A useful alternative to the Cox model is the Aalen additive hazards model ( Aalen, 1980 , in Lecture Notes in Statistics-2 , 1–25) that can easily accommodate time changing covariate effects. It is of interest to decide which of the two models that are most appropriate to apply in a given application. This is a nontrivial problem as these two classes of models are nonnested except only for special cases. In this article we explore the Mizon–Richard encompassing test for this particular problem. It turns out that it corresponds to fitting of the Aalen model to the martingale residuals obtained from the Cox regression analysis. We also consider a variant of this method, which relates to the proportional excess model ( Martinussen and Scheike, 2002 , Biometrika 89, 283–298). Large sample properties of the suggested methods under the two rival models are derived. The finite-sample properties of the proposed procedures are assessed through a simulation study. The methods are further applied to the well-known primary biliary cirrhosis data set.     

On the application of strain factors for approximation of the contribution of anisotropic cells to the mechanics of a tissue construct

Bio-artificial tissue constructs consisting of fibroblast cells embedded in a collagenous matrix are valuable in vitro systems in which to study cellular mechanics. Deriving cellular mechanics from the results of experimentation on tissue constructs requires a mathematical relationship that delineates amongst the contributions of the constituents of a tissue construct. A scaling between the average strain in a uniformly stretched tissue and the axial strain in isotropic cells was used in earlier work to study relations between cell mechanics and the overall mechanics of a tissue construct. That work showed that a scaling factor called a "strain factor" provided an accurate representation of the average axial strain in isotropic cells. The present study analyzes such relationships for anisotropic cells. We incorporate Eshelby's (1957; Proceedings of the Royal Society of London A 241, 376; 1959; Proceedings of the Royal Society of London A 252, 561) exact solution for the strain field in isolated ellipsoidal inclusions into the Zahalak (Biophysical journal 79, 2369) constitutive model for tissue constructs. Results showed that, for the case of prolate cells, the strain along the major cell axis is mostly influenced by the remote strain projected along that axis; off-axis cell mechanics plays only a small role in most tissues. The strain factor approximation is shown to be accurate for anisotropic cells to within a few percent for the vast majority of tissues. The results presented in this paper provide an explicit measure of the effects of cellular anisotropy, and a mechanism for calculating the contributions of these effects to overall tissue mechanics when these effects are important.     

Methods of estimation in log odds ratio regression models

McCullagh's (1984, Journal of the Royal Statistical Society, Series B 46, 250-256) approximation to the conditional maximum likelihood estimator in log odds ratio regression models is shown to have negligible asymptotic bias unless the odds ratios are large and the sample sizes in individual 2 X 2 tables are very small. In application to two sets of case-control data, it yields results virtually indistinguishable from those of the conditional analysis. A generalization of the Mantel-Haenszel estimator proposed by Davis (1985, Biometrics 41, 487-495) does not approximate the conditional results nearly as well.