Robustified maximum likelihood estimation in generalized partial linear mixed model for longitudinal data

Summary .  In this article, we study the robust estimation of both mean and variance components in generalized partial linear mixed models based on the construction of robustified likelihood function. Under some regularity conditions, the asymptotic properties of the proposed robust estimators are shown. Some simulations are carried out to investigate the performance of the proposed robust estimators. Just as expected, the proposed robust estimators perform better than those resulting from robust estimating equations involving conditional expectation like Sinha (2004, Journal of the American Statistical Association 99, 451–460) and Qin and Zhu (2007, Journal of Multivariate Analysis 98, 1658–1683). In the end, the proposed robust method is illustrated by the analysis of a real data set.     

Closure procedures for monotone bi-factorial dose-response designs

Summary.   Two goals of multiple-dose factorial trials are (i) demonstrating improved effectiveness of a fixed combination over each of its components as well as (ii) identifying a safe and effective dose range. The authors address both goals though with focus on the second by closure procedures that guarantee strong control of the familywise error rate. Two different families of null hypotheses are investigated for bi-factorial dose–response designs that are monotone with respect to the matrix partial order. One is suitable to find the minimum effective dose(s) and the other one is large enough to identify the highest effective dose step(s). Likelihood ratio tests and appropriate multiple contrast tests are applied to an unbalanced clinical trial example taken from Hung (2000, Statistics in Medicine 19, 2079–2087). Full computer code written in the R language is available from the Internet.     

Incorporating time postinoculation into a dose–response model of Yersinia pestis in mice

Aims:  To develop a time-dependent dose–response model for describing the survival of animals exposed to Yersinia pestis.
Methods and Results:  Candidate time-dependent dose–response models were fitted to a survival data set for mice intraperitoneally exposed to graded doses of Y. pestis using the maximum likelihood estimation method. An exponential dose–response model with the model parameter modified by an inverse-power dependency of time postinoculation provided a statistically adequate fit to the experimental survival data. This modified model was verified by comparison with prior studies.
Conclusions:  The incorporated time dependency quantifies the expected temporal effect of in vivo bacteria growth in the dose–response relationship. The modified model describes the development of animal infectious response over time and represents observed responses accurately.
Significance and Impact of the Study:  This is the first study to incorporate time in a dose–response model for Y. pestis infection. The outcome may be used for the improved understanding of in vivo bacterial dynamics, improved postexposure decision making or as a component to better assist epidemiological investigations.     

Variable Selection in the Cox Regression Model with Covariates Missing at Random

Summary .  We consider variable selection in the Cox regression model ( Cox, 1975 ,  Biometrika   362, 269–276) with covariates missing at random. We investigate the smoothly clipped absolute deviation penalty and adaptive least absolute shrinkage and selection operator (LASSO) penalty, and propose a unified model selection and estimation procedure. A computationally attractive algorithm is developed, which simultaneously optimizes the penalized likelihood function and penalty parameters. We also optimize a model selection criterion, called the   IC _Q    statistic ( Ibrahim, Zhu, and Tang, 2008 ,  Journal of the American Statistical Association   103, 1648–1658), to estimate the penalty parameters and show that it consistently selects all important covariates. Simulations are performed to evaluate the finite sample performance of the penalty estimates. Also, two lung cancer data sets are analyzed to demonstrate the proposed methodology.     

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.     

Median regression models for longitudinal data with dropouts

Summary .  Recently, median regression models have received increasing attention. When continuous responses follow a distribution that is quite different from a normal distribution, usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily. In this article, we discuss using median regression models to deal with longitudinal data with dropouts. Weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data, where the weights are determined by modeling the dropout process. Consistency and the asymptotic distribution of the resultant estimators are established. The proposed method is used to analyze a longitudinal data set arising from a controlled trial of HIV disease ( Volberding et al., 1990 , The New England Journal of Medicine 322, 941–949). Simulation studies are conducted to assess the performance of the proposed method under various situations. An extension to estimation of the association parameters is outlined.     

Estimating survival and association in a semicompeting risks model

Summary .   In many follow-up studies, patients are subject to concurrent events. In this article, we consider semicompeting risks data as defined by Fine, Jiang, and Chappell (2001, Biometrika 88 , 907–919) where one event is censored by the other but not vice versa. The proposed model involves marginal survival functions for the two events and a parametric family of copulas for their dependency. This article suggests a general method for estimating the dependence parameter when the dependency is modeled with an Archimedean copula. It uses the copula-graphic estimator of Zheng and Klein (1995, Biometrika 82 , 127–138) for estimating the survival function of the nonterminal event, subject to dependent censoring. Asymptotic properties of these estimators are derived. Simulations show that the new methods work well with finite samples. The copula-graphic estimator is shown to be more accurate than the estimator proposed by Fine et al. (2001) ; its performances are similar to those of the self-consistent estimator of Jiang, Fine, Kosorok, and Chappell (2005, Scandinavian Journal of Statistics 33, 1–20). The analysis of a data set, emphasizing the estimation of characteristics of the observable region, is presented as an illustration.     

Fast FSR variable selection with applications to clinical trials

Summary .  A new version of the false selection rate variable selection method of Wu, Boos, and Stefanski (2007,  Journal of the American Statistical Association   102, 235–243) is developed that requires no simulation. This version allows the tuning parameter in forward selection to be estimated simply by hand calculation from a summary table of output even for situations where the number of explanatory variables is larger than the sample size. Because of the computational simplicity, the method can be used in permutation tests and inside bagging loops for improved prediction. Illustration is provided in clinical trials for linear regression, logistic regression, and Cox proportional hazards regression.     

Variable Selection for Clustering with Gaussian Mixture Models

Summary .  This article is concerned with variable selection for cluster analysis. The problem is regarded as a model selection problem in the model-based cluster analysis context. A model generalizing the model of Raftery and Dean (2006,  Journal of the American Statistical Association   101, 168–178) is proposed to specify the role of each variable. This model does not need any prior assumptions about the linear link between the selected and discarded variables. Models are compared with Bayesian information criterion. Variable role is obtained through an algorithm embedding two backward stepwise algorithms for variable selection for clustering and linear regression. The model identifiability is established and the consistency of the resulting criterion is proved under regularity conditions. Numerical experiments on simulated datasets and a genomic application highlight the interest of the procedure.     

Combining Information from Cancer Registry and Medical Records Data to Improve Analyses of Adjuvant Cancer Therapies

Summary .  Cancer registry records contain valuable data on provision of adjuvant therapies for cancer patients. Previous studies, however, have shown that these therapies are underreported in registry systems. Hence direct use of the registry data may lead to invalid analysis results. We propose first to impute correct treatment status, borrowing information from an additional source such as medical records data collected in a validation sample, and then to analyze the multiply imputed data, as in Yucel and Zaslavsky (2005,  Journal of the American Statistical Association   100, 1123–1132). We extend their models to multiple therapies using multivariate probit models with random effects. Our model takes into account the associations among different therapies in both administration and probability of reporting, as well as the multilevel structure (patients clustered within hospitals) of registry data. We use Gibbs sampling to estimate model parameters and impute treatment status. The proposed methodology is applied to the data from the Quality of Cancer Care project, in which stage II or III colorectal cancer patients were eligible to receive adjuvant chemotherapy and radiation therapy.     

LTA 252GG and GA Genotypes are Associated with Diffuse-Type Noncardia Gastric Cancer Risk in the Japanese Population

Background:  There are limited numbers of reports on the association of lymphotoxin-alpha ( LTA ) genotypes with gastric cancer.
Methods:  A nested case–control study was carried out in the longitudinal cohort of atomic bomb survivors using stored sera before diagnosis (mean, 2.3 years) and blood cells. Enrolled were 287 cases with noncardia gastric cancer of diffuse and intestinal types and three controls per case selected from cohort members matched on age, gender, city, and time and type of serum storage and counter-matched on radiation dose.
Results:  LTA 252GG and GA genotypes were associated with the prevalence of Helicobacter pylori IgG seropositivity and higher antibody titer against H. pylori cytotoxin-associated gene A (CagA) protein in controls and they were an independent risk factor for noncardia gastric cancer of diffuse type (RR = 2.8 (95% CI: 1.3–6.3), p  =   .01, and RR = 2.7 (95% CI: 1.5–4.8), p  <   .001), but not for intestinal type, after adjusting for H. pylori IgG seropositivity, CagA antibody titers, chronic atrophic gastritis, smoking, and radiation dose. Cessation of smoking (RR = 0.4 (95% CI: 0.2–0.7), p  <   .001) and never smoking (RR = 0.4 (95% CI: 0.3–0.6), p  <   .001) were both protective for future noncardia gastric cancer. Radiation dose was associated with noncardia gastric cancer in subjects with both the LTA 252G -allele and never smoking/quit smoking histories (RR = 3.8 (95% CI: 1.7–5.9), p  =   .009).
Conclusion:  The LTA 252 genotype is associated with noncardia gastric cancer of diffuse type in Japan and interacted with radiation dose.     

Bounds on direct effects in the presence of confounded intermediate variables

Summary .   This article considers the problem of estimating the average controlled direct effect (ACDE) of a treatment on an outcome, in the presence of unmeasured confounders between an intermediate variable and the outcome. Such confounders render the direct effect unidentifiable even in cases where the total effect is unconfounded (hence identifiable). Kaufman et al. (2005, Statistics in Medicine 24, 1683–1702) applied a linear programming software to find the minimum and maximum possible values of the ACDE for specific numerical data. In this article, we apply the symbolic Balke–Pearl (1997, Journal of the American Statistical Association 92, 1171–1176) linear programming method to derive closed-form formulas for the upper and lower bounds on the ACDE under various assumptions of monotonicity. These universal bounds enable clinical experimenters to assess the direct effect of treatment from observed data with minimum computational effort, and they further shed light on the sign of the direct effect and the accuracy of the assessments.     

A Bayesian approach to a logistic regression model with incomplete information

Summary .   We consider a set of independent Bernoulli trials with possibly different success probabilities that depend on covariate values. However, the available data consist only of aggregate numbers of successes among subsets of the trials along with all of the covariate values. We still wish to estimate the parameters of a modeled relationship between the covariates and the success probabilities, e.g., a logistic regression model. In this article, estimation of the parameters is made from a Bayesian perspective by using a Markov chain Monte Carlo algorithm based only on the available data. The proposed methodology is applied to both simulation studies and real data from a dose–response study of a toxic chemical, perchlorate.     

A novel method for floristic quality assessment using the vegetation of the Jiuding Mountain, Sichuan, China as an example

Floristic Quality Assessment (FQA) is proposed as a new method to assess floristic integrity. In the present study, we use both the conventional method broadly adopted in the USA and a new one proposed herein to assess the floristic quality of the Jiuding Mountain. For the application of the FQA, each plant species was assigned an integer from 0 to 10 termed coefficient of conservatism (C) based on its global distribution area. The coefficient shows the degree of fidelity of each plant species to the flora of the west slope of the Jiuding Mountain and represents a rank based on its distribution area. Those species receiving a C value of 0–1 are distributed all over the world, those receiving a C value of 2–3 mostly in tropical areas, and those receiving a C value of 4–6 broadly in temperate areas. Species with C values of 7–8 are endemic to China and those with coefficients 9–10 are restricted to the Hengduan Mountains or even endemic to the Jiuding Mountain. Based on the fact that different plant species show different relative importance values (IV), the new method estimates the weighted averages for the coefficient of conservatism called the weighted mean coefficient of conservatism (     _w). The floristic quality index (FQI) was then derived from     or     _w, native species richness (N) and non-native species (A). As expected when using the new method, the dominant species of the communities obtained different Cs, which resulted in different     _ws and FQI_ws as compared to the conventional method.     

Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis

Summary .  In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose–response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose–response analysis.     

Genetic and morphological variability of the endangered Syngonanthus mucugensis Giul. (Eriocaulaceae) from the Chapada Diamantina, Brazil: implications for conservation and taxonomy

Allozymic and morphometric studies were carried out on ten populations of Syngonanthus mucugensis (Eriocaulaceae), a species from north-eastern Brazil threatened by extinction. Genetic and morphological variability was low or moderately low in all populations, being lower in populations from Rio de Contas/Catolés ( P _L = 14.3–21.4, A  = 1.1–1.2, H _e = 0.026–0.059, D2M = 26.893–33.157) than in those from Mucugê ( P _L = 28.6–35.7, A  = 1.3–1.5, H _e = 0.078–0.164, D2M = 28.999–45.077). A high coefficient of endogamy ( F _is = 0.257) was found, which can be explained by the reproductive characteristics and distribution of the species. The values for genetic and morphological structuring ( F _st = 0.512 and A _MRPP = 0.175, respectively) were high as a result of the differentiation between populations from the two areas. The mean genetic identity between populations from the two areas (0.812) was much lower than between populations from the same area (Mucugê, 0.980; Rio de Contas/Catolés, 0.997). These results indicate that we are dealing with two distinct taxa and, as a result of the nature of the morphological differences found, a new subspecies is described for the populations of the region of Rio de Contas and Catolés, Syngonanthus mucugensis ssp. riocontensis . Such conclusions raise important implications for the conservation of Syngonanthus mucugensis , and will be used in the drawing up of management plans for its conservation.  © 2007 The Linnean Society of London, Botanical Journal of the Linnean Society , 2007, 153 , 401–416.     

A simple imputation method for longitudinal studies with non-ignorable non-responses

Missing data are a common problem in longitudinal studies in the health sciences. Motivated by data from the Muscatine Coronary Risk Factor (MCRF) study, a longitudinal study of obesity, we propose a simple imputation method for handling non-ignorable non-responses (i.e., when non-response is related to the specific values that should have been obtained) in longitudinal studies with either discrete or continuous outcomes. In the proposed approach, two regression models are specified; one for the marginal mean of the response, the other for the conditional mean of the response given non-response patterns. Statistical inference for the model parameters is based on the generalized estimating equations (GEE) approach. An appealing feature of the proposed method is that it can be readily implemented using existing, widely-available statistical software. The method is illustrated using longitudinal data on obesity from the MCRF study.     

Acclimation is beneficial at extreme test temperatures in the Danube crested newt, Triturus dobrogicus (Caudata, Salamandridae)

Despite many studies demonstrating the effect of acclimation on behavioural or physiological traits, considerable debate still exists about the evolutionary significance of this phenomenon. One of the unresolved issues is whether acclimation to warmer temperature is beneficial at treatment or at more extreme test temperatures. To answer this question, we assessed the effect of thermal acclimation on preferred body temperatures ( T _ps), maximum swimming and running speed, and critical thermal maximum ( CT _max) in the Danube crested newt ( Triturus dobrogicus ). Adult newts were kept at 15 °C (control) and 25 °C (treatment) for 8 weeks prior to measurements. We measured T _ps in an aquatic thermal gradient over 24 h, maximum speeds in a linear racetrack at six temperatures (5–33 °C), and CT _max in a continuously heated water bath. T _ps were higher in newts kept at 15 °C than in those kept at 25 °C. The maximum swimming speed did not acclimate. The maximum running speed at 30–33 °C was substantially higher in newts kept at 25 °C than in those kept at 15 °C. CT _max increased with the treatment temperature. Hence, we conclude that the acclimation response to warm temperature is beneficial not at treatment but at more extreme temperatures in newts.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 90 , 627–636.     

Are myrmecophytes always better protected against herbivores than other plants?

The present field study compared the degree of defoliation of three Guianian melastome, two myrmecophytes (i.e. plants sheltering ants in hollow structures) and Clidemia sp., a nonmyrmecophytic plant serving as a control. Maieta guianensis Aubl. hosted mostly Pheidole minutula Mayr whatever the area, whereas Tococa guianensis Aubl. hosted mostly Azteca bequaerti Wheeler along streams and Crematogaster laevis Mayr or Azteca sp. 1 in the understory where it never blossomed. Only Tococa , when sheltering A. bequaerti in what can be considered as a truly mutualistic relationship, showed significantly less defoliation than control plants. In the other associations, the difference was not significant, but P. minutula is mutualistic with Maieta because it furnishes some protection (exclusion experiments) plus nutrients (previous studies). When devoid of ants, Tococa showed significantly greater defoliation than control plants; therefore, it was deduced that Tococa probably lacks certain antidefoliator metabolites that control plants possess (both Tococa and control plants are protected by ground-nesting, plant-foraging ants, which is termed 'general myrmecological protection'). Consequently, plant-ants other than A. bequaerti probably also protect Tococa slightly, thus compensating for this deficiency and permitting it to live in the understory until treefall gaps provide the conditions necessary for seed production.  © 2006 The Linnean Society of London, Biological Journal of the Linnean Society , 2006, 89 , 91–98.