Targeted maximum likelihood estimation for dynamic treatment regimes in sequentially randomized controlled trials

Sequential Randomized Controlled Trials (SRCTs) are rapidly becoming essential tools in the search for optimized treatment regimes in ongoing treatment settings. Analyzing data for multiple time-point treatments with a view toward optimal treatment regimes is of interest in many types of afflictions: HIV infection, Attention Deficit Hyperactivity Disorder in children, leukemia, prostate cancer, renal failure, and many others. Methods for analyzing data from SRCTs exist but they are either inefficient or suffer from the drawbacks of estimating equation methodology. We describe an estimation procedure, targeted maximum likelihood estimation (TMLE), which has been fully developed and implemented in point treatment settings, including time to event outcomes, binary outcomes and continuous outcomes. Here we develop and implement TMLE in the SRCT setting. As in the former settings, the TMLE procedure is targeted toward a pre-specified parameter of the distribution of the observed data, and thereby achieves important bias reduction in estimation of that parameter. As with the so-called Augmented Inverse Probability of Censoring Weight (A-IPCW) estimator, TMLE is double-robust and locally efficient. We report simulation results corresponding to two data-generating distributions from a longitudinal data structure.     

Direct fitness for dynamic kin selection

The direct-fitness approach to modelling the evolution of social traits is an alternative to the classical inclusive-fitness-based approach. Despite both its utility and popularity, the direct-fitness approach has not yet been extended to include the analysis of dynamic traits, i.e. traits whose level of expression may vary over time. In this article, I apply the direct-fitness approach to cope with the evolution of a dynamic resource-allocation behaviour when this behaviour influences the fitness of relatives. I am able to implement the direct-fitness approach using components (reproductive value, fitness changes and measures of relatedness) found in standard, social-evolutionary models. I illustrate the modified direct-fitness model with an example studied by previous authors, and I show how the direct-fitness perspective can aid the validation of analytical results by means of a genetic algorithm.     

Gene selection: a Bayesian variable selection approach

Selection of significant genes via expression patterns is an important problem in microarray experiments. Owing to small sample size and the large number of variables (genes), the selection process can be unstable. This paper proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables to specialize the model to a regression setting and uses a Bayesian mixture prior to perform the variable selection. We control the size of the model by assigning a prior distribution over the dimension (number of significant genes) of the model. The posterior distributions of the parameters are not in explicit form and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the parameters from the posteriors. The Bayesian model is flexible enough to identify significant genes as well as to perform future predictions. The method is applied to cancer classification via cDNA microarrays where the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify a set of significant genes. The method is also applied successfully to the leukemia data. SUPPLEMENTARY INFORMATION: http://stat.tamu.edu/people/faculty/bmallick.html.     

The effect of dynamic light regimes on Chlorella

The patterns of diurnal variations in pigmentation and optical cross-section were compared for two cyclostat cultures of Chlorella pyrenoidosa, where the dynamics of the photoperiod differed. Populations were light-limited, nutrient rich and growing on an 8:16 light-dark (LD) cycle. One light regime was an 8 h sine function of the light period (sinusoidal culture), while the second had an 1 h sine function super-imposed on the 8 hour sine function (oscillating sinusoidal culture). Hourly samples were taken throughout a 12 h period including the light period. Determinations were made of chlorophyll (Chl) a and b abundance, in vivo absorption spectra, cell number and volume and used to derive both cell-specific (cell) and optical chlorophyll specific (chl) cross sections, as well as the absorption efficiency, Q, of the cells. The results indicate that C. pyrenoidosa is capable of adapting to dynamics in light intensity within an 8 h photoperiod. The sinusoidal culture showed a constant decrease in the Chl a/b ratio of 28% while the total Chl content per cell increased slightly and chl and Q remained constant, suggesting coordinated changes in reaction centers and light harvesting complexes. Over the oscillating photoperiod, however, the second culture displayed a diurnal variation in Chl a/b ratio, a 20% increase in chl and an apparent oscillation in Q. These observations suggest that an oscillating photoperiod promoted the capability of Chl molecules to collect light and that the fractional area of all Chl molecules exposed to the photon flux is inversely related to the photon flux.     

Comparison of mixed-model approaches for association mapping

Association-mapping methods promise to overcome the limitations of linkage-mapping methods. The main objectives of this study were to (i) evaluate various methods for association mapping in the autogamous species wheat using an empirical data set, (ii) determine a marker-based kinship matrix using a restricted maximum-likelihood (REML) estimate of the probability of two alleles at the same locus being identical in state but not identical by descent, and (iii) compare the results of association-mapping approaches based on adjusted entry means (two-step approaches) with the results of approaches in which the phenotypic data analysis and the association analysis were performed in one step (one-step approaches). On the basis of the phenotypic and genotypic data of 303 soft winter wheat (Triticum aestivum L.) inbreds, various association-mapping methods were evaluated. Spearman's rank correlation between P-values calculated on the basis of one- and two-stage association-mapping methods ranged from 0.63 to 0.93. The mixed-model association-mapping approaches using a kinship matrix estimated by REML are more appropriate for association mapping than the recently proposed QK method with respect to (i) the adherence to the nominal alpha-level and (ii) the adjusted power for detection of quantitative trait loci. Furthermore, we showed that our data set could be analyzed by using two-step approaches of the proposed association-mapping method without substantially increasing the empirical type I error rate in comparison to the corresponding one-step approaches.     

Comparison of three sedation regimes for spinal anesthesia in sheep

The authors considered three protocols for spinal anesthesia using sheep as a model. An appropriate spinal anesthesia method would obviate the need for general anesthesia in certain surgical approaches.     

Dynamic regimes in a model of single-locus density-dependent selection

A model of density-dependent selection in a Mendelian single-locus population was analyzed in the case where the fitnesses of genotypic forms are exponential functions of the population size. Analytical and numerical studies of the model were performed for a diallelic locus, and parametric regions were established for different dynamic behaviors of the model. The diallelic model of density-dependent selection was generalized to a multiallelic locus; the results of its analysis are described.     

Ultrahigh-dimensional variable selection method for whole-genome gene-gene interaction analysis

ABSTRACT: BACKGROUND: Genome-wide gene-gene interaction analysis using single nucleotide polymorphisms (SNPs) is an attractive way for identification of genetic components that confers susceptibility of human complex diseases. Individual hypothesis testing for SNP-SNP pairs as in common genome-wide association study (GWAS) however involves difficulty in setting overall p-value due to complicated correlation structure, namely, the multiple testing problem that causes unacceptable false negative results. A large number of SNP-SNP pairs than sample size, so-called the large p small n problem, precludes simultaneous analysis using multiple regression. The method that overcomes above issues is thus needed. RESULTS: We adopt an up-to-date method for ultrahigh-dimensional variable selection termed the sure independence screening (SIS) [17] for appropriate handling of numerous number of SNP-SNP interactions by including them as predictor variables in logistic regression. We propose ranking strategy using promising dummy coding methods and following variable selection procedure in the SIS method suitably modified for gene-gene interaction analysis. We also implemented the procedures in a software program, EPISIS, using the cost-effective GPGPU (General-purpose computing on graphics processing units) technology. EPISIS can complete exhaustive search for SNP-SNP interactions in standard GWAS dataset within several hours. The proposed method works successfully in simulation experiments and in application to real WTCCC (Wellcome Trust Case-Control Consortium) data. CONCLUSIONS: Based on the machine-learning principle, the proposed method gives powerful and flexible genome-wide search for various patterns of gene-gene interaction.     

Group selection and kin selection: formally equivalent approaches

Inclusive fitness theory, summarised in Hamilton's rule, is a dominant explanation for the evolution of social behaviour. A parallel thread of evolutionary theory holds that selection between groups is also a candidate explanation for social evolution. The mathematical equivalence of these two approaches has long been known. Several recent papers, however, have objected that inclusive fitness theory is unable to deal with strong selection or with non-additive fitness effects, and concluded that the group selection framework is more general, or even that the two are not equivalent after all. Yet, these same problems have already been identified and resolved in the literature. Here, I survey these contemporary objections, and examine them in the light of current understanding of inclusive fitness theory.     

Habitat selection in a variable environment

A Monte Carlo simulation scheme was utilized to determine optimal strategies of habitat utilization in a variable environment. The model allows for differences in quality among habitats at any one time and for varying levels of environmental variance and autocorrelation. When habitats are on the average equal in quality, tracking of temporal fluctuations in environment through variable habitat selection is universally advantageous with the gain in fitness limited by environmental variance, autocorrelation, and number of available habitats. Average differences in quality among habitats will restrict the advantage of variable habitat utilization (over complete usage of the average better habitat) to cases of high environmental autocorrelation or high ratios of enviromental variance to mean habitat separation. Extending an earlier prediction of Levins (1965), the average heterozygosity per individual in a natural population should increase with increasing environmental variance.     

Bayesian variable selection for detecting adaptive genomic differences among populations

We extend an F(st)-based Bayesian hierarchical model, implemented via Markov chain Monte Carlo, for the detection of loci that might be subject to positive selection. This model divides the F(st)-influencing factors into locus-specific effects, population-specific effects, and effects that are specific for the locus in combination with the population. We introduce a Bayesian auxiliary variable for each locus effect to automatically select nonneutral locus effects. As a by-product, the efficiency of the original approach is improved by using a reparameterization of the model. The statistical power of the extended algorithm is assessed with simulated data sets from a Wright-Fisher model with migration. We find that the inclusion of model selection suggests a clear improvement in discrimination as measured by the area under the receiver operating characteristic (ROC) curve. Additionally, we illustrate and discuss the quality of the newly developed method on the basis of an allozyme data set of the fruit fly Drosophila melanogaster and a sequence data set of the wild tomato Solanum chilense. For data sets with small sample sizes, high mutation rates, and/or long sequences, however, methods based on nucleotide statistics should be preferred.     

Evaluating machine learning approaches for aiding probe selection for gene-expression arrays

MOTIVATION: Microarrays are a fast and cost-effective method of performing thousands of DNA hybridization experiments simultaneously. DNA probes are typically used to measure the expression level of specific genes. Because probes greatly vary in the quality of their hybridizations, choosing good probes is a difficult task. If one could accurately choose probes that are likely to hybridize well, then fewer probes would be needed to represent each gene in a gene-expression microarray, and, hence, more genes could be placed on an array of a given physical size. Our goal is to empirically evaluate how successfully three standard machine-learning algorithms-na?ve Bayes, decision trees, and artificial neural networks-can be applied to the task of predicting good probes. Fortunately it is relatively easy to get training examples for such a learning task: place various probes on a gene chip, add a sample where the corresponding genes are highly expressed, and then record how well each probe measures the presence of its corresponding gene. With such training examples, it is possible that an accurate predictor of probe quality can be learned. RESULTS: Two of the learning algorithms we investigate-na?ve Bayes and neural networks-learn to predict probe quality surprisingly well. For example, in the top ten predicted probes for a given gene not used for training, on average about five rank in the top 2.5% of that gene's hundreds of possible probes. Decision-tree induction and the simple approach of using predicted melting temperature to rank probes perform significantly worse than these two algorithms. The features we use to represent probes are very easily computed and the time taken to score each candidate probe after training is minor. Training the na?ve Bayes algorithm takes very little time, and while it takes over 10 times as long to train a neural network, that time is still not very substantial (on the order of a few hours on a desktop workstation). We also report the information contained in the features we use to describe the probes. We find the fraction of cytosine in the probe to be the most informative feature. We also find, not surprisingly, that the nucleotides in the middle of the probes sequence are more informative than those at the ends of the sequence.     

Stochastic search variable selection for identifying multiple quantitative trait loci

In this article, we utilize stochastic search variable selection methodology to develop a Bayesian method for identifying multiple quantitative trait loci (QTL) for complex traits in experimental designs. The proposed procedure entails embedding multiple regression in a hierarchical normal mixture model, where latent indicators for all markers are used to identify the multiple markers. The markers with significant effects can be identified as those with higher posterior probability included in the model. A simple and easy-to-use Gibbs sampler is employed to generate samples from the joint posterior distribution of all unknowns including the latent indicators, genetic effects for all markers, and other model parameters. The proposed method was evaluated using simulated data and illustrated using a real data set. The results demonstrate that the proposed method works well under typical situations of most QTL studies in terms of number of markers and marker density.