Calculating sample size for studies with expected all-or-none nonadherence and selection bias

Summary .  We develop sample size formulas for studies aiming to test mean differences between a treatment and control group when all-or-none nonadherence (noncompliance) and selection bias are expected. Recent work by Fay, Halloran, and Follmann (2007, Biometrics 63, 465–474) addressed the increased variances within groups defined by treatment assignment when nonadherence occurs, compared to the scenario of full adherence, under the assumption of no selection bias. In this article, we extend the authors' approach to allow selection bias in the form of systematic differences in means and variances among latent adherence subgroups. We illustrate the approach by performing sample size calculations to plan clinical trials with and without pilot adherence data. Sample size formulas and tests for normally distributed outcomes are also developed in a Web Appendix that account for uncertainty of estimates from external or internal pilot data.     

Confidence intervals and P-values for meta-analysis with publication bias

We study publication bias in meta-analysis by supposing there is a population (y, sigma) of studies which give treatment effect estimates y approximately N(theta, sigma(2)). A selection function describes the probability that each study is selected for review. The overall estimate of theta depends on the studies selected, and hence on the (unknown) selection function. Our previous paper, Copas and Jackson (2004, Biometrics 60, 146-153), studied the maximum bias over all possible selection functions which satisfy the weak condition that large studies (small sigma) are as likely, or more likely, to be selected than small studies (large sigma). This led to a worst-case sensitivity analysis, controlling for the overall fraction of studies selected. However, no account was taken of the effect of selection on the uncertainty in estimation. This article extends the previous work by finding corresponding confidence intervals and P-values, and hence a new sensitivity analysis for publication bias. Two examples are discussed.     

Index versus tandem selection after repeated generations of selection

Summary A theoretical comparison between two multiple-trait selection methods, index and tandem selection, after several generations of selection was carried out. An infinite number of loci determining the traits, directional and truncation selection, discrete generations and infinite population size were assumed. Under these assumptions, changes in genetic parameters over generations are due to linkage disequilibrium generated by selection. Changes continue for several generations until equilibrium is approached. Algebraic expressions for asymptotic responses from index selection can be derived if index weights are maintained constant across generations. Expressions at equilibrium for genetic parameters and responses are given for the index and its component traits. The loss in response by using initial index weights throughout all generations, instead of updating them to account for changes in genetic parameters, was analyzed. The benefit of using optimum weights was very small ranging from 0% to about 1.5% for all cases studied. Recurrence formulae to predict genetic parameters and responses at each generation of selection are given for both index and tandem selection. A comparison between expected response in the aggregate genotype at equilibrium from index and tandem selection is made considering two traits of economic importance. The results indicate that although index selection is more efficient for improving the aggregate breeding value, its relative efficiency with respect to tandem selection decreases after repeated cycles of selection. The reduction in relative efficiency is highest with the highest selection intensity and heritabilities and with negative correlations between the two traits. The advantage of index over tandem selection might be further reduced if changes in genetic parameters due to gene frequency changes produced by selection, random fluctuations due to the finite size of the population, and errors in estimation of parameters, were also considered.     

Effects of random and non-random errors on phenotypic selection in autotetraploids

Summary A theoretical investigation was made to ascertain the effects of random and non-random deviations, called errors, of phenotypic from genotypic values on population means and on the response to phenotypic recurrent selection. The study was motivated as a selection experiment for disease resistance where there was either variability in the inoculation or environment (the random errors) or where the inoculation was above or below the the optimum rate where genetic differences in resistance are maximized (the non-random errors). The study was limited to the genetics at a diallelic locus (alleles B and b) in an autotetraploid population in random mating equilibrium. The response to selection was measured as the covariance of selection and compared to the exact covariance which was the covariance of selection without errors in phenotype. The random errors were modeled by assuming that a given percentage () of the population was uniformly distributed among the five possible genotype classes independent of their true genotypes. This model was analyzed numerically for a theoretical population with the frequency of the B allele (p) ranging from 0.0 to 1.0 and assumed errors of=0.1 and 0.5 for the following six types of genic action of the B allele: additive, monoplex dominance, partial monoplex dominance, duplex dominance, partial duplex dominance, and recessive. The effect of random error was to consistently reduce the response to selection by a percentage independent of the type of genic action at the locus. The effect on the population mean was an upward bias when p was low and a downward bias when p approached unity. In the non-random error model below optimum inoculations altered the phenotypes by systematically including percentage of susceptible genotypes into one or more other genotype classes with more genetic resistance (a positive shift). With above optimum inoculations, some resistant genotypes are classed with the non-resistant genotypes (a negative shift). The effects on the covariance of selection were found by numerical analysis for the same types of genic action and's as investigated for random error. With a negative shift and a low p, the covariance of selection was always reduced, but for an increasing p the covariance approached and exceeded the exact covariance for all types of genic action except additive. With a positive shift and a low p, response to selection was greatly improved for three types of genic action: duplex dominance, partial duplex dominance, and recessive. The effect of a non-random error on population means was to greatly bias the means upwards for a low p and positive shift, but with increasing p the bias decreased. A relatively slight decrease in the mean occurred with a negative shift. This study indicated check varieties commonly used to monitor selection pressures in screening programs are very responsive to positive non-random shifts, but are relatively unresponsive to negative shifts. The interaction of selection pressure, types of genic action, and genotypes in the class shift models was suggested as a partial explanation for the lack of response to increasing selection pressures observed in some breeding programs.Cooperative investigations of the Alfalfa Production Research Unit, United States Department of Agriculture, Agricultural Research Service, and the Nevada Agricultural Experiment Station, Reno, Nevada. Paper No. 404 Scientific Journal Series. Nevada Agricultural Experiment Station     

Sensitivity analysis for the assessment of causal vaccine effects on viral load in HIV vaccine trials

Vaccines with limited ability to prevent HIV infection may positively impact the HIV/AIDS pandemic by preventing secondary transmission and disease in vaccine recipients who become infected. To evaluate the impact of vaccination on secondary transmission and disease, efficacy trials assess vaccine effects on HIV viral load and other surrogate endpoints measured after infection. A standard test that compares the distribution of viral load between the infected subgroups of vaccine and placebo recipients does not assess a causal effect of vaccine, because the comparison groups are selected after randomization. To address this problem, we formulate clinically relevant causal estimands using the principal stratification framework developed by Frangakis and Rubin (2002, Biometrics 58, 21-29), and propose a class of logistic selection bias models whose members identify the estimands. Given a selection model in the class, procedures are developed for testing and estimation of the causal effect of vaccination on viral load in the principal stratum of subjects who would be infected regardless of randomization assignment. We show how the procedures can be used for a sensitivity analysis that quantifies how the causal effect of vaccination varies with the presumed magnitude of selection bias.     

ESTIMATING UNCERTAINTY IN MULTIVARIATE RESPONSES TO SELECTION

Predicting the responses to natural selection is one of the key goals of evolutionary biology. Two of the challenges in fulfilling this goal have been the realization that many estimates of natural selection might be highly biased by environmentally induced covariances between traits and fitness, and that many estimated responses to selection do not incorporate or report uncertainty in the estimates. Here we describe the application of a framework that blends the merits of the Robertson–Price Identity approach and the multivariate breeder's equation to address these challenges. The approach allows genetic covariance matrices, selection differentials, selection gradients, and responses to selection to be estimated without environmentally induced bias, direct and indirect selection and responses to selection to be distinguished, and if implemented in a Bayesian‐MCMC framework, statistically robust estimates of uncertainty on all of these parameters to be made. We illustrate our approach with a worked example of previously published data. More generally, we suggest that applying both the Robertson–Price Identity and the multivariate breeder's equation will facilitate hypothesis testing about natural selection, genetic constraints, and evolutionary responses.     

Integrating fossil preservation biases in the selection of calibrations for molecular divergence time estimation

The selection of fossil data to use as calibration age priors in molecular divergence time estimates inherently links neontological methods with paleontological theory. However, few neontological studies have taken into account the possibility of a taphonomic bias in the fossil record when developing approaches to fossil calibration selection. The Sppil-Rongis effect may bias the first appearance of a lineage toward the recent causing most objective calibration selection approaches to erroneously exclude appropriate calibrations or to incorporate multiple calibrations that are too young to accurately represent the divergence times of target lineages. Using turtles as a case study, we develop a Bayesian extension to the fossil selection approach developed by Marshall (2008. A simple method for bracketing absolute divergence times on molecular phylogenies using multiple fossil calibrations points. Am. Nat. 171:726-742) that takes into account this taphonomic bias. Our method has the advantage of identifying calibrations that may bias age estimates to be too recent while incorporating uncertainty in phylogenetic parameter estimates such as tree topology and branch lengths. Additionally, this method is easily adapted to assess the consistency of potential calibrations to any one calibration in the candidate pool.     

Simple methods for the estimation and sensitivity analysis of principal strata effects using marginal structural models: Application to a bone fracture prevention trial

In randomized clinical trials, it is often of interest to estimate the effect of treatment on quality of life (QOL), in addition to those on the event itself. When an event occurs in some patients prior to QOL score assessment, investigators may compare QOL scores between patient subgroups defined by the event after randomization. However, owing to postrandomization selection bias, this analysis can mislead investigators about treatment efficacy and result in paradoxical findings. The recent Japanese Osteoporosis Intervention Trial (JOINT‐02), which compared the benefits of a combination therapy for fracture prevention with those of a monotherapy, exemplifies the case in point; the average QOL score was higher in the combination therapy arm for the unfractured subgroup but was lower for the fractured subgroup. To address this issue, principal strata effects (PSEs), which are treatment effects estimated within subgroups of individuals stratified by potential intermediate variable, have been discussed in the literature. In this paper, we describe a simple procedure for estimating the PSEs using marginal structural models. This procedure utilizes SAS code for the estimation. In addition, we present a simple sensitivity analysis method for examining the resulting estimates. The analyses of JOINT‐02 data using these methods revealed that QOL scores were higher in the combination therapy arm than in the monotherapy arm for both subgroups.     

New insights into the interplay between codon bias determinants in plants

Codon bias is the non-random use of synonymous codons, a phenomenon that has been observed in species as diverse as bacteria, plants and mammals. The preferential use of particular synonymous codons may reflect neutral mechanisms (e.g. mutational bias, G|C-biased gene conversion, genetic drift) and/or selection for mRNA stability, translational efficiency and accuracy. The extent to which these different factors influence codon usage is unknown, so we dissected the contribution of mutational bias and selection towards codon bias in genes from 15 eudicots, 4 monocots and 2 mosses. We analysed the frequency of mononucleotides, dinucleotides and trinucleotides and investigated whether the compositional genomic background could account for the observed codon usage profiles. Neutral forces such as mutational pressure and G|C-biased gene conversion appeared to underlie most of the observed codon bias, although there was also evidence for the selection of optimal translational efficiency and mRNA folding. Our data confirmed the compositional differences between monocots and dicots, with the former featuring in general a lower background compositional bias but a higher overall codon bias.     

Matched Case—Control Data Analysis with Selection Bias

Case-control studies offer a rapid and efficient way to evaluate hypotheses. On the other hand, proper selection of the controls is challenging, and the potential for selection bias is a major weakness. Valid inferences about parameters of interest cannot be drawn if selection bias exists. Furthermore, the selection bias is difficult to evaluate. Even in situations where selection bias can be estimated, few methods are available. In the matched case-control Northern Manhattan Stroke Study (NOMASS), stroke-free controls are sampled in two stages. First, a telephone survey ascertains demographic and exposure status from a large random sample. Then, in an in-person interview, detailed information is collected for the selected controls to be used in a matched case-control study. The telephone survey data provides information about the selection probability and the potential selection bias. In this article, we propose bias-corrected estimators in a case-control study using a joint estimating equation approach. The proposed bias-corrected estimate and its standard error can be easily obtained by standard statistical software.     

Bayesian models of eye movement selection with retinotopic maps

Among the various possible criteria guiding eye movement selection, we investigate the role of position uncertainty in the peripheral visual field. In particular, we suggest that, in everyday life situations of object tracking, eye movement selection probably includes a principle of reduction of uncertainty. To evaluate this hypothesis, we confront the movement predictions of computational models with human results from a psychophysical task. This task is a freely moving eye version of the multiple object tracking task, where the eye movements may be used to compensate for low peripheral resolution. We design several Bayesian models of eye movement selection with increasing complexity, whose layered structures are inspired by the neurobiology of the brain areas implied in this process. Finally, we compare the relative performances of these models with regard to the prediction of the recorded human movements, and show the advantage of taking explicitly into account uncertainty for the prediction of eye movements.     

Potential for improvement by selection for reducing sugar content after cold storage for three potato populations

The objectives of this study were to examine the expected response to selection for reducing-sugar content after cold storage in three hybrid populations, to determine whether these populations included clones low in reducing sugars, and to investigate the effectiveness of indirect selection for chip colour based on selection of sugar content after cold storage. The three hybrid populations included: a random sample of 39 clones of Population 1, which was derived from crossing ND860-2 (a clone low in reducing sugars) with F58089 (a clone intermediate in reducing sugars); 40 clones of Population 2, which was obtained from crossing ND860-2 with Russette (a clone high in reducing sugars); and 40 clones of Population 3, which was derived from crossing Russette with F58089. Sugar content and chip colour were assessed in tubers stored for 2 months at 4 °C at Cambridge, Ontario, and at 3 °C at Benton Ridge, New Brunswick. Population 1 had a slightly greater predicted response to selection for reduction in glucose and total reducing sugars than the other two populations. This could be attributed to higher heritability estimates for Population 1, which was a reflection of smaller clone × environment interaction mean squares. The greater potential advance by selection for fructose, glucose, and total reducing sugars, was a direct consequence of its lower means for these traits. Low reducing-sugar clones were found in all three populations, indicating their potential use for the selection of low reducing sugars. Populations 2 and 3, however, would require stronger selection pressures and, therefore, large population sizes. Expected correlated responses for chip colour by selection for fructose and glucose were similar to, and sometimes exceeded, the expected direct responses in all three populations. Indirect responses for chip colour by selection for sucrose, however, were lower than direct selection responses. These results indicate that indirect selection for chip colour, by selection for either fructose or glucose content after cold storage, is as effective as direct selection for chip colour.     

Natural selection. III. Selection versus transmission and the levels of selection

George Williams defined an evolutionary unit as hereditary information for which the selection bias between competing units dominates the informational decay caused by imperfect transmission. In this article, I extend Williams' approach to show that the ratio of selection bias to transmission bias provides a unifying framework for diverse biological problems. Specific examples include Haldane and Lande's mutation-selection balance, Eigen's error threshold and quasispecies, Van Valen's clade selection, Price's multilevel formulation of group selection, Szathmáry and Demeter's evolutionary origin of primitive cells, Levin and Bull's short-sighted evolution of HIV virulence, Frank's timescale analysis of microbial metabolism and Maynard Smith and Szathmáry's major transitions in evolution. The insights from these diverse applications lead to a deeper understanding of kin selection, group selection, multilevel evolutionary analysis and the philosophical problems of evolutionary units and individuality.     

The conflict between natural and artificial selection in finite populations

Summary A single locus model of the interaction between natural selection and artificial selection for a quantitative character in a finite population, assuming heterozygote superiority in natural fitness but additive action on the character, has been studied using transition probability matrices.If natural selection is strong enough to create a selection plateau in which genetic variance declines relatively slowly, then the total response to artificial selection prior to the plateau will be much less than that expected in the absence of natural selection, and the half-life of response will be shorter. Such a plateau is likely to have a large proportion, if not all, of the original genetic variance still present. In selection programmes using laboratory animals, it seems likely that the homozygote favoured by artificial selection must be very unfit before such a plateau will occur. A significant decrease in population fitness as a result of artificial selection does not necessarily imply that the metric character is an important adaptive character.These implications of this model of natural selection are very similar to those derived by James (1962) for the optimum model of natural selection. In fact, there seems to be no aspect of the observable response to artificial selection that would enable anyone to distinguish between these two models of natural selection.     

An approximate method for optimum independent culling level selection for n stages of selection with explicit solutions

Summary An approximate method with explicit solutions to apply independent culling levels for multiple traits in n-stages of selection was developed. An approximate solution was found for sequentially selected traits. Two assumptions were necessary. The first was to assume that subsequent selection would not appreciably change the mean of traits already selected, and the second was to approximate the variance of a correlated trait in a selected population with an upward biased projection. The procedure was shown to give near optimal results regardless of selection intensity or genetic correlations if phenotypic correlations among traits were low. The procedure gave poor results only for certain sequences of selection when phenotypic correlations were high. However, in those cases good results were obtained using a different sequence of selection. With high correlations, the procedure is recommended only after comparing solutions and expected genetic gain for all sequences of selection. If the expected aggregate gain for the sequence of selection desired is less than that of another order, culling points associated with the optimal ordering must be determined. Genetic gain from use of culling points is independent of order of selection. The procedure is recommended for use with computer programs that attempt to find optimal culling points to reduce computational time and to check results.Journal Paper No. 12448 of the Purdue University Agricultural Experiment Station     

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

长期指数选择的遗传效果分析—计算机模拟研究

本文利用Monte Carlo模拟技术研究比较了普通选择指数、实际选择指数、约束指数和单性状选择四种方法的长期选择效果及对群体遗传结构的影响。50世代的结果表明:群体大小和遗传参数能明显影响长期指数选择的反应;实际指数选择是有效的,其总体效果好于普通指数;约束选择的早期反应虽低于普通指数,但后期效果好,而且对群体遗传结构影响较小。同时,指数选择使性状加性遗传方差和遗传力衰减变化,而遗传相关依指数公式的系数呈定向改变。建议多性状长期选择时应用实际指数法或约束指数法。     

Mate selection by selection index theory

Summary Mate selection by selection index prediction of total merit in expected progeny is proposed as a rational basis for making recommendations in the choice of a bull to which a cow may be mated. Growth in USA of service programs recommending bulls to particular cows has motivated the need to rationalize mate selection processes. This paper illustrates that mate selection on the basis of highest index value for expected progeny among potential mates can justify special mate selection programs, when a nonlinear relationship exists between at least one trait in the index and merit.Contribution while on leave to Department Animal Breeding, Agricultural Research Institute of Republic of Ireland and partial support from Senior Fulbright-Hays Research Grant.Approved as Journal Article 180-79 of the Ohio Agricultural Research & Development Center, Wooster 44691     

Behavioral and neural Darwinism: Selectionist function and mechanism in adaptive behavior dynamics

An evolutionary theory of behavior dynamics and a theory of neuronal group selection share a common selectionist framework. The theory of behavior dynamics instantiates abstractly the idea that behavior is selected by its consequences. It implements Darwinian principles of selection, reproduction, and mutation to generate adaptive behavior in virtual organisms. The behavior generated by the theory has been shown to be quantitatively indistinguishable from that of live organisms. The theory of neuronal group selection suggests a mechanism whereby the abstract principles of the evolutionary theory may be implemented in the nervous systems of biological organisms. According to this theory, groups of neurons subserving behavior may be selected by synaptic modifications that occur when the consequences of behavior activate value systems in the brain. Together, these theories constitute a framework for a comprehensive account of adaptive behavior that extends from brain function to the behavior of whole organisms in quantitative detail.     

An exploration of fixed and random effects selection for longitudinal binary outcomes in the presence of nonignorable dropout

We explore a Bayesian approach to selection of variables that represent fixed and random effects in modeling of longitudinal binary outcomes with missing data caused by dropouts. We show via analytic results for a simple example that nonignorable missing data lead to biased parameter estimates. This bias results in selection of wrong effects asymptotically, which we can confirm via simulations for more complex settings. By jointly modeling the longitudinal binary data with the dropout process that possibly leads to nonignorable missing data, we are able to correct the bias in estimation and selection. Mixture priors with a point mass at zero are used to facilitate variable selection. We illustrate the proposed approach using a clinical trial for acute ischemic stroke.