Environmental and other factors influencing fertility in Sri Lanka

The study utilizes the complete tabulations from the 1971 census and data from the Registrar General's and Meteorological departments for the same year. It applies a multiple regression analysis of the total fertility rate for each district for 1971 on a series of environmental variables. These include the proportion of the rural population by district to the all-island rural population; the district mean annual rainfall and the proportion of the district population employed in the major rural occupations to the total employed. To these 3 environmental variables were added 2 socioeconomic variables: the proportion of the population aged 10+ years and who are literate, and infant mortality. Results indicate that the 5 independent variables are clearly intercorrelated. The multiple regression analysis shows that the 5 variables together account for 76.4% of the total variation in district total fertility rate. It is argued that this and other studies undertaken previously provide useful pointers to the type of variable to be considered in any policy aimed at population control and indicate where major efforts should be directed.     

Genetic steady-state under BLUP selection for an infinite and homogeneous population with discrete generations

A matrix derivation is proposed to analytically calculate the asymptotic genetic variance-covariance matrix under BLUP selection according to the initial genetic parameters in a large population with discrete generations. The asymptotic genetic evolution of a homogeneous population with discrete generations is calculated for a selection operating on an index including all information (pedigree and records) from a non-inbred and unselected base population (BLUP selection) or on an index restricted to records of a few ancestral generations. Under the first hypothesis, the prediction error variance of the selection index is independent of selection and is calculated from the genetic parameters of the base population. Under the second hypothesis, the prediction error variance depends on selection. Furthermore, records of several generations of ancestors of the candidates for selection must be used to maintain a constant prediction error variance over time. The number of ancestral generations needed depends on the population structure and on the occurrence of fixed effects. Without fixed effects to estimate, accounting for two generations of ancestors is sufficient to estimate the asymptotic prediction error variance. The amassing of information from an unselected base population proves to be important in order not to overestimate the asymptotic genetic gains and not to underestimate the asymptotic genetic variances.     

Survival Analysis with Error‐Prone Time‐Varying Covariates: A Risk Set Calibration Approach

Summary Occupational, environmental, and nutritional epidemiologists are often interested in estimating the prospective effect of time‐varying exposure variables such as cumulative exposure or cumulative updated average exposure, in relation to chronic disease endpoints such as cancer incidence and mortality. From exposure validation studies, it is apparent that many of the variables of interest are measured with moderate to substantial error. Although the ordinary regression calibration (ORC) approach is approximately valid and efficient for measurement error correction of relative risk estimates from the Cox model with time‐independent point exposures when the disease is rare, it is not adaptable for use with time‐varying exposures. By recalibrating the measurement error model within each risk set, a risk set regression calibration (RRC) method is proposed for this setting. An algorithm for a bias‐corrected point estimate of the relative risk using an RRC approach is presented, followed by the derivation of an estimate of its variance, resulting in a sandwich estimator. Emphasis is on methods applicable to the main study/external validation study design, which arises in important applications. Simulation studies under several assumptions about the error model were carried out, which demonstrated the validity and efficiency of the method in finite samples. The method was applied to a study of diet and cancer from Harvard's Health Professionals Follow‐up Study (HPFS).     

Design and analysis of multiple choice feeding preference data

Traditional analyses of feeding experiments that test consumer preference for an array of foods suffer from several defects. We have modified the experimental design to incorporate into a multivariate analysis the variance due to autogenic change in control replicates. Our design allows the multiple foods to be physically paired with their control counterparts. This physical proximity of the multiple food choices in control/experimental pairs ensures that the variance attributable to external environmental factors jointly affects all combinations within each replicate. Our variance term, therefore, is not a contrived estimate as is the case for the random pairing strategy proposed by previous studies. The statistical analysis then proceeds using standard multivariate statistical tests. We conducted a multiple choice feeding experiment using our experimental design and utilized a Monte Carlo analysis to compare our results with those obtained from an experimental design that employed the random pairing strategy. Our experimental design allowed detection of moderate differences among feeding means when the random design did not.     

Correcting for measurement error in individual ancestry estimates in structured association tests

We present theoretical explanations and show through simulation that the individual admixture proportion estimates obtained by using ancestry informative markers should be seen as an error-contaminated measurement of the underlying individual ancestry proportion. These estimates can be used in structured association tests as a control variable to limit type I error inflation or reduce loss of power due to population stratification observed in studies of admixed populations. However, the inclusion of such error-containing variables as covariates in regression models can bias parameter estimates and reduce ability to control for the confounding effect of admixture in genetic association tests. Measurement error correction methods offer a way to overcome this problem but require an a priori estimate of the measurement error variance. We show how an upper bound of this variance can be obtained, present four measurement error correction methods that are applicable to this problem, and conduct a simulation study to compare their utility in the case where the admixed population results from the intermating between two ancestral populations. Our results show that the quadratic measurement error correction (QMEC) method performs better than the other methods and maintains the type I error to its nominal level.     

Multiple outputation: inference for complex clustered data by averaging analyses from independent data

This article applies a simple method for settings where one has clustered data, but statistical methods are only available for independent data. We assume the statistical method provides us with a normally distributed estimate, theta, and an estimate of its variance sigma. We randomly select a data point from each cluster and apply our statistical method to this independent data. We repeat this multiple times, and use the average of the associated theta's as our estimate. An estimate of the variance is given by the average of the sigma2's minus the sample variance of the theta's. We call this procedure multiple outputation, as all "excess" data within each cluster is thrown out multiple times. Hoffman, Sen, and Weinberg (2001, Biometrika 88, 1121-1134) introduced this approach for generalized linear models when the cluster size is related to outcome. In this article, we demonstrate the broad applicability of the approach. Applications to angular data, p-values, vector parameters, Bayesian inference, genetics data, and random cluster sizes are discussed. In addition, asymptotic normality of estimates based on all possible outputations, as well as a finite number of outputations, is proven given weak conditions. Multiple outputation provides a simple and broadly applicable method for analyzing clustered data. It is especially suited to settings where methods for clustered data are impractical, but can also be applied generally as a quick and simple tool.     

LOGISTIC REGRESSION FOR EMPIRICAL STUDIES OF MULTIVARIATE SELECTION

Understanding the mechanics of adaptive evolution requires not only knowing the quantitative genetic bases of the traits of interest but also obtaining accurate measures of the strengths and modes of selection acting on these traits. Most recent empirical studies of multivariate selection have employed multiple linear regression to obtain estimates of the strength of selection. We reconsider the motivation for this approach, paying special attention to the effects of nonnormal traits and fitness measures. We apply an alternative statistical method, logistic regression, to estimate the strength of selection on multiple phenotypic traits. First, we argue that the logistic regression model is more suitable than linear regression for analyzing data from selection studies with dichotomous fitness outcomes. Subsequently, we show that estimates of selection obtained from the logistic regression analyses can be transformed easily to values that directly plug into equations describing adaptive microevolutionary change. Finally, we apply this methodology to two published datasets to demonstrate its utility. Because most statistical packages now provide options to conduct logistic regression analyses, we suggest that this approach should be widely adopted as an analytical tool for empirical studies of multivariate selection.     

An efficient multivariate approach for estimating preference when individual observations are dependent

1. We discuss aspects of resource selection based on observing a given vector of resource variables for different individuals at discrete time steps. A new technique for estimating preference of habitat characteristics, applicable when there are multiple individual observations, is proposed. 2. We first show how to estimate preference on the population and individual level when only a single site- or resource component is observed. A variance component model based on normal scores in used to estimate mean preference for the population as well as the heterogeneity among individuals defined by the intra-class correlation. 3. Next, a general technique is proposed for time series of observations of a vector with several components, correcting for the effect of correlations between these. The preference of each single component is analyzed under the assumption of arbitrarily complex selection of the other components. This approach is based on the theory for conditional distributions in the multi-normal model. 4. The method is demonstrated using a data set of radio-tagged dispersing juvenile goshawks and their site characteristics, and can be used as a general tool in resource or habitat selection analysis.     

False Discovery Rates in PET and CT Studies with Texture Features: A Systematic Review

PurposeA number of recent publications have proposed that a family of image-derived indices, called texture features, can predict clinical outcome in patients with cancer. However, the investigation of multiple indices on a single data set can lead to significant inflation of type-I errors. We report a systematic review of the type-I error inflation in such studies and review the evidence regarding associations between patient outcome and texture features derived from positron emission tomography (PET) or computed tomography (CT) images.MethodsFor study identification PubMed and Scopus were searched (1/2000–9/2013) using combinations of the keywords texture, prognostic, predictive and cancer. Studies were divided into three categories according to the sources of the type-I error inflation and the use or not of an independent validation dataset. For each study, the true type-I error probability and the adjusted level of significance were estimated using the optimum cut-off approach correction, and the Benjamini-Hochberg method. To demonstrate explicitly the variable selection bias in these studies, we re-analyzed data from one of the published studies, but using 100 random variables substituted for the original image-derived indices. The significance of the random variables as potential predictors of outcome was examined using the analysis methods used in the identified studies.ResultsFifteen studies were identified. After applying appropriate statistical corrections, an average type-I error probability of 76% (range: 34–99%) was estimated with the majority of published results not reaching statistical significance. Only 3/15 studies used a validation dataset. For the 100 random variables examined, 10% proved to be significant predictors of survival when subjected to ROC and multiple hypothesis testing analysis.ConclusionsWe found insufficient evidence to support a relationship between PET or CT texture features and patient survival. Further fit for purpose validation of these image-derived biomarkers should be supported by appropriate biological and statistical evidence before their association with patient outcome is investigated in prospective studies.     

A comparison of methods to partition selection acting via components of fitness: Do larger male bullfrogs have greater hatching success?

We contrast three methods for measuring selection at sequential fitness components (here called the additive, changing variance, and independent methods). The independent method (Koenig and Albano, 1987; Conner, 1988) describes the relationship between a phenotypic character and one fitness component independent of other components. This method is appropriate when the question is whether or not a character has fitness consequences independent of selection at other stages. The additive (Arnold and Wade, 1984a) and changing variance (Kalisz, 1986; Koenig and Albano, 1987) methods measure selection via one component of fitness, taking into consideration constraints imposed by selection via earlier components in the sequence. These methods therefore more accurately track selection over a sequence of fitness components. Of these latter two methods, the changing variance method yields erratic results in simulation studies and is not recommended in its unmodified form. The additive method (equivalent to the changing variance method weighted as described in Wade and Kalisz [1989]) explicitly partitions selection into additive components and is useful for measuring selection taking into account the constraints imposed by selection acting via prior fitness components. The methods often yield very different estimates of the relative degree to which the mean of a character is changed by selection acting via a particular component of fitness (the “strength” of selection). However, neither the additive nor independent method is inherently superior to the other; rather, these measures are complementary.     

Statistical approaches to interpreting diversity patterns in the Norwegian mountain flora

The richness of Norwegian mountain plants in 75 grid squares is mapped from published distributional data for 109 species. Eleven explanatory variables representing bedrock geology, geography and topography, climate, and history (relative abundance of unglaciated areas) Tor each square are used in multiple regression analysis with associated Monte Carlo permutation tests to find statistically significant predictor variables for species richness. The variance in richness explained by the four major groups or explanatory variables is established by (partial) multiple regression analysis in which the groups of predictors are entered in different orders. The variance in species richness explained by the predictor variables is partitioned into four independent components. A predictive model for species richness using partial least squares regression and all explanatory variables has a coefficient of determination (R²) of 0.79. The statistical results consistently show that species-richness patterns are well explained by modern-day factors such as climate, geology, elevation, and geography without recourse to historical variables. The nunatak hypothesis of plant survival on unglaciated areas within Norway does not explain the observed richness patterns when modern ecological factors are considered first. The nunatak hypothesis thus appears to be redundant, a view supported by recent palaeobotanical. biosystematical, and evolutionary studies.     

Estimate of within population incremental selection through branch imbalance in lineage trees

Incremental selection within a population, defined as limited fitness changes following mutation, is an important aspect of many evolutionary processes. Strongly advantageous or deleterious mutations are detected using the synonymous to non-synonymous mutations ratio. However, there are currently no precise methods to estimate incremental selection. We here provide for the first time such a detailed method and show its precision in multiple cases of micro-evolution. The proposed method is a novel mixed lineage tree/sequence based method to detect within population selection as defined by the effect of mutations on the average number of offspring. Specifically, we propose to measure the log of the ratio between the number of leaves in lineage trees branches following synonymous and non-synonymous mutations. The method requires a high enough number of sequences, and a large enough number of independent mutations. It assumes that all mutations are independent events. It does not require of a baseline model and is practically not affected by sampling biases. We show the method''s wide applicability by testing it on multiple cases of micro-evolution. We show that it can detect genes and inter-genic regions using the selection rate and detect selection pressures in viral proteins and in the immune response to pathogens.     

Mixed effects logistic regression models for multiple longitudinal binary functional limitation responses with informative drop-out and confounding by baseline outcomes

In the context of analyzing multiple functional limitation responses collected longitudinally from the Longitudinal Study of Aging (LSOA), we investigate the heterogeneity of these outcomes with respect to their associations with previous functional status and other risk factors in the presence of informative drop-out and confounding by baseline outcomes. We accommodate the longitudinal nature of the multiple outcomes with a unique extension of the nested random effects logistic model with an autoregressive structure to include drop-out and baseline outcome components with shared random effects. Estimation of fixed effects and variance components is by maximum likelihood with numerical integration. This shared parameter selection model assumes that drop-out is conditionally independent of the multiple functional limitation outcomes given the underlying random effect representing an individual's trajectory of functional status across time. Whereas it is not possible to fully assess the adequacy of this assumption, we assess the robustness of this approach by varying the assumptions underlying the proposed model such as the random effects structure, the drop-out component, and omission of baseline functional outcomes as dependent variables in the model. Heterogeneity among the associations between each functional limitation outcome and a set of risk factors for functional limitation, such as previous functional limitation and physical activity, exists for the LSOA data of interest. Less heterogeneity is observed among the estimates of time-level random effects variance components that are allowed to vary across functional outcomes and time. We also note that. under an autoregressive structure, bias results from omitting the baseline outcome component linked to the follow-up outcome component by subject-level random effects.     

Fixed and random effects selection in linear and logistic models

We address the problem of selecting which variables should be included in the fixed and random components of logistic mixed effects models for correlated data. A fully Bayesian variable selection is implemented using a stochastic search Gibbs sampler to estimate the exact model-averaged posterior distribution. This approach automatically identifies subsets of predictors having nonzero fixed effect coefficients or nonzero random effects variance, while allowing uncertainty in the model selection process. Default priors are proposed for the variance components and an efficient parameter expansion Gibbs sampler is developed for posterior computation. The approach is illustrated using simulated data and an epidemiologic example.     

Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion.

We describe an approximate method for the analysis of quantitative trait loci (QTL) based on model selection from multiple regression models with trait values regressed on marker genotypes, using a modification of the easily calculated Bayesian information criterion to estimate the posterior probability of models with various subsets of markers as variables. The BIC-delta criterion, with the parameter delta increasing the penalty for additional variables in a model, is further modified to incorporate prior information, and missing values are handled by multiple imputation. Marginal probabilities for model sizes are calculated, and the posterior probability of nonzero model size is interpreted as the posterior probability of existence of a QTL linked to one or more markers. The method is demonstrated on analysis of associations between wood density and markers on two linkage groups in Pinus radiata. Selection bias, which is the bias that results from using the same data to both select the variables in a model and estimate the coefficients, is shown to be a problem for commonly used non-Bayesian methods for QTL mapping, which do not average over alternative possible models that are consistent with the data.     

Bayesian Variable Selection with Joint Modeling of Categorical and Survival Outcomes: An Application to Individualizing Chemotherapy Treatment in Advanced Colorectal Cancer

Summary Colorectal cancer is the second leading cause of cancer related deaths in the United States, with more than 130,000 new cases of colorectal cancer diagnosed each year. Clinical studies have shown that genetic alterations lead to different responses to the same treatment, despite the morphologic similarities of tumors. A molecular test prior to treatment could help in determining an optimal treatment for a patient with regard to both toxicity and efficacy. This article introduces a statistical method appropriate for predicting and comparing multiple endpoints given different treatment options and molecular profiles of an individual. A latent variable‐based multivariate regression model with structured variance covariance matrix is considered here. The latent variables account for the correlated nature of multiple endpoints and accommodate the fact that some clinical endpoints are categorical variables and others are censored variables. The mixture normal hierarchical structure admits a natural variable selection rule. Inference was conducted using the posterior distribution sampling Markov chain Monte Carlo method. We analyzed the finite‐sample properties of the proposed method using simulation studies. The application to the advanced colorectal cancer study revealed associations between multiple endpoints and particular biomarkers, demonstrating the potential of individualizing treatment based on genetic profiles.     

Analysis of covariance in parallel-group clinical trials with pretreatment baselines

Analysis of covariance (ANCOVA) techniques are often employed in the analysis of clinical trials to try to account for the effects of varying pretreatment baseline values of an outcome variable on posttreatment measurements of the same variable. Baseline measurements of outcome variables are typically random variables, which violates the usual ANCOVA assumption that covariate values are fixed. Therefore, the usual ANCOVA hypothesis tests of treatment effects may be invalid, and the ANCOVA slope parameter estimator biased, for this application. We show, however, that if the pretreatment - posttreatment measurements have a bivariate normal distribution, then (i) the ANCOVA model with residual error independent of the covariate is a valid expression of the relationship between pretreatment and posttreatment measurements; (ii) the usual (fixed-covariate analysis) ANCOVA estimates of the slope parameter and treatment effect contrasts are unbiased; and (iii) the usual ANCOVA treatment effect contrast t-tests are valid significance tests for treatment effects. Moreover, as long as the magnitudes of the treatment effects do not depend on the "true" pretreatment value of the outcome variable, the true slope parameter must lie in the interval (0, 1) and the ANCOVA model has a clear interpretation as an adjustment (based on between- and within-subject variability) to an analysis of variance model applied to the posttreatment-pretreatment differences.     

Recombination, balancing selection and phylogenies in MHC and self-incompatibility genes.

Using a coalescent model of multiallelic balancing selection with recombination, the genealogical process as a function of recombinational distance from a site under selection is investigated. We find that the shape of the phylogenetic tree is independent of the distance to the site under selection. Only the timescale changes from the value predicted by Takahata's allelic genealogy at the site under selection, converging with increasing recombination to the timescale of the neutral coalescent. However, if nucleotide sequences are simulated over a recombining region containing a site under balancing selection, a phylogenetic tree constructed while ignoring such recombination is strongly affected. This is true even for small rates of recombination. Published studies of multiallelic balancing selection, i.e., the major histocompatibility complex (MHC) of vertebrates, gametophytic and sporophytic self-incompatibility of plants, and incompatibility of fungi, all observe allelic genealogies with unexpected shapes. We conclude that small absolute levels of recombination are compatible with these observed distortions of the shape of the allelic genealogy, suggesting a possible cause of these observations. Furthermore, we illustrate that the variance in the coalescent with recombination process makes it difficult to locate sites under selection and to estimate the selection coefficient from levels of variability.     

Lack of nonadditive genetic effects on early fecundity in Drosophila melanogaster

Fecundity is usually considered as a trait closely connected to fitness and is expected to exhibit substantial nonadditive genetic variation and inbreeding depression. However, two independent experiments, using populations of different geographical origin, indicate that early fecundity in Drosophila melanogaster behaves as a typical additive trait of low heritability. The first experiment involved artificial selection in inbred and non-inbred lines, all of them started from a common base population previously maintained in the laboratory for about 35 generations. The realized heritability estimate was 0.151 +/- 0.075 and the inbreeding depression was very small and nonsignificant (0.09 +/- 0.09% of the non-inbred mean per 1% increase in inbreeding coefficient). With inbreeding, the observed decrease in the within-line additive genetic variance and the corresponding increase of the between-line variance were very close to their expected values for pure additive gene action. This result is at odds with previous studies showing inbreeding depression and, therefore, directional dominance for the same trait and species. All experiments, however, used laboratory populations, and it is possible that the original genetic architecture of the trait in nature was subsequently altered by the joint action of random drift and adaptation to captivity. Thus, we carried out a second experiment, involving inbreeding without artificial selection in a population recently collected from the wild. In this case we obtained, again, a maximum-likelihood heritability estimate of 0.210 +/- 0.027 and very little nonsignificant inbreeding depression (0.06 +/- 0.12%). The results suggest that, for fitness-component traits, low levels of additive genetic variance are not necessarily associated with large inbreeding depression or high levels of nonadditive genetic variance.     

Genetic and phenotypic correlations in a natural population of song sparrows

We estimated heritabilities, and genetic and phenotypic correlations between beak and body traits in the song sparrow ( Melospiza melodia ). We compared these estimates to values for the same traits in the Galápagos finches, Geospiza (Boag, 1983; Grant, 1983). Morphological variance is low in the song sparrow, and our results show that genetic and phenotypic correlations are considerably lower than correlations in the morphologically more variable Geospiza. Comparison using a larger sample of Galapagos populations confirms the existence of an association between variance and correlation for phenotypic values. We suggest two possible explanations for this association. First, most traits studied are functionally related, and the joint evolution of variance and correlation may have resulted from stabilizing selection about a line of optimal allometry between traits. Alternatively, introgression between populations and species could have caused correlation and variance to evolve jointly. Both selection and introgression were probably influential in producing the observed pattern, but it is not possible to estimate their relative importance with current data. Genetic and phenotypic correlations were correlated in the song sparrow, but heritabilities of traits varied greatly. As a result, the genetic variance-covariance matrix for traits is not simply a constant multiple of the phenotypic matrix. Evolutionary response to natural selection cannot, therefore, be predicted from the measurement of phenotypic characteristics alone.