Randomized and non-randomized designs for causal inference with longitudinal data in rare disorders.

In the United States, approximately 7000 rare diseases affect 30 million patients, and only 10% of these diseases have existing therapies. Sound study design and causal inference methods are essential to demonstrate the therapeutic efficacy, safety, and effectiveness of new therapies. In the rare diseases setting, several factors challenge the use of typical parallel control designs: the small patient population size, genotypic and phenotypic diversity, and the complexity and incomplete understanding of the disorder\u27s progression. Repeated measures, when spaced appropriately relative to disease progression and exploited in design and analysis, can increase study power and reduce variability in treatment effect estimation. This paper reviews these longitudinal designs and draws the parallel between some new and existing randomized studies in rare diseases and their less well-known controlled observational study designs. We show that self-controlled randomized crossover and N-of-1 designs have similar considerations as the observational case series and case-crossover designs. Also, randomized sequential designs have similar considerations to longitudinal cohort studies using sequential matching or weighting to control confounding. We discuss design and analysis considerations for valid causal inference and illustrate them with examples of analyses in multiple rare disorders, including urea cycle disorder and cystic fibrosis

Analysis of nonlinear modes of variation for functional data

A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the linear modes of variation found by PCA are not always interpretable by the experimenters. In addition, the modes of variation of interest to the experimenter are not always linear. We present in this paper a new analysis of variance for Functional Data. Our method was motivated by decomposing the variation in the data into predetermined and interpretable directions (i.e. modes) of interest. Since some of these modes could be nonlinear, we develop a new defined ratio of sums of squares which takes into account the curvature of the space of variation. We discuss, in the general case, consistency of our estimates of variation, using mathematical tools from differential geometry and shape statistics. We successfully applied our method to a motivating example of biological data. This decomposition allows biologists to compare the prevalence of different genetic tradeoffs in a population and to quantify the effect of selection on evolution.Comment: Published in at http://dx.doi.org/10.1214/07-EJS080 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Variation in Continuous Reaction Norms: Quantifying Directions of Biological Interest

Abstract: Thermal performance curves are an example of continuous reaction norm curves of common shape. Three modes of variation in these curvesvertical shift, horizontal shift, and generalistspecialist tradeoffsare of special interest to evolutionary biologists. Since two of these modes are nonlinear, traditional methods such as principal components analysis fail to decompose the variation into biological modes and to quantify the variation associated with each mode. Here we present the results of a new method, template mode of variation (TMV), that decomposes the variation into predetermined modes of variation for a particular set of thermal performance curves. We illustrate the method using data on thermal sensitivity of growth rate in Pieris rapae caterpillars. The TMV model explains 67% of the variation in thermal performance curves among families; generalistspecialist tradeoffs account for 38% of the total betweenfamily variation. The TMV method implemented here is applicable to both differences in mean and patterns of variation, and it can be used with either phenotypic or quantitative genetic data for thermal performance curves or other continuous reaction norms that have a template shape with a single maximum. The TMV approach may also apply to growth trajectories, agespecific lifehistory traits, and other functionvalued traits

The Genetic Basis of Thermal Reaction Norm Evolution in Lab and Natural Phage Populations

Two major goals of laboratory evolution experiments are to integrate from genotype to phenotype to fitness, and to understand the genetic basis of adaptation in natural populations. Here we demonstrate that both goals are possible by re-examining the outcome of a previous laboratory evolution experiment in which the bacteriophage G4 was adapted to high temperatures. We quantified the evolutionary changes in the thermal reaction norms—the curves that describe the effect of temperature on the growth rate of the phages—and decomposed the changes into modes of biological interest. Our analysis indicated that changes in optimal temperature accounted for almost half of the evolutionary changes in thermal reaction norm shape, and made the largest contribution toward adaptation at high temperatures. Genome sequencing allowed us to associate reaction norm shape changes with particular nucleotide mutations, and several of the identified mutations were found to be polymorphic in natural populations. Growth rate measures of natural phage that differed at a site that contributed substantially to adaptation in the lab indicated that this mutation also underlies thermal reaction norm shape variation in nature. In combination, our results suggest that laboratory evolution experiments may successfully predict the genetic bases of evolutionary responses to temperature in nature. The implications of this work for viral evolution arise from the fact that shifts in the thermal optimum are characterized by tradeoffs in performance between high and low temperatures. Optimum shifts, if characteristic of viral adaptation to novel temperatures, would ensure the success of vaccine development strategies that adapt viruses to low temperatures in an attempt to reduce virulence at higher (body) temperatures

Accounting for Calibration Uncertainties in X-ray Analysis: Effective Areas in Spectral Fitting

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis results because instrumental calibration uncertainty is a form of systematic uncertainty. Ignoring it can underestimate error bars and introduce bias into the fitted values of model parameters. Accounting for such uncertainties currently requires extensive case-specific simulations if using existing analysis packages. Here we present general statistical methods that incorporate calibration uncertainties into spectral analysis of high-energy data. We first present a method based on multiple imputation that can be applied with any fitting method, but is necessarily approximate. We then describe a more exact Bayesian approach that works in conjunction with a Markov chain Monte Carlo based fitting. We explore methods for improving computational efficiency, and in particular detail a method of summarizing calibration uncertainties with a principal component analysis of samples of plausible calibration files. This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. Our procedure for incorporating effective area uncertainty is easily generalized to other types of calibration uncertainties.Comment: 61 pages double spaced, 8 figures, accepted for publication in Ap

2007): "Explaining the Low Labor Productivity in East Germany - A Spatial Analysis

This paper sheds light on the transferability of human capital in periods of dramatic structural change by analyzing the unique event of German Reunification. We explore whether the comparatively low labor productivity in East Germany after reunification is caused by the depreciation of human capital at reunification, or by unfavorable job characteristics. East German workers should have been hit harder by reunification the more specific human capital was. Treating both human capital and job characteristics as unobservables, we derive their relative importance in explaining the low labor productivity by estimating a spatial structural model that predicts commuting behavior across the former East-West border and the resulting regional unemployment rates. The identification of the model is based on the slope of the unemployment rate across the former border: the larger the human capital differences between East and West, the less commuting across the border takes place, and the sharper is the increase of the unemployment rate at the former border. The results indicate that East and West German skills are very similar, while job characteristics differ significantly between East and West. Hence, they suggest that a significant part of the human capital accumulate

Data from: Variation in continuous reaction norms: quantifying directions of biological interest

Thermal performance curves are an example of continuous reaction norm curves of common shape. Three modes of variation in these curves-- Vertical shift, horizontal shift, and generalist-specialist tradeoffs-- are of special interest to evolutionary biologists. Since two of these modes are nonlinear, traditional methods such as Principal Component Analysis fail to decompose the variation into biological modes and to quantify the variation associated with each mode. Here we present the results of a new method, Template Mode of Variation (TMV), that decomposes the variation into predetermined modes of variation for a particular set of thermal performance curves. We illustrate the method using data on thermal sensitivity of growth rate in Pieris rapae caterpillars. The TMV model explains 67% of the variation in thermal performance curves among families; generalist-specialist tradeoffs account for 38% of the total between-family variation. The TMV method implemented here is applicable to both differences in mean and patterns of variation, and can be used with either phenotypic or quantitative genetic data for thermal performance curves or other continuous reaction norms that have a template shape with a single maximum. The TMV approach may also apply to growth trajectories, age-specific life history traits and other function-valued traits

Data from: Variation in continuous reaction norms: quantifying directions of biological interest

Thermal performance curves are an example of continuous reaction norm curves of common shape. Three modes of variation in these curves-- Vertical shift, horizontal shift, and generalist-specialist tradeoffs-- are of special interest to evolutionary biologists. Since two of these modes are nonlinear, traditional methods such as Principal Component Analysis fail to decompose the variation into biological modes and to quantify the variation associated with each mode. Here we present the results of a new method, Template Mode of Variation (TMV), that decomposes the variation into predetermined modes of variation for a particular set of thermal performance curves. We illustrate the method using data on thermal sensitivity of growth rate in Pieris rapae caterpillars. The TMV model explains 67% of the variation in thermal performance curves among families; generalist-specialist tradeoffs account for 38% of the total between-family variation. The TMV method implemented here is applicable to both differences in mean and patterns of variation, and can be used with either phenotypic or quantitative genetic data for thermal performance curves or other continuous reaction norms that have a template shape with a single maximum. The TMV approach may also apply to growth trajectories, age-specific life history traits and other function-valued traits