Focused information criterion on predictive models in personalized medicine

Instead of assessing the overall fit of candidate models like the traditional model selection criteria, the focused information criterion focuses attention directly on the parameter of the primary interest and aims to select the model with the minimum estimated mean squared error for the estimate of the focused parameter. In this article we apply the focused information criterion for personalized medicine. By using individual‐level information from clinical observations, demographics, and genetics, we obtain the personalized predictive models to make the prognosis and diagnosis individually. The consideration of the heterogeneity among the individuals helps reduce the prediction uncertainty and improve the prediction accuracy. Two real data examples from biomedical research are studied as illustrations.     

A general Akaike-type criterion for model selection in robust regression

Akaike's procedure (1970) for selecting a model minimises anestimate of the expected squared error in predicting new, independentobservations. This selection criterion was designed for modelsfitted by least squares. A different model-fitting technique,such as least absolute deviation regression, requires an appropriatemodel selection procedure. This paper presents a general Akaike-typecriterion applicable to a wide variety of loss functions formodel fitting. It requires only that the function be convexwith a unique minimum, and twice differentiable in expectation.Simulations show that the estimators proposed here well approximatetheir respective prediction errors.     

A predictive model relating North American plant formations and climate

A discriminant model was produced that predicts North American plant formations with basic climatic variables (monthly mean temperatures, monthly precipitation, and latitude). The model is based on data from 176 weather stations. Climatic variables from 30 additional randomly-selected weather stations were used to test the model. The predicted formation and actual formation at each site were compared; four sites were classified into the wrong formations (87% accuracy). This predictive model indicates a strong correlation between climate and formations in North America. Vegetation-climate models produced by canonical discriminant analysis may be useful in detecting geographical localities where non-climatic factors are particularly influential.     

A Robust Alternative to the Schemper–Henderson Estimator of Prediction Error

Summary In clinical applications, the prediction error of survival models has to be taken into consideration to assess the practical suitability of conclusions drawn from these models. Different approaches to evaluate the predictive performance of survival models have been suggested in the literature. In this article, we analyze the properties of the estimator of prediction error developed by Schemper and Henderson (2000 , Biometrics 56, 249–255), which quantifies the absolute distance between predicted and observed survival functions. We provide a formal proof that the estimator proposed by Schemper and Henderson is not robust against misspecification of the survival model, that is, the estimator will only be meaningful if the model family used for deriving predictions has been specified correctly. To remedy this problem, we construct a new estimator of the absolute distance between predicted and observed survival functions. We show that this modified Schemper–Henderson estimator is robust against model misspecification, allowing its practical application to a wide class of survival models. The properties of the Schemper–Henderson estimator and its new modification are illustrated by means of a simulation study and the analysis of two clinical data sets.     

Mechanistic model of fuel selection in the muscle

Fuel selection in human muscle is key to explaining insulin resistance. In obesity and type 2 diabetes mellitus, there is an increased content of lipid within and around muscle fibers. Changes in muscle fuel partitioning of lipid, between oxidation and storage of fat, contribute to the accumulation of intramuscular triglycerides and to the pathogenesis of both obesity and type 2 diabetes mellitus. A mathematical model of the aggregated metabolism in skeletal muscle was developed and the effects of fuel selection for lean and obese individuals under fasting conditions, insulin-stimulated conditions, and oscillating insulin conditions were examined. Model results were complementary to prior observations that elevated lipid oxidation during insulin-stimulated conditions is correlated with insulin resistance. The model also adequately simulated metabolic inflexibility between fat and glucose oxidation in the obese individual. A novel sensitivity analysis indicated the strong interaction effects of parameters of glucose and lipid oxidation pathways on the variables of each pathway.     

High‐Dimensional Cox Models: The Choice of Penalty as Part of the Model Building Process

The Cox proportional hazards regression model is the most popular approach to model covariate information for survival times. In this context, the development of high‐dimensional models where the number of covariates is much larger than the number of observations ( $p \,{\gg }\, n$ ) is an ongoing challenge. A practicable approach is to use ridge penalized Cox regression in such situations. Beside focussing on finding the best prediction rule, one is often interested in determining a subset of covariates that are the most important ones for prognosis. This could be a gene set in the biostatistical analysis of microarray data. Covariate selection can then, for example, be done by L₁‐penalized Cox regression using the lasso (Tibshirani ( 1997 ). Statistics in Medicine 16 , 385–395). Several approaches beyond the lasso, that incorporate covariate selection, have been developed in recent years. This includes modifications of the lasso as well as nonconvex variants such as smoothly clipped absolute deviation (SCAD) (Fan and Li ( 2001 ). Journal of the American Statistical Association 96 , 1348–1360; Fan and Li ( 2002 ). The Annals of Statistics 30 , 74–99). The purpose of this article is to implement them practically into the model building process when analyzing high‐dimensional data with the Cox proportional hazards model. To evaluate penalized regression models beyond the lasso, we included SCAD variants and the adaptive lasso (Zou ( 2006 ). Journal of the American Statistical Association 101 , 1418–1429). We compare them with “standard” applications such as ridge regression, the lasso, and the elastic net. Predictive accuracy, features of variable selection, and estimation bias will be studied to assess the practical use of these methods. We observed that the performance of SCAD and adaptive lasso is highly dependent on nontrivial preselection procedures. A practical solution to this problem does not yet exist. Since there is high risk of missing relevant covariates when using SCAD or adaptive lasso applied after an inappropriate initial selection step, we recommend to stay with lasso or the elastic net in actual data applications. But with respect to the promising results for truly sparse models, we see some advantage of SCAD and adaptive lasso, if better preselection procedures would be available. This requires further methodological research.     

Differential equation modeling of HIV viral fitness experiments: model identification, model selection, and multimodel inference

Summary .  Many biological processes and systems can be described by a set of differential equation (DE) models. However, literature in statistical inference for DE models is very sparse. We propose statistical estimation, model selection, and multimodel averaging methods for HIV viral fitness experiments in vitro that can be described by a set of nonlinear ordinary differential equations (ODE). The parameter identifiability of the ODE models is also addressed. We apply the proposed methods and techniques to experimental data of viral fitness for HIV-1 mutant 103N. We expect that the proposed modeling and inference approaches for the DE models can be widely used for a variety of biomedical studies.     

Response to mass selection when the genotype by environment interaction is modelled as a linear reaction norm

A breeding goal accounting for the effects of genotype by environment interaction (G × E) has to define not only traits but also the environment in which those traits are to be improved. The aim of this study was to predict the selection response in the coefficients of a linear reaction norm, and response in average phenotypic value in any environment, when mass selection is applied to a trait where G × E is modelled as a linear reaction norm. The optimum environment in which to test the selection candidates for a given breeding objective was derived. Optimisation of the selection environment can be used as a means to either maximise genetic progress in a certain response environment, to keep the change in environmental sensitivity at a desired rate, or to reduce the proportion of animals performing below an acceptance level. The results showed that the optimum selection environment is not always equal to the environment in which the response is to be realised, but depends on the degree of G × E (determined by the ratio of variances in slope and level of a linear reaction norm), the correlation between level and slope, and the heritability of the trait.     

Testing the rare-alleles model of quantitative variation by artificial selection

The rare-alleles model of quantitative variation posits that a common allele (the ‘wild-type’) and one or more rare alleles segregate at each locus affecting a quantitative trait; a scenario predicted by several distinct evolutionary hypotheses. Single locus arguments suggest that artificial selection should substantially increase the genetic variance (Vg) if the rare-alleles model is accurate. This paper tests the ‘ΔVg prediction’ using a large artificial selection experiment on flower size of Mimulus guttatus. Vg for flower size does evolve, increasing with selection for larger flower while decreasing in the other direction. These data are consistent with a model in which flower size variation is caused by rare, partially dominant alleles. However, this explanation becomes increasingly tenuous when considered with other data (correlated responses to selection and the effects of inbreeding). A combination of modern (marker-based mapping) and classical (biometric) techniques will likely to be required to determine the distribution of allele frequencies at loci influencing quantitative traits.     

kakusan: a computer program to automate the selection of a nucleotide substitution model and the configuration of a mixed model on multilocus data

The application of different substitution models to each gene (a.k.a. mixed model) should be considered in model‐based phylogenetic analysis of multigene sequences. However, a single molecular evolution model is still usually applied. There are no computer programs able to conduct model selection for multiple loci at the same time, though several recently developed types of software for phylogenetic inference can handle mixed model. Here, I have developed computer software named ‘kakusan’ that enables us to solve the above problems. Major running steps are briefly described, and an analysis of results with kakusan is compared to that obtained with other program.     

Domesticated birds as a model for the genetics of speciation by sexual selection

In theory, even populations occupying identical environments can diverge in sexually selected traits, as a consequence of different mutational input. I evaluate the potential of this process by comparing the genetics of breeds of domesticated birds to what is known about the genetics of differences among species. Within domesticated species there is a strong correlation of time since domestication with the number of breeds. Descendants of the rock dove, Columba livia (the oldest domesticate) show differences in courtship, vocalizations, body shape, feather ornaments (crests and tails) and colors and color patterns. When nine other domesticated species are included there is a striking hierarchy, with more recent domesticates having a nested subset of these traits: the youngest domesticated species have breeds distinguished only by color. This suggests that selection of new, visible, mutations is driving the process of breed diversification, with mutations that appeal to the breeder happening the most frequently in color. In crosses among related species, color, feather ornaments and many vocalizations and displays show both intermediate dominance and pure dominance. Although the number of loci affecting each of these traits is typically unknown, limited evidence of the genetics of species differences suggests that some differences are due to the substitution of single genes of major effect. While neither the genetics of breeds nor the genetics of species provide a perfect model for the genetics of speciation, similarities between the two are sufficiently striking to infer that major, visible, mutations can provide the impetus underlying new directions of sexual selection.     

Evaluating the post‐copulatory sexual selection hypothesis for genital evolution reveals evidence for pleiotropic harm exerted by the male genital spines of Drosophila ananassae

The contemporary explanation for the rapid evolutionary diversification of animal genitalia is that such traits evolve by post‐copulatory sexual selection. Here, we test the hypothesis that the male genital spines of Drosophila ananassae play an adaptive role in post‐copulatory sexual selection. Whereas previous work on two Drosophila species shows that these spines function in precopulatory sexual selection to initiate genital coupling and promote male competitive copulation success, further research is needed to evaluate the potential for Drosophila genital spines to have a post‐copulatory function. Using a precision micron‐scale laser surgery technique, we test the effect of spine length reduction on copulation duration, male competitive fertilization success, female fecundity and female remating behaviour. We find no evidence that male genital spines in this species have a post‐copulatory adaptive function. Instead, females mated to males with surgically reduced/blunted genital spines exhibited comparatively greater short‐term fecundity relative to those mated by control males, indicating that the natural (i.e. unaltered) form of the trait may be harmful to females. In the absence of an effect of genital spine reduction on measured components of post‐copulatory fitness, the harm seems to be a pleiotropic side effect rather than adaptive. Results are discussed in the context of sexual conflict mediating the evolution of male genital spines in this species and likely other Drosophila.