Statistical Methods for The Analysis of Censored Family Data under Biased Sampling Schemes
Studies of the genetic basis for chronic disease often first aim to examine the nature and extend of within-family dependence in disease status. Families for such studies are typically selected using a biased sampling scheme in which affected individuals are recruited from a disease registry, followed by their consenting relatives. This gives right-censored or current status information on disease onset times. Methods for correcting this response-dependent sampling scheme have been developed for correlated binary data but variation in the age of assessment for family members makes this analysis uninterpretable. We develop likelihood and composite likelihood methods for modeling within-family associations in disease onset time using copula functions and second-order regression models in which dependencies are characterized by Kendall’s τ. Auxiliary data from an independent sample of individuals can be integrated by augmenting the composite likelihood to ensure identifiability and increase efficiency. An application to a motivating family study in psoriatic arthritis illustrates the method and provides evidence of excessive paternal transmission of risk. Ongoing work on the use of second-order estimating functions, alternative framework for dependence modeling, and approaches to efficient study design will also be discussed.
Sparse Estimation for Functional Semiparametric Additive Models
In the context of functional data analysis, functional linear regression serves as a fundamental tool to handle the relationship between a scalar response and a functional covariate. With the aid of Karhunen–Loève expansion of a stochastic process, a functional linear model can be written as an infinite linear combination of functional principal component scores. A reduced form is fitted in practice for dimension reduction; it is essentially converted to a multiple linear regression model.
Though the functional linear model is easy to implement and interpret in applications, it may suffer from an inadequate fit due to this specific linear representation. Additionally, effects of scalar predictors which may be predictive of the scalar response are neglected in the functional linear model.
Prediction accuracy can be enhanced greatly by incorporating effects of these scalar predictors.
In this talk, we propose a functional semiparametric additive model, which models the effect of a functional covariate nonparametrically and models several scalar covariates in a linear form. We develop the method for estimating the functional semiparametric additive model by smoothing and selecting non-vanishing components for the functional covariate. We show that the estimation method can consistently estimate both nonparametric and parametric parts in the model. Numerical studies will be presented to demonstrate the advantage of the proposed model in prediction.
Nonparametric Inference for Sensitivity of Haezendonck-Goovaerts Risk Measure
Recently Haezendonck-Goovaerts (H-G) risk measure has been popular in actuarial science. When it is applied to an insurance or a financial portfolio with several loss variables, sensitivity analysis becomes useful in managing the portfolio, and the assumption of independent observations may not be reasonable. This paper first derives an expression for computing the sensitivity of the H-G risk measure, which enables us to estimate the sensitivity nonparametrically via the H-G risk measure. Further, we derive the asymptotic distributions of the nonparametric estimators for the H-G risk measure and the sensitivity by assuming that loss variables in the portfolio follow from a strictly stationary ↵-mixing sequence. A simulation study is provided to examine the finite sample performance of the proposed nonparametric estimators. Finally, the method is applied to a real data set. Key words and phrases: Asymptotic distribution, Haezendonck-Goovaerts risk measure, Mixing sequence, Nonparametric estimate, Sensitivity analysis
Parametric and Nonparametric Models for Higher-order Interactions.
In this talk, I will discuss about parametric and nonparametric models for higher-order interactions with a focus on the statistical and computational aspects. In fields like social, political and biological sciences, there is a clear need for analyzing higher-order interactions as opposed to pairwise interactions, which has been the main focus of statistical networks analysis recently. Generalized Block models and hypergraphons are powerful tools for modeling higher-order interactions. The talk will introduce the models, highlight the theoretical challenges and differences that arise when analyzing higher-order interactions compared to pairwise interactions, and discuss applications and numerical results.
Inference for statistical interactions under misspecified or high-dimentional main effects
An increasing number multi-omic studies have generated complex high-dimentional data. A primary focus of these studies is to determine whether exposures interact in the effect that they produce on an outcome of interest. Interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures. When the main interest lies in interactions, the standard approach is not satisfactory because it is prone to (possibly severe) type I error inflation when the main exposure effects are misspecified or high-dimentional. I will propose generalized score type tests for high-dimentional interaction effects on correlated outcomes. I will also discuss the theoretical justification of some empirical observations regarding Type I error control, and introduce solutions to achieve robust inference for statistical interactions. The proposed methods will be illustrated using an example from the Multi-Ethnic Study of Atherosclerosis (MESA), investigating interaction between measures of neighborhood environment and genetic regions on longitudinal measures of blood pressure over a study period of about seven years with four exams.