Robust Linear Models for Cis-eQTL Analysis

Expression Quantitative Trait Loci (eQTL) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes. In outbread populations, including humans, eQTLs are commonly analysed using the conventional linear model, adjusting for relevant covariates, assuming an allelic dosage model and a Gaussian error term. However, gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations, or outliers. Such departures from modelling assumptions can lead to an increased rate of type II errors (false negatives), and to some extent also type I errors (false positives). Careful model checking can reduce the risk of type-I errors but often not type II errors, since it is generally too time-consuming to carefully check all models with a non-significant effect in large-scale and genome-wide studies. Here we propose the application of a robust linear model for eQTL analysis to reduce adverse effects of deviations from the assumption of Gaussian residuals. We present results from a simulation study as well as results from the analysis of real eQTL data sets. Our findings suggest that in many situations robust models have the potential to provide more reliable eQTL results compared to conventional linear models, particularly in respect to reducing type II errors due to non-Gaussian noise. Post-genomic data, such as that generated in genome-wide eQTL studies, are often noisy and frequently contain atypical observations. Robust statistical models have the potential to provide more reliable results and increased statistical power under non-Gaussian conditions. The results presented here suggest that robust models should be considered routinely alongside other commonly used methodologies for eQTL analysis.     

Survival Prediction Based on Compound Covariate under Cox Proportional Hazard Models

Survival prediction from a large number of covariates is a current focus of statistical and medical research. In this paper, we study a methodology known as the compound covariate prediction performed under univariate Cox proportional hazard models. We demonstrate via simulations and real data analysis that the compound covariate method generally competes well with ridge regression and Lasso methods, both already well-studied methods for predicting survival outcomes with a large number of covariates. Furthermore, we develop a refinement of the compound covariate method by incorporating likelihood information from multivariate Cox models. The new proposal is an adaptive method that borrows information contained in both the univariate and multivariate Cox regression estimators. We show that the new proposal has a theoretical justification from a statistical large sample theory and is naturally interpreted as a shrinkage-type estimator, a popular class of estimators in statistical literature. Two datasets, the primary biliary cirrhosis of the liver data and the non-small-cell lung cancer data, are used for illustration. The proposed method is implemented in R package “compound.Cox” available in CRAN at http://cran.r-project.org/.     

Bayesian Insight into a Robust Test for Linear Contrast Based on Asymmetric Censored Samples

A robust test for linear contrast using modified maximum likelihood estimators based on symmetrically censored samples proposed by Tiku (1973, 1982a) is studied in this paper from the Bayesian point of view. The effects of asymmetric censoring on this testing procedure is investigated and a good approximation to its posterior distribution in this case is worked out. We also present an example which illustrates the method of obtaining the highest posterior density interval for the linear combination of the unknown location parameters.     

On High-Dimensional Covariate Adjustment for Estimating Causal Effects in Randomized Trials with Survival Outcomes

Statistics in Biosciences - The purpose of this work is to improve the efficiency in estimating the average causal effect (ACE) on the survival scale where right censoring exists and...     

Randomization Tests for Censored Survival Distributions

This paper discusses the application of randomization tests to censored survival distributions. The three types of censoring considered are those designated by MILLER (1981) as Type 1 (fixed time termination), Type 2 (termination of experiment at r-th failure), and random censoring. Examples utilize the Gehan scoring procedure. Randomization tests for which computer programs already exist can be applied to a variety of experimental designs, regardless of the presence of censored observations.     

On Robust Linear Regression of Hepatic Extraction of Insulin

In classical linear regression model for analysis of medical data concerning hepatic extraction of insulin and c-peptide the fundamental assumption is that the subjects involved are of a similar nature. In reality, if this assumption is violated then the precision of the results is questionable. This paper suggests a robust alternative to overcome this problem. It is observed that the robustification may be a better option to determine an optimal quantity of insulin which minimizes the risk of damage associated with diabatic treatments.     

Bayesian Neural Network Models for Censored Data

Neural networks are considered by many to be very promising tools for classification and prediction. The flexibility of the neural network models often result in over-fit. Shrinking the parameters using a penalized likelihood is often used in order to overcome such over-fit. In this paper we extend the approach proposed by FARAGGI and SIMON (1995a) to modeling censored survival data using the input-output relationship associated with a single hidden layer feed-forward neural network. Instead of estimating the neural network parameters using the method of maximum likelihood, we place normal prior distributions on the parameters and make inferences based on derived posterior distributions of the parameters. This Bayesian formulation will result in shrinking the parameters of the neural network model and will reduce the over-fit compared with the maximum likelihood estimators. We illustrate our proposed method on a simulated and a real example.     

On Generalized Log-Logistic Model for Censored Survival Data

In the analysis of survival data with parametric models, it is well known that the Weibull model is not suitable for modeling cases where the hazard rate is non-monotonic. For such cases, log-logistic model is frequently used. However, due to the symmetric property of the log-logistic model, it may be poor for the cases where the hazard rate is skewed or heavily tailed. In this paper, we suggest a generalization of the log-logistic model by introducing a shape parameter. This generalized model is then applied to fit the lung cancer data of Prentice (1973). The results seem to improve over those obtained by using the log-logistic model.     

Bayes Estimator of Survival Probability from Randomly Censored Observations with Weibull Distribution of Time to Death

This paper deals with Bayes estimation of survival probability when the data are randomly censored. Such a situation arises in case of a clinical trial which extends for a limited period T. A fixed number of patients (n) are observed whose times to death have identical Weibull distribution with parameters β and θ. The maximum times of observation for different patients are also independent uniform variables as the patients arrive randomly throughout the trial. For the joint prior distribution of (β, θ) as suggested by Sinha and Kale (1980, page 137) Bayes estimator of survival probability at time t (0<t<T) has been obtained. Considering squared error loss function it is the mean of the survival probability with respect to the posterior distribution of (β, θ). This estimator is then compared with the maximum likelihood estimator, by simulation, for various values of β, θ and censoring percentage. The proposed estimator is found to be better under certain conditions.     

总体平均处理效应的拟极大似然估计

本文给出可交换条件下多维协变量的带有测量误差的多维结构回归模型,利用该模型研究总体平均处理效应的估计,给出当暴露组和对照组的协变量测量误差同分布时总体平均处理效应的拟极大似然估计及其性质．     

Identifying Change Points in a Covariate Effect on Time-to-Event Analysis with Reduced Isotonic Regression

Isotonic regression is a useful tool to investigate the relationship between a quantitative covariate and a time-to-event outcome. The resulting non-parametric model is a monotonic step function of a covariate X and the steps can be viewed as change points in the underlying hazard function. However, when there are too many steps, over-fitting can occur and further reduction is desirable. We propose a reduced isotonic regression approach to allow combination of small neighboring steps that are not statistically significantly different. In this approach, a second stage, the reduction stage, is integrated into the usual monotonic step building algorithm by comparing the adjacent steps using appropriate statistical testing. This is achieved through a modified dynamic programming algorithm. We implemented the approach with the simple exponential distribution and then its extension, the Weibull distribution. Simulation studies are used to investigate the properties of the resulting isotonic functions. We apply this methodology to the Diabetes Control and Complication Trial (DCCT) data set to identify potential change points in the association between HbA1c and the risk of severe hypoglycemia.     

单个协变量带有测量误差的多维结构回归模型

给出可交换条件下单个协变量的带有测量误差的多维结构回归模型,利用该模型研究总体平均处理效应的估计,给出当暴露组和对照组的协变量测量误差同分布时总体平均处理效应的拟极大似然估计及其性质.     

Use of Generalised Linear Mixed Models for the Analysis of Clustered Survival Data

Data from a litter matched tumorigenesis experiment are analysed using a generalised linear mixed model (GLMM) approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same litter. Maximum likelihood (ML) and residual maximum likelihood (REML) estimates of risk variable parameters, variance component parameters and the prediction of random effects are given. Estimation of treatment effect parameter (carcinogen effect) has good agreement with previous analyses obtained in the literature though the dependence structure within a litter is modelled in different ways. The variance component estimation provides the estimated dispersion of the random effects. The prediction of random effects, is useful, for instance, in identifying high risk litters and individuals. The present analysis illustrates its wider application to detecting increased risk of occurrence of disease in particular families of a study population.     

A Test of Equality of Survival Distributions for Two Sample Censored Grouped Survival Data

A common testing problem for a life table or survival data is to test the equality of two survival distributions when the data is both grouped and censored. Several tests have been proposed in the literature which require various assumptions about the censoring distributions. It is shown that if these conditions are relaxed then the tests may no longer have the stated properties. The maximum likelihood test of equality when no assumptions are made about the censoring marginal distributions is derived. The properties of the test are found and it is compared to the existing tests. The fact that no assumptions are required about the censoring distributions make the test a useful initial testing procedure.     

Distance-Based Analysis with Quantile Regression Models

Statistics in Biosciences - Non-standard structured, multivariate data are emerging in many research areas, including genetics and genomics, ecology, and social science. Suitably defined pairwise...