Estimation with correlated censored survival data with missing covariates

Incomplete covariate data are a common occurrence in studies in which the outcome is survival time. Further, studies in the health sciences often give rise to correlated, possibly censored, survival data. With no missing covariate data, if the marginal distributions of the correlated survival times follow a given parametric model, then the estimates using the maximum likelihood estimating equations, naively treating the correlated survival times as independent, give consistent estimates of the relative risk parameters Lipsitz et al. 1994 50, 842-846. Now, suppose that some observations within a cluster have some missing covariates. We show in this paper that if one naively treats observations within a cluster as independent, that one can still use the maximum likelihood estimating equations to obtain consistent estimates of the relative risk parameters. This method requires the estimation of the parameters of the distribution of the covariates. We present results from a clinical trial Lipsitz and Ibrahim (1996b) 2, 5-14 with five covariates, four of which have some missing values. In the trial, the clusters are the hospitals in which the patients were treated.     

Boosting method for nonlinear transformation models with censored survival data

We propose a general class of nonlinear transformation models for analyzing censored survival data, of which the nonlinear proportional hazards and proportional odds models are special cases. A cubic smoothing spline-based component-wise boosting algorithm is derived to estimate covariate effects nonparametrically using the gradient of the marginal likelihood, that is computed using importance sampling. The proposed method can be applied to survival data with high-dimensional covariates, including the case when the sample size is smaller than the number of predictors. Empirical performance of the proposed method is evaluated via simulations and analysis of a microarray survival data.     

To identify associations with rare variants, just WHaIT: Weighted haplotype and imputation-based tests

Empirical evidences suggest that both common and rare variants contribute to complex disease etiology. Although the effects of common variants have been thoroughly assessed in recent genome-wide association studies (GWAS), our knowledge of the impact of rare variants on complex diseases remains limited. A number of methods have been proposed to test for rare variant association in sequencing-based studies, a study design that is becoming popular but is still not economically feasible. On the contrary, few (if any) methods exist to detect rare variants in GWAS data, the data we have collected on thousands of individuals. Here we propose two methods, a weighted haplotype-based approach and an imputation-based approach, to test for the effect of rare variants with GWAS data. Both methods can incorporate external sequencing data when available. We evaluated our methods and compared them with methods proposed in the sequencing setting through extensive simulations. Our methods clearly show enhanced statistical power over existing methods for a wide range of population-attributable risk, percentage of disease-contributing rare variants, and proportion of rare alleles working in different directions. We also applied our methods to the IFIH1 region for the type 1 diabetes GWAS data collected by the Wellcome Trust Case-Control Consortium. Our methods yield p values in the order of 10⁻³, whereas the most significant p value from the existing methods is greater than 0.17. We thus demonstrate that the evaluation of rare variants with GWAS data is possible, particularly when public sequencing data are incorporated.     

A method for analyzing censored survival phenotype with gene expression data

Background  

Survival time is an important clinical trait for many disease studies. Previous works have shown certain relationship between patients' gene expression profiles and survival time. However, due to the censoring effects of survival time and the high dimensionality of gene expression data, effective and unbiased selection of a gene expression signature to predict survival probabilities requires further study.     

The association of H-2 haplotype with implantation,survival, and growth of murine embryos

Using three congenic strains, C57BL/10Sn (H-2 ^b), B10.A/SnSg (H-2 ^a), and B10.D2/nSn (H-2 ^d), we sought to investigate the possible association of H-2 haplotype with the number of implants, fetal survival, and fetal weight, as well as to analyze the possible effects of hybrid vigor and maternal-fetal histoincompatibility in primigravidae mice. The results of this study indicate a significant association between genes at or near the H-2 complex and both fetal loss and fetal weight, but not the number of implants. Haplotype variation accounted for 14 percent of the variation in fetal loss and 20 percent of the variation in fetal weight. With the exception of fetal loss, there was no evidence of a maternal effect. There was also no clear evidence of hybrid vigor or histoincompatibility effects for any of the three variables studied. In summary, the data suggests that particular allelic variants at or near the H-2 complex confer some selective advantage as measured by differential fetal survival and fetal growth.     

Bayesian variable selection for the analysis of microarray data with censored outcomes

MOTIVATION: A common task in microarray data analysis consists of identifying genes associated with a phenotype. When the outcomes of interest are censored time-to-event data, standard approaches assess the effect of genes by fitting univariate survival models. In this paper, we propose a Bayesian variable selection approach, which allows the identification of relevant markers by jointly assessing sets of genes. We consider accelerated failure time (AFT) models with log-normal and log-t distributional assumptions. A data augmentation approach is used to impute the failure times of censored observations and mixture priors are used for the regression coefficients to identify promising subsets of variables. The proposed method provides a unified procedure for the selection of relevant genes and the prediction of survivor functions. RESULTS: We demonstrate the performance of the method on simulated examples and on several microarray datasets. For the simulation study, we consider scenarios with large number of noisy variables and different degrees of correlation between the relevant and non-relevant (noisy) variables. We are able to identify the correct covariates and obtain good prediction of the survivor functions. For the microarray applications, some of our selected genes are known to be related to the diseases under study and a few are in agreement with findings from other researchers. AVAILABILITY: The Matlab code for implementing the Bayesian variable selection method may be obtained from the corresponding author. CONTACT: mvannucci@stat.tamu.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Dimension reduction methods for microarrays with application to censored survival data

MOTIVATION: Recent research has shown that gene expression profiles can potentially be used for predicting various clinical phenotypes, such as tumor class, drug response and survival time. While there has been extensive studies on tumor classification, there has been less emphasis on other phenotypic features, in particular, patient survival time or time to cancer recurrence, which are subject to right censoring. We consider in this paper an analysis of censored survival time based on microarray gene expression profiles. RESULTS: We propose a dimension reduction strategy, which combines principal components analysis and sliced inverse regression, to identify linear combinations of genes, that both account for the variability in the gene expression levels and preserve the phenotypic information. The extracted gene combinations are then employed as covariates in a predictive survival model formulation. We apply the proposed method to a large diffuse large-B-cell lymphoma dataset, which consists of 240 patients and 7399 genes, and build a Cox proportional hazards model based on the derived gene expression components. The proposed method is shown to provide a good predictive performance for patient survival, as demonstrated by both the significant survival difference between the predicted risk groups and the receiver operator characteristics analysis. AVAILABILITY: R programs are available upon request from the authors. SUPPLEMENTARY INFORMATION: http://dna.ucdavis.edu/~hli/bioinfo-surv-supp.pdf.     

Nonparametric estimation of age-at-onset distributions from censored kin-cohort data

We present a nonparametric estimator of genotype-specific age-at-onsetdistributions from kin-cohort data. Standard error calculationsare derived and the methodology is illustrated through an analysisof the influence of mutations of the Parkin gene on Parkinson'sdisease. Semiparametric efficiency considerations are brieflydiscussed.