Survival associated pathway identification with group Lp penalized global AUC maximization

It has been demonstrated that genes in a cell do not act independently. They interact with one another to complete certain biological processes or to implement certain molecular functions. How to incorporate biological pathways or functional groups into the model and identify survival associated gene pathways is still a challenging problem. In this paper, we propose a novel iterative gradient based method for survival analysis with group Lp penalized global AUC summary maximization. Unlike LASSO, Lp (p < 1) (with its special implementation entitled adaptive LASSO) is asymptotic unbiased and has oracle properties [1]. We first extend Lp for individual gene identification to group Lp penalty for pathway selection, and then develop a novel iterative gradient algorithm for penalized global AUC summary maximization (IGGAUCS). This method incorporates the genetic pathways into global AUC summary maximization and identifies survival associated pathways instead of individual genes. The tuning parameters are determined using 10-fold cross validation with training data only. The prediction performance is evaluated using test data. We apply the proposed method to survival outcome analysis with gene expression profile and identify multiple pathways simultaneously. Experimental results with simulation and gene expression data demonstrate that the proposed procedures can be used for identifying important biological pathways that are related to survival phenotype and for building a parsimonious model for predicting the survival times

Fast cross-validation for multi-penalty ridge regression

High-dimensional prediction with multiple data types needs to account for potentially strong differences in predictive signal. Ridge regression is a simple model for high-dimensional data that has challenged the predictive performance of many more complex models and learners, and that allows inclusion of data type specific penalties. The largest challenge for multi-penalty ridge is to optimize these penalties efficiently in a cross-validation (CV) setting, in particular for GLM and Cox ridge regression, which require an additional estimation loop by iterative weighted least squares (IWLS). Our main contribution is a computationally very efficient formula for the multi-penalty, sample-weighted hat-matrix, as used in the IWLS algorithm. As a result, nearly all computations are in low-dimensional space, rendering a speed-up of several orders of magnitude. We developed a flexible framework that facilitates multiple types of response, unpenalized covariates, several performance criteria and repeated CV. Extensions to paired and preferential data types are included and illustrated on several cancer genomics survival prediction problems. Moreover, we present similar computational shortcuts for maximum marginal likelihood and Bayesian probit regression. The corresponding R-package, multiridge, serves as a versatile standalone tool, but also as a fast benchmark for other more complex models and multi-view learners

Kernel based methods for accelerated failure time model with ultra-high dimensional data

<p>Abstract</p> <p>Background</p> <p>Most genomic data have ultra-high dimensions with more than 10,000 genes (probes). Regularization methods with <it>L</it>₁and <it>L_p</it>penalty have been extensively studied in survival analysis with high-dimensional genomic data. However, when the sample size <it>n </it>≪ <it>m </it>(the number of genes), directly identifying a small subset of genes from ultra-high (<it>m </it>> 10, 000) dimensional data is time-consuming and not computationally efficient. In current microarray analysis, what people really do is select a couple of thousands (or hundreds) of genes using univariate analysis or statistical tests, and then apply the LASSO-type penalty to further reduce the number of disease associated genes. This two-step procedure may introduce bias and inaccuracy and lead us to miss biologically important genes.</p> <p>Results</p> <p>The accelerated failure time (AFT) model is a linear regression model and a useful alternative to the Cox model for survival analysis. In this paper, we propose a nonlinear kernel based AFT model and an efficient variable selection method with adaptive kernel ridge regression. Our proposed variable selection method is based on the kernel matrix and dual problem with a much smaller <it>n </it>× <it>n </it>matrix. It is very efficient when the number of unknown variables (genes) is much larger than the number of samples. Moreover, the primal variables are explicitly updated and the sparsity in the solution is exploited.</p> <p>Conclusions</p> <p>Our proposed methods can simultaneously identify survival associated prognostic factors and predict survival outcomes with ultra-high dimensional genomic data. We have demonstrated the performance of our methods with both simulation and real data. The proposed method performs superbly with limited computational studies.</p

Network-Based Biomarker Discovery : Development of Prognostic Biomarkers for Personalized Medicine by Integrating Data and Prior Knowledge

Advances in genome science and technology offer a deeper understanding of biology while at the same time improving the practice of medicine. The expression profiling of some diseases, such as cancer, allows for identifying marker genes, which could be able to diagnose a disease or predict future disease outcomes. Marker genes (biomarkers) are selected by scoring how well their expression levels can discriminate between different classes of disease or between groups of patients with different clinical outcome (e.g. therapy response, survival time, etc.). A current challenge is to identify new markers that are directly related to the underlying disease mechanism

Modeling and prediction of advanced prostate cancer

Background: Prostate cancer (PCa) is the most commonly diagnosed cancer and second leading cause of cancer-related deaths for men in Western countries. The advanced form of the disease is life-threatening with few options for curative therapies. The development of novel therapeutic alternatives would greatly benefit from a more comprehensive and tailored mathematical and statistical methodology. In particular, statistical inference of treatment effects and the prediction of time-dependent effects in both preclinical and clinical studies remains a challenging yet interesting opportunity for applied mathematicians. Such methods are likely to improve the reproducibility and translatability of results and offer possibility for novel holistic insights into disease progression, diagnosis, and prognosis. Methods: Several novel statistical and mathematical techniques were developed over the course of this thesis work for the in vivo modeling of PCa treatment responses. A matching-based, blinded randomized allocation procedure for preclinical experiments was developed that provides assistance for the statistical design of animal intervention studies, e.g., through power analysis and accounting for the stratification of individuals. For the post-intervention testing of treatment effects, two novel mixed-effects models were developed that aim to address the characteristic challenges of preclinical longitudinal experiments, including the heterogeneous response profiles observed in animal studies. Subsequently, a Finnish clinical PCa hospital registry cohort was inspected with a strong emphasis on prostate-specific antigen (PSA), the most commonly used PCa marker. After exploring the PSA trends using penalized splines, a generalized mixed-effects prediction model was implemented with a focus on the ultra-sensitive range of the PSA assay. Finally, for metastatic, aggressive PCa, an ensemble Cox regression methodology was developed for overall survival prediction in the DREAM 9.5 mCRPC Challenge based on open datasets from controlled clinical trials. Results: The advantages of the improved experimental design and two proposed statistical models were demonstrated in terms of both increased statistical power and accuracy in simulated and real preclinical testing settings. Penalized regression models applied to the clinical patient datasets support the use of PSA in the ultra-sensitive range together with a model for relapse prediction. Furthermore, the novel ensemble-based Cox regression model that was developed for the overall survival prediction in advanced PCa outperformed the state-of-the-art benchmark and all other models submitted to the Challenge and provided novel predictors of disease progression and treatment responses. Conclusions: The methods and results provide preclinical researchers and clinicians with novel tools for comprehensive modeling and prediction of PCa. All methodology is available as open source R statistical software packages and/or web-based graphical user interfaces

Modeling and simulation applications with potential impact in drug development and patient care

Indiana University-Purdue University Indianapolis (IUPUI)Model-based drug development has become an essential element to potentially make drug development more productive by assessing the data using mathematical and statistical approaches to construct and utilize models to increase the understanding of the drug and disease. The modeling and simulation approach not only quantifies the exposure-response relationship, and the level of variability, but also identifies the potential contributors to the variability. I hypothesized that the modeling and simulation approach can: 1) leverage our understanding of pharmacokinetic-pharmacodynamic (PK-PD) relationship from pre-clinical system to human; 2) quantitatively capture the drug impact on patients; 3) evaluate clinical trial designs; and 4) identify potential contributors to drug toxicity and efficacy. The major findings for these studies included: 1) a translational PK modeling approach that predicted clozapine and norclozapine central nervous system exposures in humans relating these exposures to receptor binding kinetics at multiple receptors; 2) a population pharmacokinetic analysis of a study of sertraline in depressed elderly patients with Alzheimer’s disease that identified site specific differences in drug exposure contributing to the overall variability in sertraline exposure; 3) the utility of a longitudinal tumor dynamic model developed by the Food and Drug Administration for predicting survival in non-small cell lung cancer patients, including an exploration of the limitations of this approach; 4) a Monte Carlo clinical trial simulation approach that was used to evaluate a pre-defined oncology trial with a sparse drug concentration sampling schedule with the aim to quantify how well individual drug exposures, random variability, and the food effects of abiraterone and nilotinib were determined under these conditions; 5) a time to event analysis that facilitated the identification of candidate genes including polymorphisms associated with vincristine-induced neuropathy from several association analyses in childhood acute lymphoblastic leukemia (ALL) patients; and 6) a LASSO penalized regression model that predicted vincristine-induced neuropathy and relapse in ALL patients and provided the basis for a risk assessment of the population. Overall, results from this dissertation provide an improved understanding of treatment effect in patients with an assessment of PK/PD combined and with a risk evaluation of drug toxicity and efficacy