A Data-Analytic Strategy for Protein-Biomarker Discovery: Profiling of High-Dimensional Proteomic Data for Cancer Detection

With recent advances in mass spectrometry techniques, it is now possible to investigate proteins over a wide range of molecular weights in small biological specimens. This advance has generated data-analytic challenges in proteomics, similar to those created by microarray technologies in genetics, namely, discovery of "signature" protein profiles specific to each pathologic state (e.g., normal vs. cancer) or differential profiles between experimental conditions (e.g., treated by a drug of interest vs. untreated) from high-dimensional data. We propose a data analytic strategy for discovering protein biomarkers based on such high-dimensional mass-spectrometry data. A real biomarker-discovery project on prostate cancer is taken as a concrete example throughout the paper: the project aims to identify proteins in serum that distinguish cancer, benign hyperplasia, and normal states of prostate using the Surface Enhanced Laser Desorption/Ionization (SELDI) technology, a recently developed mass spectrometry technique. Our data analytic strategy takes properties of the SELDI mass-spectrometer into account: the SELDI output of a specimen contains about 48,000 (x, y) points where x is the protein mass divided by the number of charges introduced by ionization and y is the protein intensity of the corresponding mass per charge value, x, in that specimen. Given high coefficients of variation and other characteristics of protein intensity measures (y values), we reduce the measures of protein intensities to a set of binary variables that indicate peaks in the y-axis direction in the nearest neighborhoods of each mass per charge point in the x-axis direction. We then account for a shifting (measurement error) problem of the x-axis in SELDI output. After these pre-analysis processing of data, we combine the binary predictors to generate classification rules for cancer, benign hyperplasia, and normal states of prostate. Our approach is to apply the boosting algorithm to select binary predictors and construct a summary classifier. We empirically evaluate sensitivity and specificity of the resulting summary classifiers with a test dataset that is independent from the training dataset used to construct the summary classifiers. The proposed method performed nearly perfectly in distinguishing cancer and benign hyperplasia from normal. In the classification of cancer vs. benign hyperplasia, however, an appreciable proportion of the benign specimens were classified incorrectly as cancer. We discuss practical issues associated with our proposed approach to the analysis of SELDI output and its application in cancer biomarker discovery.

Computational Techniques for Spatial Logistic Regression with Large Datasets

In epidemiological work, outcomes are frequently non-normal, sample sizes may be large, and effects are often small. To relate health outcomes to geographic risk factors, fast and powerful methods for fitting spatial models, particularly for non-normal data, are required. We focus on binary outcomes, with the risk surface a smooth function of space. We compare penalized likelihood models, including the penalized quasi-likelihood (PQL) approach, and Bayesian models based on fit, speed, and ease of implementation. A Bayesian model using a spectral basis representation of the spatial surface provides the best tradeoff of sensitivity and specificity in simulations, detecting real spatial features while limiting overfitting and being more efficient computationally than other Bayesian approaches. One of the contributions of this work is further development of this underused representation. The spectral basis model outperforms the penalized likelihood methods, which are prone to overfitting, but is slower to fit and not as easily implemented. Conclusions based on a real dataset of cancer cases in Taiwan are similar albeit less conclusive with respect to comparing the approaches. The success of the spectral basis with binary data and similar results with count data suggest that it may be generally useful in spatial models and more complicated hierarchical models.

Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models

Suppose that we are interested in establishing simple, but reliable rules for predicting future t-year survivors via censored regression models. In this article, we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models we derive consistent estimators for the above measures via substitution and cross validation estimation procedures. Furthermore, we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All the proposals are illustrated with two real examples and their finite sample properties are evaluated via a simulation study.