Nonparametric flow cytometry analysis.

A nonparametric statistical test for the analysis of flow cytometry derived histograms is presented. The method involves smoothing and translocation of data, area normalization, channel by channel determination of the mean and S.D., and use of Bayes' theorem for unknown histogram classification. With this statistical method, different sets of histograms from numerous biological systems can be compared.     

Nonparametric analysis of recurrent events and death

This article is concerned with the analysis of recurrent events in the presence of a terminal event such as death. We consider the mean frequency function, defined as the marginal mean of the cumulative number of recurrent events over time. A simple nonparametric estimator for this quantity is presented. It is shown that the estimator, properly normalized, converges weakly to a zero-mean Gaussian process with an easily estimable covariance function. Nonparametric statistics for comparing two mean frequency functions and for combining data on recurrent events and death are also developed. The asymptotic null distributions of these statistics, together with consistent variance estimators, are derived. The small-sample properties of the proposed estimators and test statistics are examined through simulation studies. An application to a cancer clinical trial is provided.     

Nonparametric association analysis of exchangeable clustered competing risks data

Summary .  The work is motivated by the Cache County Study of Aging, a population-based study in Utah, in which sibship associations in dementia onset are of interest. Complications arise because only a fraction of the population ever develops dementia, with the majority dying without dementia. The application of standard dependence analyses for independently right-censored data may not be appropriate with such multivariate competing risks data, where death may violate the independent censoring assumption. Nonparametric estimators of the bivariate cumulative hazard function and the bivariate cumulative incidence function are adapted from the simple nonexchangeable bivariate setup to exchangeable clustered data, as needed with the large sibships in the Cache County Study. Time-dependent association measures are evaluated using these estimators. Large sample inferences are studied rigorously using empirical process techniques. The practical utility of the methodology is demonstrated with realistic samples both via simulations and via an application to the Cache County Study, where dementia onset clustering among siblings varies strongly by age.     

Nonparametric analysis of delayed treatment effects using single-crossing constraints

Clinical trials involving novel immuno-oncology therapies frequently exhibit survival profiles which violate the proportional hazards assumption due to a delay in treatment effect, and, in such settings, the survival curves in the two treatment arms may have a crossing before the two curves eventually separate. To flexibly model such scenarios, we describe a nonparametric approach for estimating the treatment arm-specific survival functions which constrains these two survival functions to cross at most once without making any additional assumptions about how the survival curves are related. A main advantage of our approach is that it provides an estimate of a crossing time if such a crossing exists, and, moreover, our method generates interpretable measures of treatment benefit including crossing-conditional survival probabilities and crossing-conditional estimates of restricted residual mean life. Our estimates of these measures may be used together with efficacy measures from a primary analysis to provide further insight into differences in survival across treatment arms. We demonstrate the use and effectiveness of our approach with a large simulation study and an analysis of reconstructed outcomes from a recent combination therapy trial.     

Nonparametric pathway-based regression models for analysis of genomic data

High-throughout genomic data provide an opportunity for identifying pathways and genes that are related to various clinical phenotypes. Besides these genomic data, another valuable source of data is the biological knowledge about genes and pathways that might be related to the phenotypes of many complex diseases. Databases of such knowledge are often called the metadata. In microarray data analysis, such metadata are currently explored in post hoc ways by gene set enrichment analysis but have hardly been utilized in the modeling step. We propose to develop and evaluate a pathway-based gradient descent boosting procedure for nonparametric pathways-based regression (NPR) analysis to efficiently integrate genomic data and metadata. Such NPR models consider multiple pathways simultaneously and allow complex interactions among genes within the pathways and can be applied to identify pathways and genes that are related to variations of the phenotypes. These methods also provide an alternative to mediating the problem of a large number of potential interactions by limiting analysis to biologically plausible interactions between genes in related pathways. Our simulation studies indicate that the proposed boosting procedure can indeed identify relevant pathways. Application to a gene expression data set on breast cancer distant metastasis identified that Wnt, apoptosis, and cell cycle-regulated pathways are more likely related to the risk of distant metastasis among lymph-node-negative breast cancer patients. Results from analysis of other two breast cancer gene expression data sets indicate that the pathways of Metalloendopeptidases (MMPs) and MMP inhibitors, as well as cell proliferation, cell growth, and maintenance are important to breast cancer relapse and survival. We also observed that by incorporating the pathway information, we achieved better prediction for cancer recurrence.     

Nonparametric and semiparametric trend analysis for stratified recurrence times

Recurrent event data are frequently encountered in longitudinal follow-up studies when the occurrences of multiple events are considered as the major outcomes. Suppose that the recurrent events are of the same type and the variable of interest is the recurrence time between successive events. In many applications, the distributional pattern of recurrence times can be used as an index for the progression of a disease. Such a distributional pattern is important for understanding the natural history of a disease or for confirming long-term treatment effect. In this article, we discuss and define the comparability of recurrence times. Nonparametric and semiparametric methods are developed for testing trend of recurrence time distributions and estimating trend parameters in regression models. The construction of the methods is based on comparable recurrence times from stratified data. A real data example is presented to illustrate the use of methodology.     

Nonparametric discriminant analysis of phytoplankton species using data from analytical flow cytometry

BACKGROUND: Analytical flow cytometry (AFC) provides rapid and accurate measurement of particles from heterogeneous populations. AFC has been used to classify and identify phytoplankton species, but most methods of discriminant analysis of resulting data have depended on normality assumptions and outcomes have been disappointing. METHODS AND RESULTS: In this study, we consider nonparametric methods based on density estimation. In addition to the familiar kernel method, methods based on wavelets are also implemented. Full five-dimensional wavelet estimation proves to be computationally prohibitive with current workstation power, so we employ projection pursuit for reduction of dimensionality. AFC typically produces very large samples, so we also investigate data simplification through binning. Further modifications to the discrimination strategy are suggested by specific features of phytoplankton data, namely, a hierarchical group structure, the possible presence of many groups, and the likelihood of encountering an aberrant group in a test sample. CONCLUSIONS: We apply all the resultant procedures to appropriate subsets of a very large data set, demonstrate their efficacy, and compare their error rates with those of more conventional methods. We further show that incorporation of the specific features of phytoplankton data into the analysis leads to improved results and provides a general framework for analysis of such data.     

Nonparametric association analysis of bivariate left‐truncated competing risks data

We develop time‐varying association analyses for onset ages of two lung infections to address the statistical challenges in utilizing registry data where onset ages are left‐truncated by ages of entry and competing‐risk censored by deaths. Two types of association estimators are proposed based on conditional cause‐specific hazard function and cumulative incidence function that are adapted from unconditional quantities to handle left truncation. Asymptotic properties of the estimators are established by using the empirical process techniques. Our simulation study shows that the estimators perform well with moderate sample sizes. We apply our methods to the Cystic Fibrosis Foundation Registry data to study the relationship between onset ages of Pseudomonas aeruginosa and Staphylococcus aureus infections.     

Nonparametric variance estimation in the analysis of microarray data: a measurement error approach

We investigate the effects of measurement error on the estimationof nonparametric variance functions. We show that either ignoringmeasurement error or direct application of the simulation extrapolation,SIMEX, method leads to inconsistent estimators. Nevertheless,the direct SIMEX method can reduce bias relative to a naiveestimator. We further propose a permutation SIMEX method thatleads to consistent estimators in theory. The performance ofboth the SIMEX methods depends on approximations to the exactextrapolants. Simulations show that both the SIMEX methods performbetter than ignoring measurement error. The methodology is illustratedusing microarray data from colon cancer patients.     

Nonparametric longitudinal allele-sharing model

Basically no methods are available for the analysis of quantitative traits in longitudinal genetic epidemiological studies. We introduce a nonparametric factorial design for longitudinal data on independent sib pairs, modelling the phenotypic quadratic differences as the dependent variable. Factors are the number of alleles shared identically by descent (IBD) and the age categories at which the dependent variable is measured, allowing for dependence due to age. To identify a linked marker a rank statistic tests the influence of IBD group on phenotypic quadratic differences. No assumptions are made on normality or variances of the dependent variable. We apply our method to 71 sib pairs from the Framingham Heart Study data provided at the Genetic Analysis Workshop 13. For all 15 available markers on chromosome 17 we analyzed the influence on systolic blood pressure. In addition, different selection strategies to sample from the whole data are discussed.