Statistical power of QTL mapping methods applied to bacteria counts

Most QTL mapping methods assume that phenotypes follow a normal distribution, but many phenotypes of interest are not normally distributed, e.g. bacteria counts (or colony-forming units, CFU). Such data are extremely skewed to the right and can present a high amount of zero values, which are ties from a statistical point of view. Our objective is therefore to assess the efficiency of four QTL mapping methods applied to bacteria counts: (1) least-squares (LS) analysis, (2) maximum-likelihood (ML) analysis, (3) non-parametric (NP) mapping and (4) nested ANOVA (AN). A transformation based on quantiles is used to mimic observed distributions of bacteria counts. Single positions (1 marker, 1 QTL) as well as chromosome scans (11 markers, 1 QTL) are simulated. When compared with the analysis of a normally distributed phenotype, the analysis of raw bacteria counts leads to a strong decrease in power for parametric methods, but no decrease is observed for NP. However, when a mathematical transformation (MT) is applied to bacteria counts prior to analysis, parametric methods have the same power as NP. Furthermore, parametric methods, when coupled with MT, outperform NP when bacteria counts have a very high proportion of zeros (70.8%). Our results show that the loss of power is mainly explained by the asymmetry of the phenotypic distribution, for parametric methods, and by the existence of ties, for the non-parametric method. Therefore, mapping of QTL for bacterial diseases, as well as for other diseases assessed by a counting process, should focus on the occurrence of ties in phenotypes before choosing the appropriate QTL mapping method.     

A non-parametric approach for identifying differentially expressed genes in factorial microarray experiments

We introduce a non-parametric approach using bootstrap-assisted correspondence analysis to identify and validate genes that are differentially expressed in factorial microarray experiments. Model comparison showed that although both parametric and non-parametric methods capture the different profiles in the data, our method is less inclined to false positive results due to dimension reduction in data analysis.     

Two-sample density-based empirical likelihood tests for incomplete data in application to a pneumonia study

In clinical trials examining the incidence of pneumonia it is a common practice to measure infection via both invasive and non-invasive procedures. In the context of a recently completed randomized trial comparing two treatments the invasive procedure was only utilized in certain scenarios due to the added risk involved, and given that the level of the non-invasive procedure surpassed a given threshold. Hence, what was observed was bivariate data with a pattern of missingness in the invasive variable dependent upon the value of the observed non-invasive observation within a given pair. In order to compare two treatments with bivariate observed data exhibiting this pattern of missingness we developed a semi-parametric methodology utilizing the density-based empirical likelihood approach in order to provide a non-parametric approximation to Neyman-Pearson-type test statistics. This novel empirical likelihood approach has both a parametric and non-parametric components. The non-parametric component utilizes the observations for the non-missing cases, while the parametric component is utilized to tackle the case where observations are missing with respect to the invasive variable. The method is illustrated through its application to the actual data obtained in the pneumonia study and is shown to be an efficient and practical method.     

Testing quantitative traits for association and linkage in the presence or absence of parental data

Zhu and Elston developed a transmission disequilibrium test for quantitative traits by defining a linear transformation to condition out founder information. The method tests the null hypothesis of no linkage or association and can be applied to general pedigree structures. However, this method requires both genotype and phenotype parental information, which may be difficult to obtain. In this paper, we describe parametric and non-parametric methods to relax this requirement when only nuclear families are sampled. We show that neither method is affected by population stratification in the absence of linkage. The statistical power and validity of the tests are investigated by simulation. A simple simulation method to calculate the power of the nonparametric method is also discussed. In practice, the data may have some families with parental phenotype and genotype information available and some without. We briefly discuss how all the data may be analyzed jointly.     

Non-parametric optimal design in dose finding studies

We describe a non-parametric optimal design as a theoretical gold standard for dose finding studies. Its purpose is analogous to the Cramer-Rao bound for unbiased estimators, i.e. it provides a bound beyond which improvements are not generally possible. The bound applies to the class of non-parametric designs where the data are not assumed to be generated by any known parametric model. Whenever parametric assumptions really hold it may be possible to do better than the optimal non-parametric design. The goal is to be able to compare any potential dose finding scheme with the optimal non-parametric benchmark. This paper makes precise what is meant by optimal in this context and also why the procedure is described as non-parametric.     

Parametric and non-parametric modeling of short-term synaptic plasticity. Part II: Experimental study

This paper presents a synergistic parametric and non-parametric modeling study of short-term plasticity (STP) in the Schaffer collateral to hippocampal CA1 pyramidal neuron (SC) synapse. Parametric models in the form of sets of differential and algebraic equations have been proposed on the basis of the current understanding of biological mechanisms active within the system. Non-parametric Poisson–Volterra models are obtained herein from broadband experimental input–output data. The non-parametric model is shown to provide better prediction of the experimental output than a parametric model with a single set of facilitation/depression (FD) process. The parametric model is then validated in terms of its input–output transformational properties using the non-parametric model since the latter constitutes a canonical and more complete representation of the synaptic nonlinear dynamics. Furthermore, discrepancies between the experimentally-derived non-parametric model and the equivalent non-parametric model of the parametric model suggest the presence of multiple FD processes in the SC synapses. Inclusion of an additional set of FD process in the parametric model makes it replicate better the characteristics of the experimentally-derived non-parametric model. This improved parametric model in turn provides the requisite biological interpretability that the non-parametric model lacks.     

Non-parametric quantification of protein lysate arrays

MOTIVATION: Proteins play a crucial role in biological activity, so much can be learned from measuring protein expression and post-translational modification quantitatively. The reverse-phase protein lysate arrays allow us to quantify the relative expression levels of a protein in many different cellular samples simultaneously. Existing approaches to quantify protein arrays use parametric response curves fit to dilution series data. The results can be biased when the parametric function does not fit the data. RESULTS: We propose a non-parametric approach which adapts to any monotone response curve. The non-parametric approach is shown to be promising via both simulation and real data studies; it reduces the bias due to model misspecification and protects against outliers in the data. The non-parametric approach enables more reliable quantification of protein lysate arrays. AVAILABILITY: Code to implement the proposed method in the statistical package R is available at: http://odin.mdacc.tmc.edu/jhu/lysatearray-analysis/     

Parametric and non-parametric modeling of short-term synaptic plasticity. Part I: Computational study

Parametric and non-parametric modeling methods are combined to study the short-term plasticity (STP) of synapses in the central nervous system (CNS). The nonlinear dynamics of STP are modeled by means: (1) previously proposed parametric models based on mechanistic hypotheses and/or specific dynamical processes, and (2) non-parametric models (in the form of Volterra kernels) that transforms the presynaptic signals into postsynaptic signals. In order to synergistically use the two approaches, we estimate the Volterra kernels of the parametric models of STP for four types of synapses using synthetic broadband input–output data. Results show that the non-parametric models accurately and efficiently replicate the input–output transformations of the parametric models. Volterra kernels provide a general and quantitative representation of the STP.     

Comparing a template approach and complex bandpass filtering for single-trial analysis of auditory evoked M100.

Two methods for single-trial analysis were compared, an established parametric template approach and a recently proposed non-parametric method based on complex bandpass filtering. The comparison was carried out by means of pseudo-real simulations based on magnetoencephalography measurements of cortical responses to auditory signals. The comparison focused on amplitude and latency estimation of the M100 response. The results show that both methods are well suited for single-trial analysis of the auditory evoked M100. While both methods performed similarly with respect to latency estimation, the non-parametric approach was observed to be more robust for amplitude estimation. The non-parametric approach can thus be recommended as an additional valuable tool for single-trial analysis.     

The area between ROC curves,a non-parametric method to evaluate a biomarker for patient treatment selection

Treatment selection markers are generally sought for when the benefit of an innovative treatment in comparison with a reference treatment is considered, and this benefit is suspected to vary according to the characteristics of the patients. Classically, such quantitative markers are detected through testing a marker-by-treatment interaction in a parametric regression model. Most alternative methods rely on modeling the risk of event occurrence in each treatment arm or the benefit of the innovative treatment over the marker values, but with assumptions that may be difficult to verify. Herein, a simple non-parametric approach is proposed to detect and assess the general capacity of a quantitative marker for treatment selection when no overall difference in efficacy could be demonstrated between two treatments in a clinical trial. This graphical method relies on the area between treatment-arm-specific receiver operating characteristic curves (ABC), which reflects the treatment selection capacity of the marker. A simulation study assessed the inference properties of the ABC estimator and compared them with other parametric and non-parametric indicators. The simulations showed that the estimate of the ABC had low bias, power comparable to parametric indicators, and that its confidence interval had a good coverage probability (better than the other non-parametric indicator in some cases). Thus, the ABC is a good alternative to parametric indicators. The ABC method was applied to data of the PETACC-8 trial that investigated FOLFOX4 versus FOLFOX4 + cetuximab in stage III colon adenocarcinoma. It enabled the detection of a treatment selection marker: the DDR2 gene.     

Non-parametric change-point method for differential gene expression detection

Background

We proposed a non-parametric method, named Non-Parametric Change Point Statistic (NPCPS for short), by using a single equation for detecting differential gene expression (DGE) in microarray data. NPCPS is based on the change point theory to provide effective DGE detecting ability.

Methodology

NPCPS used the data distribution of the normal samples as input, and detects DGE in the cancer samples by locating the change point of gene expression profile. An estimate of the change point position generated by NPCPS enables the identification of the samples containing DGE. Monte Carlo simulation and ROC study were applied to examine the detecting accuracy of NPCPS, and the experiment on real microarray data of breast cancer was carried out to compare NPCPS with other methods.

Conclusions

Simulation study indicated that NPCPS was more effective for detecting DGE in cancer subset compared with five parametric methods and one non-parametric method. When there were more than 8 cancer samples containing DGE, the type I error of NPCPS was below 0.01. Experiment results showed both good accuracy and reliability of NPCPS. Out of the 30 top genes ranked by using NPCPS, 16 genes were reported as relevant to cancer. Correlations between the detecting result of NPCPS and the compared methods were less than 0.05, while between the other methods the values were from 0.20 to 0.84. This indicates that NPCPS is working on different features and thus provides DGE identification from a distinct perspective comparing with the other mean or median based methods.     

Detection of quadratic phase coupling between EEG signal components by nonparamatric and parametric methods of bispectral analysis]

Recently the assumption of the independence of individual frequency components in a signal has been rejected, for example, for the EEG during defined physiological states such as sleep or sedation [9, 10]. Thus, the use of higher-order spectral analysis capable of detecting interrelations between individual signal components has proved useful. The aim of the present study was to investigate the quality of various non-parametric and parametric estimation algorithms using simulated as well as true physiological data. We employed standard algorithms available for the MATLAB. The results clearly show that parametric bispectral estimation is superior to non-parametric estimation in terms of the quality of peak localisation and the discrimination from other peaks.     

Three-parameter lognormal distribution ubiquitously found in cDNA microarray data and its application to parametric data treatment

Background  

To cancel experimental variations, microarray data must be normalized prior to analysis. Where an appropriate model for statistical data distribution is available, a parametric method can normalize a group of data sets that have common distributions. Although such models have been proposed for microarray data, they have not always fit the distribution of real data and thus have been inappropriate for normalization. Consequently, microarray data in most cases have been normalized with non-parametric methods that adjust data in a pair-wise manner. However, data analysis and the integration of resultant knowledge among experiments have been difficult, since such normalization concepts lack a universal standard.     

Non-parametric smoothing of multivariate genetic distances in the analysis of spatial population structure at fine scale

Species dispersal studies provide valuable information in biological research. Restricted dispersal may give rise to a non-random distribution of genotypes in space. Detection of spatial genetic structure may therefore provide valuable insight into dispersal. Spatial structure has been treated via autocorrelation analysis with several univariate statistics for which results could dependent on sampling designs. New geostatistical approaches (variogram-based analysis) have been proposed to overcome this problem. However, modelling parametric variograms could be difficult in practice. We introduce a non-parametric variogram-based method for autocorrelation analysis between DNA samples that have been genotyped by means of multilocus-multiallele molecular markers. The method addresses two important aspects of fine-scale spatial genetic analyses: the identification of a non-random distribution of genotypes in space, and the estimation of the magnitude of any non-random structure. The method uses a plot of the squared Euclidean genetic distances vs. spatial distances between pairs of DNA-samples as empirical variogram. The underlying spatial trend in the plot is fitted by a non-parametric smoothing (LOESS, Local Regression). Finally, the predicted LOESS values are explained by segmented regressions (SR) to obtain classical spatial values such as the extent of autocorrelation. For illustration we use multivariate and single-locus genetic distances calculated from a microsatellite data set for which autocorrelation was previously reported. The LOESS/SR method produced a good fit providing similar value of published autocorrelation for this data. The fit by LOESS/SR was simpler to obtain than the parametric analysis since initial parameter values are not required during the trend estimation process. The LOESS/SR method offers a new alternative for spatial analysis.     

A novel statistical analysis of cnidocysts in acontiarian sea anemones (Cnidaria, Actiniaria) using generalized linear models with gamma errors

Comparative studies on cnidocysts, involving adequate statistical treatment, are very scarce. Classical statistical tests are frequently used assuming normal frequency distributions of capsule lengths, but many distributions are non-normal in acontiarian sea anemones. A traditional choice in these situations are non-parametric tests, although they are not as powerful as parametric tests. An extension of classical methods was developed by some authors; these models, called Generalized Linear Models (GLM), can be used under certain conditions with non-normal data. In view of the properties of our data, that are positive, skewed and with constant coefficient of variation, a GLM with gamma distribution and inverse link function was chosen to analyse the cnidae of acontia from the species Haliplanella lineata, Tricnidactis errans and Anthothoe chilensis. Graphical analysis of residuals showed that these assumptions were reasonable. This method allowed us to avoid transformation of data set and controversial cases in the limit of significance level. For this task, appropriate subroutines in GLIM language were written. In all cases highly significant differences were found between the specimens considered for every species and nematocyst type (b-rhabdoids, p-rhabdoids B1b and p-rhabdoids B2a).     

On the statistical evaluation of adherence assays

Parametric (unpaired t-test) and non-parametric (Mann-Whitney U-test) methods have been used in the evaluation of adherence assays on the non-antibiotic antimicrobial agent, Taurolin. In all but one case, where the anti-adherence effect was known to be marginal, both statistical methods gave similar results although there were some minor differences in the levels of significance achieved. The effect of the agent on the deviation of adherence data from normality was quantified by calculation of the skewness coefficient for each data set. A significant anti-adherence effect appears to result in a decrease in the skewness of the adherence assay data. It was concluded that either parametric or non-parametric statistical evaluation of adherence assay data is valid for large numbers of observations. In future studies of this type it is suggested that attention should also be given to the effect of the anti-adherence agent on the deviation of adherence data from normality as denoted by the skewness coefficient.     

On the statistical evaluation of adherence assays

Parametric (unpaired t -test) and non-parametric (Mann-Whitney U-test) methods have been used in the evaluation of adherence assays on the non-antibiotic antimicrobial agent, Taurolin. In all but one case, where the anti-adherence effect was known to be marginal, both statistical methods gave similar results although there were some minor differences in the levels of significance achieved. The effect of the agent on the deviation of adherence data from normality was quantified by calculation of the skewness coefficient for each data set. A significant anti-adherence effect appears to result in a decrease in the skewness of the adherence assay data. It was concluded that either parametric or non-parametric statistical evaluation of adherence assay data is valid for large numbers of observations. In future studies of this type it is suggested that attention should also be given to the effect of the anti-adherence agent on the deviation of adherence data from normality as denoted by the skewness coefficient.     

Variance Calculations for Direct Adjusted Survival Curves,with Applications to Testing for No Treatment Effect

Several investigators have recently constructed survival curves adjusted for imbalances in prognostic factors by a method which we call direct adjustment. We present methods for calculating variances of these direct adjusted survival curves and their differences. Estimates of the adjusted curves, their variances, and the variances of their differences are compared for non-parametric (Kaplan-Meier), semi-parametric (Cox) and parametric (Weibull) models applied to censored exponential data. Semi-parametric proportional hazards models were nearly fully efficient for estimating differences in adjusted curves, but parametric estimates of individual adjusted curves may be substantially more precise. Standardized differences between direct adjusted survival curves may be used to test the null hypothesis of no treatment effect. This procedure may prove especially useful when the proportional hazards assumption is questionable.     

Differential and trajectory methods for time course gene expression data

MOTIVATION: The issue of high dimensionality in microarray data has been, and remains, a hot topic in statistical and computational analysis. Efficient gene filtering and differentiation approaches can reduce the dimensions of data, help to remove redundant genes and noises, and highlight the most relevant genes that are major players in the development of certain diseases or the effect of drug treatment. The purpose of this study is to investigate the efficiency of parametric (including Bayesian and non-Bayesian, linear and non-linear), non-parametric and semi-parametric gene filtering methods through the application of time course microarray data from multiple sclerosis patients being treated with interferon-beta-1a. The analysis of variance with bootstrapping (parametric), class dispersion (semi-parametric) and Pareto (non-parametric) with permutation methods are presented and compared for filtering and finding differentially expressed genes. The Bayesian linear correlated model, the Bayesian non-linear model the and non-Bayesian mixed effects model with bootstrap were also developed to characterize the differential expression patterns. Furthermore, trajectory-clustering approaches were developed in order to investigate the dynamic patterns and inter-dependency of drug treatment effects on gene expression. RESULTS: Results show that the presented methods performed significant differently but all were adequate in capturing a small number of the potentially relevant genes to the disease. The parametric method, such as the mixed model and two Bayesian approaches proved to be more conservative. This may because these methods are based on overall variation in expression across all time points. The semi-parametric (class dispersion) and non-parametric (Pareto) methods were appropriate in capturing variation in expression from time point to time point, thereby making them more suitable for investigating significant monotonic changes and trajectories of changes in gene expressions in time course microarray data. Also, the non-linear Bayesian model proved to be less conservative than linear Bayesian correlated growth models to filter out the redundant genes, although the linear model showed better fit than non-linear model (smaller DIC). We also report the trajectories of significant genes-since we have been able to isolate trajectories of genes whose regulations appear to be inter-dependent.     

SLEB3 in systemic lupus erythematosus (SLE) is strongly related to SLE families ascertained through neuropsychiatric manifestations

Seizures and psychosis are neuropsychiatric (NP) manifestations of a large number of systemic lupus erythematosus (SLE) patients. Since NP manifestations were part of the SLE phenotype for some, but not all SLE affecteds, we hypothesized that those SLE patient families with NP manifestations might be more genetically homogeneous at loci important to NP-related SLE, and hence have increased power to detect linkage. We identified 23 families of European-American (EA) origin and 20 families of African-American (AA) origin, in which at least one SLE patient in each family was diagnosed with the presence of NP manifestations. A total of 318 microsatellite markers at an average marker density of 11 cM were genotyped. Uncertainty of the genetic model led us to perform the initial genome scan by a multipoint non-parametric allele sharing linkage method. Once the evidence of linkage was suggestive, we then performed parametric model-based linkage by maximizing the relevant parameters to define a parsimonious genetic model. We found the maximum multipoint parametric LOD score was 5.19 and the non-parametric linkage score (Zlr) was 3.12 ( P=9x10(-4)) for EA NP pedigrees at 4p16, previously identified as SLEB3. The segregation behavior of this linked locus suggests a dominant mode of inheritance with an almost 100% homogeneous genetic effect in these pedigrees. The results demonstrated a significant increase of LOD score to detect SLEB3 when the families were further ascertained through NP, compared with the analysis of all EA SLE families together.