A global goodness-of-fit statistic for Cox regression models

In this paper, a global goodness-of-fit test statistic for a Cox regression model, which has an approximate chi-squared distribution when the model has been correctly specified, is proposed. Our goodness-of-fit statistic is global and has power to detect if interactions or higher order powers of covariates in the model are needed. The proposed statistic is similar to the Hosmer and Lemeshow (1980, Communications in Statistics A10, 1043-1069) goodness-of-fit statistic for binary data as well as Schoenfeld's (1980, Biometrika 67, 145-153) statistic for the Cox model. The methods are illustrated using data from a Mayo Clinic trial in primary billiary cirrhosis of the liver (Fleming and Harrington, 1991, Counting Processes and Survival Analysis), in which the outcome is the time until liver transplantation or death. The are 17 possible covariates. Two Cox proportional hazards models are fit to the data, and the proposed goodness-of-fit statistic is applied to the fitted models.     

Power of the classical twin design revisited.

Statistical power of the classical twin design was revisited. The approximate sampling variances of a least-squares estimate of the heritability in a univariate analysis and estimate of the genetic correlation coefficient in a bivariate analysis were derived analytically for the ACE model. Statistical power to detect additive genetic variation under the ACE model was derived analytically for least-squares, goodness-of-fit and maximum likelihood-based test statistics. The noncentrality parameter for the likelihood ratio test statistic is shown to be a simple function of the MZ and DZ intraclass correlation coefficients and the proportion of MZ and DZ twin pairs in the sample. All theoretical results were validated using simulation. The derived expressions can be used to calculate power of the classical twin design in a simple and rapid manner.     

Use of the score test as a goodness-of-fit measure of the covariance structure in genetic analysis of longitudinal data

Model selection is an essential issue in longitudinal data analysis since many different models have been proposed to fit the covariance structure. The likelihood criterion is commonly used and allows to compare the fit of alternative models. Its value does not reflect, however, the potential improvement that can still be reached in fitting the data unless a reference model with the actual covariance structure is available. The score test approach does not require the knowledge of a reference model, and the score statistic has a meaningful interpretation in itself as a goodness-of-fit measure. The aim of this paper was to show how the score statistic may be separated into the genetic and environmental parts, which is difficult with the likelihood criterion, and how it can be used to check parametric assumptions made on variance and correlation parameters. Selection of models for genetic analysis was applied to a dairy cattle example for milk production.     

A chi-square goodness-of-fit analysis of dependent resource selection data

The chi2 goodness-of-fit test is commonly used for testing if animals use resources in proportion to availability. This method assumes independence of resource selection among animals. In reality, this assumption is violated if animals display antisocial or gregarious behavior. Data from a study of sharp-tailed grouse in eastern Washington suggested some dependency among observations. Realizing that this dependency can have a great influence on inference for resource selection data, we develop a technique to incorporate information on dependent observations through a simple adjustment of the usual goodness-of-fit statistic. We also demonstrate how confidence intervals on proportional use may be modified for dependent observations. Simulation is used to compare our method to other methods.     

Measures of Imbalance for Unbalanced Models

In this paper we present a procedure to measure the degree of imbalance of an unbalanced data set. The procedure is based on choosing an appropriate loglinear model for the subclass frequencies of the data. A measure of imbalance is then introduced as some function of the chi-squared statistic used in the goodness-of-fit test for the loglinear model. The proposed procedure can also be used to measure departures from certain types of balance, such as proportionality of subclass frequencies, partial balance, and last-stage uniformity.     

Testing goodness-of-fit in logistic case-control studies

We present a goodness-of-fit test for the logistic regressionmodel under case-control sampling. The test statistic is constructedvia a discrepancy between two competing kernel density estimatorsof the underlying conditional distributions given case-controlstatus. The proposed goodness-of-fit test is shown to comparevery favourably with previously proposed tests for case-controlsampling in terms of power. The test statistic can be easilycomputed as a quadratic form in the residuals from a prospectivelogistic regression maximum likelihood fit. In addition, theproposed test is affine invariant and has an alternative representationin terms of empirical characteristic functions.     

Testing Genetic Association by Regressing Genotype over Multiple Phenotypes

Complex disorders are typically characterized by multiple phenotypes. Analyzing these phenotypes jointly is expected to be more powerful than dealing with one of them at a time. A recent approach (O''Reilly et al. 2012) is to regress the genotype at a SNP marker on multiple phenotypes and apply the proportional odds model. In the current research, we introduce an explicit expression for the score test statistic and its non-centrality parameter that determines its power. Same simulation studies as those reported in Galesloot et al. (2014) were conducted to assess its performance. We demonstrate by theoretical arguments and simulation studies that, despite its potential usefulness for multiple phenotypes, the proportional odds model method can be less powerful than regular methods for univariate traits. We also introduce an implementation of the proposed score statistic in an R package named iGasso.     

Goodness-of-fit in generalized nonlinear mixed-effects models

In recent years, generalized linear and nonlinear mixed-effects models have proved to be powerful tools for the analysis of unbalanced longitudinal data. To date, much of the work has focused on various methods for estimating and comparing the parameters of mixed-effects models. Very little work has been done in the area of model selection and goodness-of-fit, particularly with respect to the assumed variance-covariance structure. In this paper, we present a goodness-of-fit statistic which can be used in a manner similar to the R2 criterion in linear regression for assessing the adequacy of an assumed mean and variance-covariance structure. In addition, we introduce an approximate pseudo-likelihood ratio test for testing the adequacy of the hypothesized convariance structure. These methods are illustrated and compared to the usual normal theory likelihood methods (Akaike's information criterion and the likelihood ratio test) using three examples. Simulation results indicate the pseudo-likelihood ratio test compares favorably with the standard normal theory likelihood ratio test, but both procedures are sensitive to departures from normality.     

An information ratio-based goodness-of-fit test for copula models on censored data

Copula is a popular method for modeling the dependence among marginal distributions in multivariate censored data. As many copula models are available, it is essential to check if the chosen copula model fits the data well for analysis. Existing approaches to testing the fitness of copula models are mainly for complete or right-censored data. No formal goodness-of-fit (GOF) test exists for interval-censored or recurrent events data. We develop a general GOF test for copula-based survival models using the information ratio (IR) to address this research gap. It can be applied to any copula family with a parametric form, such as the frequently used Archimedean, Gaussian, and D-vine families. The test statistic is easy to calculate, and the test procedure is straightforward to implement. We establish the asymptotic properties of the test statistic. The simulation results show that the proposed test controls the type-I error well and achieves adequate power when the dependence strength is moderate to high. Finally, we apply our method to test various copula models in analyzing multiple real datasets. Our method consistently separates different copula models for all these datasets in terms of model fitness.     

Phenostat: visualization and statistical tool for analysis of phenotyping data

The effective extraction of information from multidimensional data sets derived from phenotyping experiments is a growing challenge in biology. Data visualization tools are important resources that can aid in exploratory data analysis of complex data sets. Phenotyping experiments of model organisms produce data sets in which a large number of phenotypic measures are collected for each individual in a group. A critical initial step in the analysis of such multidimensional data sets is the exploratory analysis of data distribution and correlation. To facilitate the rapid visualization and exploratory analysis of multidimensional complex trait data, we have developed a user-friendly, web-based software tool called Phenostat. Phenostat is composed of a dynamic graphical environment that allows the user to inspect the distribution of multiple variables in a data set simultaneously. Individuals can be selected by directly clicking on the graphs and thus displaying their identity, highlighting corresponding values in all graphs, allowing their inclusion or exclusion from the analysis. Statistical analysis is provided by R package functions. Phenostat is particularly suited for rapid distribution and correlation analysis of subsets of data. An analysis of behavioral and physiologic data stemming from a large mouse phenotyping experiment using Phenostat reveals previously unsuspected correlations. Phenostat is freely available to academic institutions and nonprofit organizations and can be used from our website at .     

MIR: a versatile program for the statistical analysis of enzyme kinetic data

We have developed a package program for the estimation of Michaelis-Menten parameters for enzymes that conform to different kinetic mechanisms. Data from different experimental schemes can be fitted with appropriate weighing factors to any of 6 mathematical models, corresponding to 5 kinetic mechanisms: ordered bi-bi, Theorell-Chance, rapid equilibrium random bi-bi, rapid equilibrium ordered bi-bi and ping pong bi-bi. The program also performs a significance test to discriminate between different candidate models. To illustrate the performance of the program, real data from kinetic experiments with glucose 6-phosphate from Leuconostoc mesenteroides have been fitted to different mathematical models, and the results are discussed. The program can be easily implemented for the fitting of kinetic data to any other model.     

Smooth tests for the zero-inflated poisson distribution

In this article we construct three smooth goodness-of-fit tests for testing for the zero-inflated Poisson (ZIP) distribution against general smooth alternatives in the sense of Neyman. We apply our tests to a data set previously claimed to be ZIP distributed, and show that the ZIP is not a good model to describe the data. At rejection of the null hypothesis of ZIP, the individual components of the test statistic, which are directly related to interpretable parameters in a smooth model, may be used to gain insight into an alternative distribution.     

Integrated function of a kinetic proofreading mechanism: steady-state analysis testing internal consistency of data obtained in vivo and in vitro and predicting parameter values

Experimental measurements of the kinetic mechanism involving isoleucyl-tRNA synthetase proofreading valyl-tRNAIle in Escherichia coli have been incorporated into the conventional Michaelis-Menten model for this system. The model was subjected to a detailed mathematical analysis in the steady state. The results of this analysis provide an excellent illustration of the value of integrating fragmentary data into a model of the intact system. (1) Such integration provides a rigorous test for consistency of the individual measurements. For the above synthetase system, the published experimental data were found to be internally inconsistent. (2) Such integration predicts which experimental data are most suspect. In this case, one of the three most questionable measurements, the isoleucine pool size in vivo, was found upon reexamination to be in error by 10-15-fold. Correction of this error produced a self-consistent set of parameter values. (3) The integrated analysis provides predictions for various parameter values. In many cases, these predictions provide estimates for parameter values that are difficult to determine directly or that have yet to be measured experimentally. (4) A sensitivity analysis provides an indication of the relative importance of various parameter values and, hence, an indication of where future experimental effort might be focused most profitably.     

Analysis of the volume of red blood cells: application of the expectation-maximization algorithm to grouped data from the doubly-truncated lognormal distribution

In accordance with general principles recommended by the International Committee for Standardization in Haematology (1982, Journal of Clinical Pathology 35, 1320-1322), we have developed statistical methods for the analysis of red cell volume distributions. To select an appropriate reference distribution for goodness-of-fit testing, we derived a mathematical model of erythropoiesis that predicted a lognormal form for the distribution of erythrocyte volumes. Model predictions were then tested using samples obtained from 50 healthy individuals. Each grouped red cell volume distribution was doubly-truncated to eliminate artifactual frequency counts. Distribution parameter estimates were computed using the expectation-maximization algorithm, a missing information technique. Results of the one-sample chi-square goodness-of-fit test showed a fairly even distribution of P-values over the interval. Examples of the application of these statistical procedures to distributions from patients with anemia are given. Our results suggest that, for the analysis of red blood cell volumes, (i) parameter estimation should be made with the expectation-maximization method, and (ii) the truncated lognormal distribution should be used as a reference distribution for goodness-of-fit testing. This method could be applied to any set of grouped doubly-truncated data which, after transformation, follows the normal model.     

A convenient and adaptable package of DNA sequence analysis programs for microcomputers

We describe a package of DNA data handling and analysis programs designed for microcomputers. The package is convenient for immediate use by persons with little or no computer experience, and has been optimized by trial in our group for a year. By typing a single command, the user enters a system which asks questions or gives instructions in English. The system will enter, alter, and manage sequence files or a restriction enzyme library. It generates the reverse complement, translates, calculates codon usage, finds restriction sites, finds homologies with various degrees of mismatch, and graphs amino acid composition or base frequencies. A number of options for data handling and printing can be used to produce figures for publication. The package will be available in ANSI Standard FORTRAN for use with virtually any FORTRAN compiler.     

A goodness-of-fit test for multinomial logistic regression

This article presents a score test to check the fit of a logistic regression model with two or more outcome categories. The null hypothesis that the model fits well is tested against the alternative that residuals of samples close to each other in covariate space tend to deviate from the model in the same direction. We propose a test statistic that is a sum of squared smoothed residuals, and show that it can be interpreted as a score test in a random effects model. By specifying the distance metric in covariate space, users can choose the alternative against which the test is directed, making it either an omnibus goodness-of-fit test or a test for lack of fit of specific model variables or outcome categories.     

Parameter estimation in topological analysis of binary tree structures

Different types of random binary topological trees (like neuronal processes and rivers) occur with relative frequencies that can be explained in terms of growth models. It will be shown how the model parameter determining the mode of growth can be estimated with the maximum likelihood procedure from observed data. Monte Carlo simulations were used to study the distributional properties of this estimator which appeared to have a negligible bias. It is shown that the minimum chi-square procedure yields an estimate that is very close to the maximum likelihood estimate. Moreover, the goodness-of-fit of the growth model can be inferred directly from the chi-square statistic. To illustrate the procedures we examined axonal trees from the goldfish tectum. A notion of complete partition randomness is presented as an alternative to our growth hypotheses.     

Comparisons of predictive values of binary medical diagnostic tests for paired designs

Positive and negative predictive values of a diagnostic test are key clinically relevant measures of test accuracy. Surprisingly, statistical methods for comparing tests with regard to these parameters have not been available for the most common study design in which each test is applied to each study individual. In this paper, we propose a statistic for comparing the predictive values of two diagnostic tests using this paired study design. The proposed statistic is a score statistic derived from a marginal regression model and bears some relation to McNemar's statistic. As McNemar's statistic can be used to compare sensitivities and specificities of diagnostic tests, parameters that condition on disease status, our statistic can be considered as an analog of McNemar's test for the problem of comparing predictive values, parameters that condition on test outcome. We report on the results of a simulation study designed to examine the properties of this test under a variety of conditions. The method is illustrated with data from a study of methods for diagnosis of coronary artery disease.     

FLOSS: flexible ordered subset analysis for linkage mapping of complex traits

The FLOSS software package is a flexible framework for ordered subset analysis. FLOSS is specifically designed for use with the Merlin linkage analysis package, but FLOSS can be used with any linkage analysis software package that reports NPL Z-scores for each locus and family. When FLOSS is used with the Merlin linkage analysis package, one can use either non-parametric Z-scores or Kong and Cox linear allele sharing model LOD scores. Monte Carlo P-values are calculated using a permutation test with an efficient Besag-Clifford sequential stopping rule. FLOSS also has a flexible tool for assigning family covariate scores from Merlin input files. FLOSS includes user documentation and is written in Java for easy portability. The FLOSS source code is documented and designed to be extensible.