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PubMed1988

Segregation analysis with uncertain ascertainment: application to Fanconi anemia.

A Bayesian solution for making inferences about segregation parameters with no information about the ascertainment is presented. Inferences about the segregation probability and the probability of being sporadic are made through the posterior marginal distribution of these parameters after integrating out the ascertainment probability, the nuisance parameter. The method was tested with real and simulated data and performed well. Original Fanconi anemia data, for which no information about the ascertainment was available, were then analyzed, with results that confirmed a monogenic autosomal recessive mode of inheritance.

Anemia, Aplastic↗
PubMed2005

Quantitative magnetic resonance spectroscopy: semi-parametric modeling and determination of uncertainties.

A semi-parametric approach for the quantitative analysis of magnetic resonance (MR) spectra is proposed and an uncertainty analysis is given. Single resonances are described by parametric models or by parametrized in vitro spectra and the baseline is determined nonparametrically by regularization. By viewing baseline estimation in a reproducing kernel Hilbert space, an explicit parametric solution for the baseline is derived. A Bayesian point of view is adopted to derive uncertainties, and the many parameters associated with the baseline solution are treated as nuisance parameters. The derived uncertainties formally reduce to Cramér-Rao lower bounds for the parametric part of the model in the case of a vanishing baseline. The proposed uncertainty calculation was applied to simulated and measured MR spectra and the results were compared to Cramér-Rao lower bounds derived after the nonparametrically estimated baselines were subtracted from the spectra. In particular, for high SNR and strong baseline contributions the proposed procedure yields a more appropriate characterization of the accuracy of parameter estimates than Crémer-Rao lower bounds, which tend to overestimate accuracy.

Bayes Theorem↗
PubMed2004

Synchronous cultures from the baby machine. A model for animal cells.

A baby-machine system that produces newborn Escherichia coli cells from cultures immobilised on a membrane was developed many years ago in an attempt to attain optimal synchrony with minimal disturbance of steady-state growth, and a model designed to characterise the nature and quality of the synchrony of such cells in a quantitative manner has been published. The baby machine has now been adapted for animal cells, and the present article is an attempt to modify the model to include these cells as well. The model consists of five elements, giving rise to five adjustable parameters (and a proportionality constant): a major, essentially synchronous group of cells with ages distributed normally about zero; a minor, random component from a steady-state population on the membrane that had undergone only very little age selection during the elution process; a fixed background count, to allow for the signals recorded by the electronic particle counter produced by debris and electronic noise; a time-shift, to account for differences between time of cell division and end of sample collection; and the coefficient of variation of the interdivision-time distribution, taken to be reciprocal-normal. It is this last feature, a reciprocal-normal rather than a Pearson type III interdivision-time distribution, that distinguishes this version of the model from its predecessor. The model is fitted by unconstrained non-linear least-squares to data from three different leukemia cell lines. The standard errors of the parameters are quite small in all cases, making their estimates highly significant; the quality of the fit is striking. The five parameters of the model can be divided into two nuisance parameters, two that are associated with the methodology and one that describes an inherent property of the cell itself; it turns out that both methodology parameters are zero in all three data sets studied. We also discuss the partition of the transition-time dispersion between the age distribution of the newborn cells and the age distribution of dividing cells and show that a reliable estimate of the corresponding parameters requires an experiment that extends over at least two and a half doubling times.

Animals↗
PubMed2005

A simple loglinear model for haplotype effects in a case-control study involving two unphased genotypes.

Because haplotypes may parsimoniously summarize the effect of genes on disease, there is great interest in using haplotypes in case-control studies of unphased genotype data. Previous methods for investigating haplotypes effects in case-control studies have not allowed for both of the following two scenarios that could have a large impact on results (i) departures from Hardy-Weinberg equilibrium in controls as well as cases, and (ii) an interactive effect of haplotypes and environmental covariates on the probability of disease. A new method is proposed that generalizes the model of Epstein and Satten to incorporate both (i) and (ii). Computations are relatively simple involving a single loglinear design matrix for parameters modeling the distribution of haplotype frequencies in controls, parameters modeling the effect of haplotypes and covariate-haplotype interactions on disease, and nuisance parameters required for correct inference. Based on simulations with realistic sample sizes, the method is recommended with data from two genotypes, a recessive or dominant model linking haplotypes to disease, and estimates of haplotype effects among haplotypes with a frequency greater than 10%. The methodology is most useful with candidate genotype pairs or for searching through pairs of genotypes when scenarios (i) and (ii) are likely. An example without a covariate illustrates the importance of modeling a departure from Hardy-Weinberg equilibrium in controls.

Journal Article↗
PubMed1999

Approximate Monte Carlo conditional inference in exponential families.

This article presents an algorithm for approximate frequentist conditional inference on two or more parameters for any regression model in the Generalized Linear Model (GLIM) family. We thereby extend highly accurate inference beyond the cases of logistic regression and contingency tables implimented in commercially available software. The method makes use of the double saddlepoint approximations of Skovgaard (1987, Journal of Applied Probability 24, 875-887) and Jensen (1992, Biometrika 79, 693-703) to the conditional cumulative distribution function of a sufficient statistic given the remaining sufficient statistics. This approximation is then used in conjunction with noniterative Monte Carlo methods to generate a sample from a distribution that approximates the joint distribution of the sufficient statistics associated with the parameters of interest conditional on the observed values of the sufficient statistics associated with the nuisance parameters. This algorithm is an alternate approach to that presented by Kolassa and Tanner (1994, Journal of the American Statistical Association 89, 697-702), in which a Markov chain is generated whose equilibrium distribution under certain regularity conditions approximates the joint distribution of interest. In Kolassa and Tanner (1994), the Gibbs sampler was used in conjunction with these univariate conditional distribution function approximations. The method of this paper does not require the construction and simulation of a Markov chain, thus avoiding the need to develop regularity conditions under which the algorithm converges and the need for the data analyst to check convergence of the particular chain. Examples involving logistic and truncated Poisson regression are presented.

Algorithms↗
PubMed2003

Likelihood approaches to sensory coding in auditory cortex.

Likelihood methods began their evolution in the early 1920s with R A Fisher, and have developed into a rich framework for inferential statistics. This framework offers tools for the analysis of the differential geometry of the full likelihood function based on observed data. We examine likelihood functions derived from inverse Gaussian (IG) probability density models of cortical ensemble responses of single units. Specifically, we investigate the problem of sound localization from the observation of an ensemble of neural responses recorded from the primary (Al) field of the auditory cortex. The problem is framed as a probabilistic inverse problem with multiple sources of ambiguity. Observed and expected Fisher information are defined for the IG cortical ensemble likelihood functions. Receptive field functions of multiple acoustic parameters are constructed and linked to the IG density. The impact of estimating multiple acoustic parameters related to the direction of a sound is discussed, and the implications of eliminating nuisance parameters are considered. We examine the degree of acuity afforded by a small ensemble of cortical neurons for locating sounds in space, and show the predicted patterns of estimation errors, which tend to follow psychophysical performance.

Acoustic Stimulation↗
PubMed2000

Ability of geometric morphometric methods to estimate a known covariance matrix.

Landmark-based morphometric methods must estimate the amounts of translation, rotation, and scaling (or, nuisance) parameters to remove nonshape variation from a set of digitized figures. Errors in estimates of these nuisance variables will be reflected in the covariance structure of the coordinates, such as the residuals from a superimposition, or any linear combination of the coordinates, such as the partial warp and standard uniform scores. A simulation experiment was used to compare the ability of the generalized resistant fit (GRF) and a relative warp analysis (RWA) to estimate known covariance matrices with various correlations and variance structures. Random covariance matrices were perturbed so as to vary the magnitude of the average correlation among coordinates, the number of landmarks with excessive variance, and the magnitude of the excessive variance. The covariance structure was applied to random figures with between 6 and 20 landmarks. The results show the expected performance of GRF and RWA across a broad spectrum of conditions. The performance of both GRF and RWA depended most strongly on the number of landmarks. RWA performance decreased slightly when one or a few landmarks had excessive variance. GRF performance peaked when approximately 25% of the landmarks had excessive variance. In general, both RWA and GRF performed better at estimating the direction of the first principal axis of the covariance matrix than the structure of the entire covariance matrix. RWA tended to outperform GRF when > approximately 75% of the coordinates had excessive variance. When < 75% of the coordinates had excessive variance, the relative performance of RWA and GRF depended on the magnitude of the excessive variance; when the landmarks with excessive variance had standard deviations (sigma) > or = 4 sigma minimum, GRF regularly outperformed RWA.

Analysis of Variance↗
PubMed2005

Information geometry of interspike intervals in spiking neurons.

An information geometrical method is developed for characterizing or classifying neurons in cortical areas, whose spike rates fluctuate in time. Under the assumption that the interspike intervals of a spike sequence of a neuron obey a gamma process with a time-variant spike rate and a fixed shape parameter, we formulate the problem of characterization as a semiparametric statistical estimation, where the spike rate is a nuisance parameter. We derive optimal criteria from the information geometrical viewpoint when certain assumptions are added to the formulation, and we show that some existing measures, such as the coefficient of variation and the local variation, are expressed as estimators of certain functions under the same assumptions.

Action Potentials↗
PubMed1993

Relative risk, risk difference and rate difference models for sparse stratified data: a pseudo likelihood approach.

We consider a relative risk and a risk difference model for binomial data, and a rate difference model for Poisson (person year) data. It is assumed that the data are stratified in a large number of small strata. If each stratum has its own parameter in the model, then, due to the large number of parameters, straightforward maximum likelihood leads to inconsistent estimates of the relevant parameters. By contrast to the logistic model, conditioning on the number of events per stratum does not help in eliminating the stratum nuisance parameters. We propose a pseudo likelihood method to overcome these consistency problems. The resulting pseudo maximum likelihood estimates can easily be computed with standard statistical software. Our approach gives a more general framework for the Mantel-Haenszel type estimators proposed in the literature. In the special case of a series of 2 x 2 tables, for the risk and rate difference models, our approach yields exactly these ad hoc Mantel-Haenszel estimators, while for the relative risk model it gives a close approximation of the Mantel-Haenszel relative risk estimator. For the regression models corresponding to the association measures relative risk, risk difference and rate difference, our method provides analogues of conditional logistic regression, which were not previously available.

Analysis of Variance↗
PubMed2004

Frailty models for arbitrarily censored and truncated data.

In this paper, we propose a frailty model for statistical inference in the case where we are faced with arbitrarily censored and truncated data. Our results extend those of Alioum and Commenges (1996), who developed a method of fitting a proportional hazards model to data of this kind. We discuss the identifiability of the regression coefficients involved in the model which are the parameters of interest, as well as the identifiability of the baseline cumulative hazard function of the model which plays the role of the infinite dimensional nuisance parameter. We illustrate our method with the use of simulated data as well as with a set of real data on transfusion-related AIDS.

Acquired Immunodeficiency Syndrome↗
PubMed2002

HLODs, trait models, and ascertainment: implications of admixture for parameter estimation and linkage detection.

Maximizing the homogeneity lod is known to be an appropriate procedure for estimating parameters of the trait model in an approximately 'ascertainment assumption free' (AAF) manner. We have investigated whether this same property also holds for the heterogeneity lod (HLOD). We show that, when the genetic models at linked and unlinked loci differ, HLODs are not AAF, and maximizing the HLOD yields parameter estimates that are for all practical purposes meaningless; indeed, the admixture parameter alpha does not even measure the proportion of linked families within the sample, as is commonly supposed. In spite of this, our results confirm a large body of evidence supporting the use of HLODs as robust tools for linkage detection, and suggest further that maximizing the HLOD over both alpha and parameters of the trait model can improve accuracy in estimation of the recombination fraction theta;. These findings have important implications for the optimal handling of nuisance parameters in linkage analysis, particularly when evaluating the evidence for or against linkage based on multiple independent heterogeneous sets of data.

Animals↗
PubMed1998

The use of simulation and bootstrap in information-based group sequential studies.

In this paper, we present an information-based design and monitoring procedure which applies to any type of model for any type of group sequential study provided there is a unique parameter of interest one can estimate efficiently. Simulation techniques are described to handle the design phase of this procedure. Since designs depend on potentially unreliable guesses of nuisance parameters, we propose a bootstrap method that uses the information available at the interim analysis times to generate projections and prediction intervals for the time at which the study will be fully powered. A monitoring board can use this information to decide whether a redesign of the trial is warranted. We also show how to use simulation to redesign studies in progress. We illustrate all of these techniques with data from AIDS Clinical Trial Group Protocol 021.

AIDS-Related Opportunistic Infections↗
PubMed2006

Power analyses for correlations from clustered study designs.

Power analysis constitutes an important component of modern clinical trials and research studies. Although a variety of methods and software packages are available, almost all of them are focused on regression models, with little attention paid to correlation analysis. However, the latter is arguably a simpler and more appropriate approach for modelling concurrent events, especially in psychosocial research. In this paper, we discuss power and sample size estimation for correlation analysis arising from clustered study designs. Our approach is based on the asymptotic distribution of correlated Pearson-type estimates. Although this asymptotic distribution is easy to use in data analysis, the presence of a large number of parameters creates a major problem for power analysis due to the lack of real data to estimate them. By introducing a surrogacy-type assumption, we show that all nuisance parameters can be eliminated, making it possible to perform power analysis based only on the parameters of interest. Simulation results suggest that power and sample size estimates obtained under the proposed approach are robust to this assumption.

Clinical Trials as Topic↗
PubMed2006

Sample size recalculation in internal pilot study designs: a review.

The adequacy of sample size is important to clinical trials. In the planning phase of a trial, however, the investigators are often quite uncertain about the sizes of parameters which are needed for sample size calculations. A solution to this problem is mid-course recalculation of the sample size during the ongoing trial. In internal pilot study designs, nuisance parameters are estimated on the basis of interim data and the sample size is adjusted accordingly. This review attempts to give an overview on the available methods. It is written not only for biometricians who are already familar with the the topic and wish to update their knowledge but also for users new to the subject.

Clinical Trials as Topic↗
PubMed2006

Bayesian approach for quantifying the uncertainty of neutron doses derived from spectrometric measurements.

Bayesian methods provide a unified framework for combining information in the presence of uncertainty. All uncertainties that enter into the description of a measurement are modelled using probability distributions, and these are handled according to the rules of probability theory, ensuring that the approach is free of inconsistencies. The final result of the analysis is the full probability distribution for the parameter of interest, and from this distribution an appropriate uncertainty interval can be obtained. Some of the advantages of a Bayesian analysis include a straightforward approach to the problem of dealing with nuisance parameters, the ability to incorporate prior information in a natural way and the flexibility that is necessary for a realistic modelling of the measurement process. As an example, the problem of deriving neutron dose estimates and their uncertainties based on measurements carried out using a Bonner sphere spectrometer is considered.

Bayes Theorem↗
PubMed2006

Estimating haplotype relative risks in complex disease from unphased SNPs data in families using a likelihood adjusted for ascertainment.

The understanding of complex diseases and insights to improve their medical management may be achieved through the deduction of how specific haplotypes may play a joint effect to change relative risk information. In this paper we describe an ascertainment adjusted likelihood-based method to estimate haplotype relative risks using pooled family data coming from association and/or linkage studies that were used to identify specific haplotypes. Haplotype-based analysis tends to require a large amount of parameters to capture all the information that leads to efficiency problems. An adaptation of the Stochastic Expectation Maximization algorithm is used for haplotypes inference from genotypic data and to reduce the number of nuisance parameters for risk estimation. Using different simulations, we show that this method provides unbiased relative risk estimates even in case of departure from Hardy-Weinberg equilibrium.

Algorithms↗
PubMed1993

Exact conditional and unconditional sample size for pair-matched studies with binary outcome: a practical guide.

Tables of sample sizes for pair-matched studies with binary outcome are presented. They are based on conditional and unconditional approaches using the 'exact' (binomial) test. An approximate procedure is suggested to estimate the sample size for parameter values that do not correspond exactly with table entries. The procedure utilizes a minor modification of the large-sample formula given by Connett et al. A practical strategy for estimating the overall sample size in the presence of a nuisance parameter (the proportion of discordant pairs) is recommended. An example from a proposed clinical trial is given.

Binomial Distribution↗
PubMed1994

Constructing confidence intervals for QTL location.

We describe a method for constructing the confidence interval of the QTL location parameter. This method is developed in the local asymptotic framework, leading to a linear model at each position of the putative QTL. The idea is to construct a likelihood ratio test, using statistics whose asymptotic distribution does not depend on the nuisance parameters and in particular on the effect of the QTL. We show theoretical properties of the confidence interval built with this test, and compare it with the classical confidence interval using simulations. We show in particular, that our confidence interval has the correct probability of containing the true map location of the QTL, for almost all QTLs, whereas the classical confidence interval can be very biased for QTLs having small effect.

Chromosome Mapping↗