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Results for “Nuisance parameters”

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8 recordsLinked to original sources

PubMed2000

Linkage analysis in the presence of errors III: marker loci and their map as nuisance parameters.

In linkage and linkage disequilibrium (LD) analysis of complex multifactorial phenotypes, various types of errors can greatly reduce the chance of successful gene localization. The power of such studies-even in the absence of errors-is quite low, and, accordingly, their robustness to errors can be poor, especially in multipoint analysis. For this reason, it is important to deal with the ramifications of errors up front, as part of the analytical strategy. In this study, errors in the characterization of marker-locus parameters-including allele frequencies, haplotype frequencies (i.e., LD between marker loci), recombination fractions, and locus order-are dealt with through the use of profile likelihoods maximized over such nuisance parameters. It is shown that the common practice of assuming fixed, erroneous values for such parameters can reduce the power and/or increase the probability of obtaining false positive results in a study. The effects of errors in assumed parameter values are generally more severe when a larger number of less informative marker loci, like the highly-touted single nucleotide polymorphisms (SNPs), are analyzed jointly than when fewer but more informative marker loci, such as microsatellites, are used. Rather than fixing inaccurate values for these parameters a priori, we propose to treat them as nuisance parameters through the use of profile likelihoods. It is demonstrated that the power of linkage and/or LD analysis can be increased through application of this technique in situations where parameter values cannot be specified with a high degree of certainty.

Alleles↗

PubMed1992

A Gibbs sampling approach to linkage analysis.

We present a Monte Carlo approach to estimation of the recombination fraction theta and the profile likelihood for a dichotomous trait and a single marker gene with 2 alleles. The method is an application of a technique known as 'Gibbs sampling', in which random samples of each of the unknowns (here genotypes, theta and nuisance parameters, including the allele frequencies and the penetrances) are drawn from their posterior distributions, given the data and the current values of all the other unknowns. Upon convergence, the resulting samples derive from the marginal distribution of all the unknowns, given only the data, so that the uncertainty in the specification of the nuisance parameters is reflected in the variance of the posterior distribution of theta. Prior knowledge about the distribution of theta and the nuisance parameters can be incorporated using a Bayesian approach, but adoption of a flat prior for theta and point priors for the nuisance parameters would correspond to the standard likelihood approach. The method is easy to program, runs quickly on a microcomputer, and could be generalized to multiple alleles, multipoint linkage, continuous phenotypes and more complex models of disease etiology. The basic approach is illustrated by application to data on cholesterol levels and an a low-density lipoprotein receptor gene in a single large pedigree.

Animals↗

PubMed1977

Sequential allocation in clinical trials comparing two exponential survival curves.

The problem of comparing two medical treatments with respect to survival is considered. Treatment outcome is assumed to follow an exponential distribution. The ratio of expected survivals associated with the two treatments is the clinical parameter of interest. A nuisance parameter is present, but it is removed by an invariance reduction and a sequential probability ratio test is applied to the invariant likelihood ratio. A class of data-dependent treatment assignment rules is identified over which the probability of correct treatment selection at the termination of the trial is approximately constant. A cost function, the weighted sum of total patients in the trial and the number assigned to the inferior treatment is introduced, and a treatment allocation rule conjectured to minimize the expected cost is constructed. Both analytic and simulation results show that it is an improvement over rules previously proposed. The methodology contained herein can be used to construct near-optimal rules in other testing contexts.

Biometry↗

PubMed1979

Analysis of life tables with grouping and withdrawals.

A number of individuals is observed at the beginning of a period. At the end of the period the number is surviving, the number who have died and the number who have withdrawn are noted. From these three numbers it is required to estimate the death rate for the period. All relevant quantities are supposed independent and identically distributed for the individuals. The likelihood is calculated and found to depend on two parameters, other than the death rate, and to be unidenttifiable so that no consistent estimators exist. For large numbers, the posterior distribution of the death rate is approximated by a normal distribution whose mean is the root of a quadratic equation and whose variance is the sum of two terms; the first is proportional to the reciprocal of the number of individuals, as usually happens with a consistent estimator; the second does not tend to zero and depends on initial opinions about one of the nuisance parameters. The paper is a simple exercise in the routine use of coherent, Bayesian methodology. Numerical calucations illustrate the results.

Actuarial Analysis↗

PubMed1992

Exact unconditional tables for significance testing in the 2 x 2 multinomial trial.

This paper presents tables analogous to T-tables for use in the 2 x 2 multinomial trial, where the continuity corrected Z-statistic is used to make exact unconditional inference. This is the first solution of a discrete exact unconditional inference problem involving a multivariate nuisance parameter for which no ancillary statistic exists.

Bias↗

PubMed1992

Bayesian analysis of stochastic constraints in structural equation models.

Structural equation models are analysed in the presence of stochastic constraints. Based on a Bayesian perspective, a prior distribution on nuisance parameters in the unknown covariance matrix of error measurements with stochastic constraints is considered. An iterative procedure is implemented to produce the various Bayesian estimates with stochastic constraints. A simulation study is conducted to illustrate the accuracy and behaviour of this Bayesian approach. A real-life example is provided to illustrate the theory.

Bayes Theorem↗

PubMed2025

Simultaneous inference for generalized linear models with unmeasured confounders.

Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes. However, due to unmeasured confounders, many standard statistical approaches may be substantially biased. This paper investigates the large-scale hypothesis testing problem for multivariate generalized linear models in the presence of confounding effects. Under arbitrary confounding mechanisms, we propose a unified statistical estimation and inference framework that harnesses orthogonal structures and integrates linear projections into three key stages. It begins by disentangling marginal and uncorrelated confounding effects to recover the latent coefficients. Subsequently, latent factors and primary effects are jointly estimated through lasso-type optimization. Finally, we incorporate projected and weighted bias-correction steps for hypothesis testing. Theoretically, we establish the identification conditions of various effects and non-asymptotic error bounds. We show effective Type-I error control of asymptotic-tests as sample and response sizes approach infinity. Numerical experiments demonstrate that the proposed method controls the false discovery rate by the Benjamini-Hochberg procedure and is more powerful than alternative methods. By comparing single-cell RNA-seq counts from two groups of samples, we demonstrate the suitability of adjusting confounding effects when significant covariates are absent from the model.

Hidden variables↗

PubMed1992

Role of the alveolar macrophage in lung injury: studies with ultrafine particles.

We conducted a series of experiments with ultrafine particles (approximately 20 nm) and larger particles (less than 200 nm) of "nuisance" dusts to evaluate the involvement of alveolar macrophages (AM) in particle-induced lung injury and particle translocation in rats. After intratracheal instillation of both ultrafine particles and larger particles of TiO2, we found a highly increased interstitial access of the ultrafine particles combined with a large acute inflammatory reaction as determined by lung lavage parameters. An additional experiment revealed that intratracheal instillation of phagocytized ultrafine TiO2 particles (inside AM) prevented both the pulmonary inflammatory reaction and the interstitial access of the ultrafine particles. Another experiment showed that the influx of polymorphonuclear cells (PMN) into the alveolar space unexpectedly decreased with higher doses of ultrafine particles, whereas alveolar epithelial permeability (protein leakage) increased. The divergence between PMN influx into the alveolar space and changes in alveolar epithelial permeability implies that they are separate events. Pulmonary inflammatory parameters determined by lung lavage analysis correlated best with the surface area of the retained particles rather than with their mass, volume, or numbers. Because higher doses resulted in an increased interstitialized fraction of particles, we suggest that inflammatory events induced by particles in the interstitial space can modify the inflammation in the alveolar space detectable by lung lavage. Our results demonstrate the dual role of AM for modifying particle-induced lung injury, i.e., both preventing such injury and contributing to it. We conclude that the increased pulmonary toxicity of ultrafine particles is related to their larger surface area and to their increased interstitial access.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗