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Results for “Likelihood Functions”

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PubMed2004

Increasing incidence of Type 1 diabetes--role for genes?

BACKGROUND: The incidence of Type 1 diabetes (T1DM) is increasing fast in many populations. The reasons for this are not known, although an increase in the penetrance of the diabetes-associated alleles, through changes in the environment, might be the most plausible mechanism. After the introduction of insulin treatment in 1930s, an increase in the pool of genetically susceptible individuals has been suggested to contribute to the increase in the incidence of Type 1 diabetes. RESULTS: To explore this hypothesis, the authors formulate a simple population genetic model for the incidence change driven by non-Mendelian transmission of a single susceptibility factor, either allele(s) or haplotype(s). A Poisson mixture model is used to model the observed number of cases. Model parameters were estimated by maximizing the log-likelihood function. Based on the Finnish incidence data 1965-1996 the point estimate of the transmission probability was 0.998. Given our current knowledge of the penetrance of the most diabetic gene variants in the HLA region and their transmission probabilities, this value is exceedingly unrealistic. CONCLUSIONS: As a consequence, non-Mendelian transmission of diabetic allele(s)/haplotype(s) if present, could explain only a small part of the increase in incidence in Finland. Hence, the importance of other, probably environmental factors modifying the disease incidence is emphasized.

Diabetes Mellitus, Type 1↗

PubMed2005

Randomization-based nonparametric methods for the analysis of multicentre trials.

Multicentre trials offer several advantages over single centre trials in clinical research, including the ability to recruit patients at a faster rate over the course of the study, increased generalizability through the use of a broader patient population, and the ability to shed light on the replication of findings at multiple centres in a single study. A nonparametric approach to the analysis of multicentre trial data provides a convenient way for addressing the role of centres as well as baseline covariables during data analysis. With the use of randomization-based nonparametric methods, the strategy for evaluating the null hypothesis of no treatment effect can be prespecified during study planning without requiring a specific structure for the relationship of response criteria (or endpoints) to centres, covariables, or potential interaction terms. Further, the basis of inference for the application of these methods is the randomization mechanism, and the population to which inference can be directly made is the study population itself. No assumptions about underlying distributions, data structures, likelihood functions, or samples from super populations of inference are required. A three-step approach is proposed for handling centres via randomization-based nonparametric methods. In Step 1, a test of overall treatment effect is carried out using data from all centres simultaneously, without any assumption about treatment by centre interaction. In Step 2, the question of treatment by centre interaction is addressed, usually through the use of parametric multiple regression methods. In cases with suggestion of such interaction, Step 3 is conducted to evaluate different weighting schemes in forming pairwise treatment comparisons averaged across centres to assess the robustness of treatment effects observed in Step 1. An attractive inferential feature of this three-step approach is that the Type I error for the test of treatment effect is controlled by requiring statistical significance at each step to proceed to the next step. Extended Mantel-Haenszel methods with stratification adjustment for centre can be used to provide a nonparametric assessment of treatment effect. When adjustment for other covariates, such as baseline values, is desired, the more recent nonparametric analysis of covariance methods are available. Both methods are easy to use, require no assumptions beyond that of a valid randomization mechanism, and can be applied in a similar manner to dichotomous, ordinal, failure time, or continuous response criteria (endpoints). The methods are illustrated using data from a confirmatory clinical trial of a therapeutic agent for the treatment of dry eye disease.

Drugs, Investigational↗

PubMed2003

Three-mode analysis of multimode covariance matrices.

Multimode covariance matrices, such as multitrait-multimethod matrices, contain the covariances of subject scores on variables for different occasions or conditions. This paper presents a comparison of three-mode component analysis and three-mode factor analysis applied to such covariance matrices. The differences and similarities between the non-stochastic and stochastic approaches are demonstrated by two examples, one of which has a longitudinal design. The empirical comparison is facilitated by deriving, as a heuristic device, a statistic based on the maximum likelihood function for three-mode factor analysis and its associated degrees of freedom for the three-mode component models. Furthermore, within the present context a case is made for interpreting the core array as second-order components.

Analysis of Variance↗

PubMed2001

Optimum receivers for pattern recognition in the presence of Gaussian noise with unknown statistics.

We develop algorithms to detect a known pattern or a reference signal in the presence of additive, disjoint background, and multiplicative white Gaussian noise with unknown statistics. The presence of three different types of noise processes with unknown statistics presents difficulties in estimating the unknown parameters. The standard methods such as expected-maximization-type algorithms are iterative, and in the framework of hypothesis testing they are time-consuming, because corresponding to each hypothesis one must estimate a set of parameters. Other standard methods such as setting the gradient of the likelihood function with respect to the unknown parameters will lead to a nonlinear system of equations that do not have a closed-form solution and require iterative methods. We develop an approach to overcome these handicaps and derive algorithms to detect a known object. We present new methods to estimate unknown parameters within the framework of hypothesis testing. The methods that we present are direct and provide closed-form estimates of the unknown parameters. Computer simulations are used to show that for the images tested, the receivers that we have designed perform better than existing receivers.

Journal Article↗

PubMed2000

Transformation in the PC-aided biochemical data analysis.

Data transformations enable expression of original data in a new scale, more suitable for data analysis. In computer-aided interactive analysis of biochemical and clinical data an exploratory data analysis often finds that the sample distribution is systematically skewed or does not accept a sample homogeneity. Under such circumstances the original data should be transformed. The power transformation and the Box-Cox transformation improve sample symmetry and also stabilize variance. Both the Hines-Hines selection graph and the plot of logarithm of a maximum likelihood function allow selection of an optimum transformation parameter. The proposed procedure of data transformation in univariate data analysis is illustrated on a determination of 17-hydroxypregnenolone in umbilical blood of a population of newborns. Lower levels of free 5-ene steroids in umbilical blood and elevated levels of 5-ene steroid sulfates indicate a congenital sex-specific placental sulfatase insufficiency. After examination of statistical assumptions by diagnostic plots of an exploratory data analysis the best estimate of a mean value of 17-hydroxypregnenolone is derived.

17-alpha-Hydroxypregnenolone↗

PubMed1992

Temporal coupling among luteinizing hormone, follicle stimulating hormone, beta-endorphin and cortisol pulse episodes in vivo.

We have applied explicit probability equations to assess possible non-random associations among four distinct hormone series consisting of episodic luteinizing hormone, follicle stimulating hormone, beta-endorphin, and/or cortisol pulses observed under physiological conditions in normal men. Closed-form likelihood functions permitted us to demonstrate significantly coordinated patterns of multiple hormone release. A specific quadruple co-pulsatility pattern was observed, in which the two gonadotropic hormones (luteinizing hormone and follicle stimulating hormone) were co-secreted and coupled by a 10-20 min lag to the later release of beta-endorphin. In turn, beta-endorphin release episodes were followed within 0-30 min by cortisol bursts. Conditional probability analysis allowed us to reject with high statistical confidence the null hypothesis that this unique temporally specified pattern of quadruple hormone release was due to purely random associations among the four pulsatile series. We conclude that discrete hormone release episodes associated with four hormones within the gonadotropic and corticotropic axes in man exhibit significantly lagged non-random temporal coupling in vivo.

Adult↗

PubMed2004

Simultaneous detection of linkage disequilibrium and genetic differentiation of subdivided populations.

We propose a new method for simultaneously detecting linkage disequilibrium and genetic structure in subdivided populations. Taking subpopulation structure into account with a hierarchical model, we estimate the magnitude of genetic differentiation and linkage disequilibrium in a metapopulation on the basis of geographical samples, rather than decompose a population into a finite number of random-mating subpopulations. We assume that Hardy-Weinberg equilibrium is satisfied in each locality, but do not assume independence between marker loci. Linkage states remain unknown. Genetic differentiation and linkage disequilibrium are expressed as hyperparameters describing the prior distribution of genotypes or haplotypes. We estimate related parameters by maximizing marginal-likelihood functions and detect linkage equilibrium or disequilibrium by the Akaike information criterion. Our empirical Bayesian model analyzes genotype and haplotype frequencies regardless of haploid or diploid data, so it can be applied to most commonly used genetic markers. The performance of our procedure is examined via numerical simulations in comparison with classical procedures. Finally, we analyze isozyme data of ayu, a severely exploited fish species, and single-nucleotide polymorphisms in human ALDH2.

Animals↗

PubMed2004

The population structure of African cultivated rice oryza glaberrima (Steud.): evidence for elevated levels of linkage disequilibrium caused by admixture with O. sativa and ecological adaptation.

Genome-wide linkage disequilibrium (LD) was investigated for 198 accessions of Oryza glaberrima using 93 nuclear microsatellite markers. Significantly elevated levels of LD were detected, even among distantly located markers. Free recombination among loci at the population genetic level was shown (1) by a lack of decay in LD among markers on the same chromosome and (2) by a strictly increasing composite likelihood function for the recombination parameter. This suggested that the elevation in LD was due not to physical linkage but to other factors, such as population structure. A Bayesian clustering analysis confirmed this hypothesis, indicating that the sample of O. glaberrima in this study was subdivided into at least five cryptic subpopulations. Two of these subpopulations clustered with control samples of O. sativa, subspecies indica and japonica, indicating that some O. glaberrima accessions represent admixtures. The remaining three O. glaberrima subpopulations were significantly associated with specific combinations of phenotypic traits-possibly reflecting ecological adaptation to different growing environments.

Acclimatization↗

PubMed1993

Bayesian analysis of lamb survival using Monte Carlo numerical integration with importance sampling.

Approximate and exact Bayesian analyses of survival from birth to weaning measured as an "all or none" trait were conducted on 2,554 Rambouillet lambs using an asymptotic normal approximation and Monte Carlo numerical integration with importance sampling, respectively. A linear logistic model was used to assess the effects of year, age of dam, sex of lamb, and type of birth on the survival probability. A least squares analysis of the data, ignoring their discrete nature, was also performed. The Bayesian analyses were compared by plotting the marginal posterior distributions and by constructing 95% highest-posterior-density regions for some parameters of interest. The analyses were repeated for a reduced data set consisting of 300 observations selected at random from the original file. For all practical purposes, the Bayesian and non-Bayesian analyses yielded identical results despite their different interpretations. Also, the asymptotic normal approximations to the true posterior distributions were excellent. Undoubtedly, this is because the likelihood functions contained a large amount of information about the parameters. Four-year-old ewes produced lambs with greater survival rates than either younger or older ewes. Female and male lambs had similar rates, and single-born lambs had a 10% higher survival rate than multiple-born lambs.

Age Factors↗

PubMed1998

Litter, permanent environmental, ram-flock, and genetic effects on early weight gain of lambs.

Twelve models were fitted to early growth data of two Swiss sheep breeds to investigate their suitability for evaluation of breeding values. Models were identical for fixed parity, litter size, sex and lambing season effects, random flock-year, and direct genetic effects but differed for combinations of random litter, permanent environmental, ram-flock, and maternal genetic effects. Records of average daily gain to 30 d of 25,564 lambs of the Black-Brown Mountain Sheep (SBS) and of 26,391 lambs of the White Alpine Sheep (WAS) born 1989 to 1995 and their pedigrees were available. A single-trait animal model was fitted by the restricted maximum likelihood method. The information criterion of a particular model (i.e., the maximum of the likelihood function adjusted for the number of independently estimated parameters) was used to evaluate the models for their fitting power. The litter effect accounted for between 26 and 31% of the phenotypic variance, with little variation within breed. Models containing the ram-flock effect provided a better fit of the data than otherwise identical models. This effect contributed 6 and 4% to the phenotypic variance in the two breeds and strongly influenced estimates of other components. The proportion of phenotypic variance due to the flock-year effect was 23 and 25% without and 19 and 23% including the ram-flock effect in the model in the two breeds. Including permanent environmental effect of the ewe in addition to litter effect led to a better fit of the data. Depending on the model, it then contributed between 3 and 6% to the phenotypic variance. Fitting the ram-flock effect reduced heritability considerably and increased the breed difference of the estimates of this parameter. Estimates ranging from .16 to .10 and from .08 to .14 were obtained for the SBS and WAS breeds, respectively. For models without the ram-flock effect, negative estimates of the direct-maternal correlation of between -.38 and -.45 were observed. Including the ram-flock effect reduced this correlation substantially to between -.08 and -.17. Including the direct-maternal covariance in addition to the ram-flock effect did not improve the fit any further in either breed. Ranking of the models investigated differed between breeds, but the same model provided the best fit. It contained the random litter, permanent environmental, ram-flock, direct, and maternal genetic effects, but not the covariance between the last two.

Aging↗

PubMed2005

Genetic parameters for stayability, stayability at calving, and stayability at weaning to specified ages for Hereford cows.

Genetic parameters for stayability to six ages (ST1, . . ., ST6), for five measures of stayability to calving (SC2, . . ., SC6), and for five measures of stayability to weaning (SW2, . . ., SW6), were estimated using records of 2,019 Hereford cows collected from 1964 to 1979 from a selection experiment with a control line and three lines selected for weaning weight, yearling weight, and an index of yearling weight and muscle score. The model included birth year of the cow as a fixed effect and the cow's sire as a random effect. Analyses were performed with 1) a generalized linear mixed model for binary data using a probit link with a penalized quasi-likelihood function, and 2) with a linear mixed model using REML. Genetic trends were estimated by regressing weighted means of estimated transmitting abilities (ETA) of sires by birth year of their daughters on birth year. Environmental trends were estimated by regressing solutions for year of birth on birth year. Estimates of heritability (SE) for ST were between 0.09 (0.08) and 0.30 (0.14) for threshold model and between 0.05 (0.04) and 0.19 (0.09) for linear model. Estimates of heritability from linear model analyses transformed to an underlying normal scale were between 0.09 and 0.35. Estimates of heritability (SE) for SC were between 0.29 (0.10) and 0.39 (0.11) and between 0.18 (0.09) and 0.25 (0.08) with threshold and linear models. Estimates of heritability transformed to an underlying normal scale were between 0.30 and 0.40. Estimates of heritability (SE) for SW were between 0.21 (0.14) and 0.47 (0.19) and between 0.12 (0.08) and 0.26 (0.12) with threshold and linear models, respectively. Estimates of heritability transformed to an underlying normal scale were between 0.21 and 0.50. Estimates of genetic and environmental trends for all lines were nearly zero for all traits. Correlations between ETA of sires for stayability to specific ages, for stayability to calving, and for stayability to weaning with threshold and linear models ranged from 0.09 to 0.82, from 0.68 to 0.90, and from 0.67 to 0.87, respectively. Selection for stayability would be possible in a breeding program and could be relatively effective as a result of the moderate estimates of heritability, which would allow selection of sires whose daughters are more likely to remain longer in the herd. Selection for weaning and yearling weights resulted in little correlated response for any of the measures of stayability.

Age Factors↗

PubMed1989

[Risk assessment of factors related to lactation of breast-feeding women by multichotomous logistic regression with stepwise procedure].

Based on Dubin and Pasternack's solution of parsimonious parameters, the authors proposed a procedure of stepwise selection of factors for establishing the Multichotomous logistic regression "best" model. Score statistic was used to select factors into model. Ratio of likelihood function was used to eliminate factors from model. The data of lactation from 129 breast-feeding women living in rural area have been analysed by the procedure. It showed that the first breast-feeding to the newborn of over 48 hours from her childbirth has negative effect while good appetite has positive effect on milk secretion. The epidemiological meaning of parameters estimated from the data was illustrated in detail.

Breast Feeding↗

PubMed1985

[Control of the efficacy of anti-arrhythmia drug therapy with the ambulatory electrocardiogram. Proposal for a new analytical statistical model].

Ambulatory electrocardiography is used for evaluating antiarrhythmic drug effectiveness. Statistical methods based on the analysis of the number of ventricular ectopic beats are currently employed. These techniques are not useful to compare groups of patients with different therapies, due to the wide spontaneous variability of the ectopic beats. We propose a new statistical method, based on the likelihood function. The new method has been tested both retrospectively on 102 patients treated with different antiarrhythmic drugs and prospectively on 12 patients subjected to three consecutive control ambulatory electrocardiograms and to a fourth one after treatment with propafenone. This new statistical method was found to be useful for comparing therapeutic effectiveness between groups of patients, whereas the traditional quantitative methods are to be preferred when drug effectiveness is evaluated in the single patient.

Adrenergic beta-Antagonists↗

PubMed1987

[Estimate of the penetrance of genotypes in a monolocus model taking into account environmental factors].

Based on ITO matrices, a method for parameter estimation of the monolocus diallele model (MDM) of qualitative trait is described, taking account of non-genetic (environmental) factors. The model parameters, probabilities of relatives' affection, constructing the likelihood function and testing hypotheses of the effect of environmental factors on the penetrations of MDM genotypes are outlined. Examples are given, concerning estimation of epilepsy MDM parameters, taking account of two factors-harmfulness of antenatal ontogenesis period and harmfulness which provokes paroxysms.

Alleles↗

PubMed1982

Modelling fingerprint pattern inheritance.

The authors compare some genetic triallelic models for finger-print pattern inheritance built according to the Galton classification. These models keep at the same time into account the available information on fingerprints: population frequencies for individuals, matchings in couples of MZ-twins and in families composed of parents and their offspring. For every finger, on the basis of the data for individuals and twins, the probabilities of the genotypic population frequencies and a penetrance value are evaluated as parameters of a support (likelihood) function for each model. Then, by utilizing the data on families, the support given to the proposed models is evaluated. Finally, the support of the alternative models is synoptically considered for comparative purposes. In the present paper these models are tried with reliable data, collected and classified by Alciati and Folin, of the Institute of Anthropology of the University of Padua. The results substantially agree with the hypotheses formulated by other authors who did not utilize statistical models.

Dermatoglyphics↗

PubMed1995

An empirical Bayes approach to smoothing in backcalculation of HIV infection rates.

Backcalculation is a methodology to reconstruct the past human immunodeficiency virus (HIV) infection rates from the AIDS incidence data and incubation distribution by deconvolution. Smoothing has proved important in backcalculation, and a key question is how to choose the amount of smoothing. This paper proposes an empirical Bayes approach in which the smoothing parameter is estimated from the data. We introduce a family of priors that reflect the notion of closeness of neighboring infection rates. The variance parameter in the prior family plays the role of the smoothing parameter and is estimated by a method similar to the residual maximum likelihood in linear random effects model through an efficient EM (expectation/maximization) algorithm. A number of penalized likelihood functions that have been used in backcalculation have an empirical Bayes formulation. A bootstrap confidence interval for the infection rates is proposed. The methodology is illustrated with United States AIDS incidence data.

Acquired Immunodeficiency Syndrome↗

PubMed1994

The use of logistic models for the analysis of codon frequencies of DNA sequences in terms of explanatory variables.

The development of the regressive logistic model applicable to the analysis of codon frequencies of DNA sequences in terms of explanatory variables is presented. A codon is a triplet of nucleotides that code for an amino acid, and may be considered as a trivariate response (B1, B2, B3), where Bi (i = 1, 2, 3) is a categorical random variable with values A, C, G, T. The linear order of bases in the DNA and possible statistical dependence of the bases in a given codon make the regressive logistic model a suitable tool for the analysis of codon frequencies. A problem of structural zeros arises from the fact that the stopping codons (terminators) do not code for amino acids; this is solved by normalizing the likelihood function. Codon frequencies may also depend on the function of the gene and they are known to differ between genes of the same genome. Differences also occur between synonymous codons for the same amino acid. Thus, the use of covariates that differ between synonymous codons as well as covariates that are constant within codons of the same amino acid may be useful in explaining the frequencies. As an illustration, the method is applied to the human mitochondrial genome using the following as explanatory variables: (1) TSCORE, a measure of the number of single base mutations required for a given codon to become a terminator; (2) AARISK, an indicator of a codon's ability of changing by a single base substitution to triplets coding for amino acids with very different characteristics; (3) AVDIST, a measure of the typicality of the amino acid coded for by the triplets. The results indicate that models that incorporate dependency structure and covariates are to be preferred to either the models comprising covariates alone or dependency structure alone.

Amino Acid Sequence↗

PubMed1994

Finding noncommunicating sets for Markov chain Monte Carlo estimations on pedigrees.

Markov chain Monte Carlo (MCMC) has recently gained use as a method of estimating required probability and likelihood functions in pedigree analysis, when exact computation is impractical. However, when a multiallelic locus is involved, irreducibility of the constructed Markov chain, an essential requirement of the MCMC method, may fail. Solutions proposed by several researchers, which do not identify all the noncommunicating sets of genotypic configurations, are inefficient with highly polymorphic loci. This is a particularly serious problem in linkage analysis, because highly polymorphic markers are much more informative and thus are preferred. In the present paper, we describe an algorithm that finds all the noncommunicating classes of genotypic configurations on any pedigree. This leads to a more efficient method of defining an irreducible Markov chain. Examples, including a pedigree from a genetic study of familial Alzheimer disease, are used to illustrate how the algorithm works and how penetrances are modified for specific individuals to ensure irreducibility.

Algorithms↗