The transform likelihood ratio method for rare event simulation with heavy tails

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.

A comparison of lipid variables as predictors of cardiovascular disease in the Asia Pacific Region

PURPOSE: Many guidelines advocate measurement of total or low density lipoprotein cholesterol (LDL), high density lipoprotein cholesterol (HDL), and triglycerides (TG) to determine treatment recommendations for preventing coronary heart disease (CHD) and cardiovascular disease (CVD). This analysis is a comparison of lipid variables as predictors of cardiovascular disease. METHODS: Hazard ratios for coronary and cardiovascular deaths by fourths of total cholesterol (TC), LDL, HDL, TG, non-HDL, TC/HDL, and TG/HDL values, and for a one standard deviation change in these variables, were derived in an individual participant data meta-analysis of 32 cohort studies conducted in the Asia-Pacific region. The predictive value of each lipid variable was assessed using the likelihood ratio statistic. RESULTS: Adjusting for confounders and regression dilution, each lipid variable had a positive (negative for HDL) log-linear association with fatal CHD and CVD. Individuals in the highest fourth of each lipid variable had approximately twice the risk of CHD compared with those with lowest levels. TG and HDL were each better predictors of CHD and CVD risk compared with TC alone, with test statistics similar to TC/HDL and TG/HDL ratios. Calculated LDL was a relatively poor predictor. CONCLUSIONS: While LDL reduction remains the main target of intervention for lipid-lowering, these data support the potential use of TG or lipid ratios for CHD risk prediction. (c) 2005 Elsevier Inc. All rights reserved.

A mixture model-based approach to the clustering of microarray expression data

Motivation: This paper introduces the software EMMIX-GENE that has been developed for the specific purpose of a model-based approach to the clustering of microarray expression data, in particular, of tissue samples on a very large number of genes. The latter is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. A feasible approach is provided by first selecting a subset of the genes relevant for the clustering of the tissue samples by fitting mixtures of t distributions to rank the genes in order of increasing size of the likelihood ratio statistic for the test of one versus two components in the mixture model. The imposition of a threshold on the likelihood ratio statistic used in conjunction with a threshold on the size of a cluster allows the selection of a relevant set of genes. However, even this reduced set of genes will usually be too large for a normal mixture model to be fitted directly to the tissues, and so the use of mixtures of factor analyzers is exploited to reduce effectively the dimension of the feature space of genes. Results: The usefulness of the EMMIX-GENE approach for the clustering of tissue samples is demonstrated on two well-known data sets on colon and leukaemia tissues. For both data sets, relevant subsets of the genes are able to be selected that reveal interesting clusterings of the tissues that are either consistent with the external classification of the tissues or with background and biological knowledge of these sets.

On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples

We consider the problem of assessing the number of clusters in a limited number of tissue samples containing gene expressions for possibly several thousands of genes. It is proposed to use a normal mixture model-based approach to the clustering of the tissue samples. One advantage of this approach is that the question on the number of clusters in the data can be formulated in terms of a test on the smallest number of components in the mixture model compatible with the data. This test can be carried out on the basis of the likelihood ratio test statistic, using resampling to assess its null distribution. The effectiveness of this approach is demonstrated on simulated data and on some microarray datasets, as considered previously in the bioinformatics literature. (C) 2004 Elsevier Inc. All rights reserved.

Geographical variation in the penetrance of CDKN2A mutations for melanoma

Background: Germline mutations in the CDKN2A gene, which encodes two proteins (p16INK4A and p14ARF), are the most common cause of inherited susceptibility to melanoma. We examined the penetrance of such mutations using data from eight groups from Europe, Australia and the United States that are part of The Melanoma Genetics Consortium Methods: We analyzed 80 families with documented CDKN2A mutations and multiple cases of cutaneous melanoma. We modeled penetrance for melanoma using a logistic regression model incorporating survival analysis. Hypothesis testing was based on likelihood ratio tests. Covariates included gender, alterations in p14APF protein, and population melanoma incidence rates. All statistical tests were two-sided. Results: The 80 analyzed families contained 402 melanoma patients, 320 of whom were tested for mutations and 291 were mutation carriers. We also tested 713 unaffected family members for mutations and 194 were carriers. Overall, CDKN2A mutation penetrance was estimated to be 0.30 (95% confidence interval (CI) = 0.12 to 0.62) by age 50 years and 0.67 (95% CI = 0.31 to 0.96) by age 80 years. Penetrance was not statistically significantly modified by gender or by whether the CDKN2A mutation altered p14ARF protein. However, there was a statistically significant effect of residing in a location with a high population incidence rate of melanoma (P = .003). By age 50 years CDKN2A mutation penetrance reached 0.13 in Europe, 0.50 in the United States, and 0.32 in Australia; by age 80 years it was 0.58 in Europe, 0.76 in the United States, and 0.91 in Australia. Conclusions: This study, which gives the most informed estimates of CDKN2A mutation penetrance available, indicates that the penetrance varies with melanoma population incidence rates. Thus, the same factors that affect population incidence of melanoma may also mediate CDKN2A penetrance.

Modelling the distribution of stamp paper thickness via finite normal mixtures: The 1872 Hidalgo stamp issue of Mexico revisited

Izenman and Sommer (1988) used a non-parametric Kernel density estimation technique to fit a seven-component model to the paper thickness of the 1872 Hidalgo stamp issue of Mexico. They observed an apparent conflict when fitting a normal mixture model with three components with unequal variances. This conflict is examined further by investigating the most appropriate number of components when fitting a normal mixture of components with equal variances.

A parent-completed developmental questionnaire: Follow up of ex-premature infants

Objective: premature infants are at increased risk of developmental disability. Early identification of problems allows intervention to ameliorate or attenuate problems. A reliable screening tool allows triage of children in this high-risk population by identifying those unlikely to need full developmental assessment. To explore the test characteristics of an established parent-completed developmental assessment questionnaire 'Ages and Stages Questionnaire' (ASQ) in follow up of an Australian population of premature infants. Methodology: One hundred and sixty-seven children born prematurely with corrected ages 12- to 48-months attending the Growth and Development Clinic at the Mater Children's Hospital in Brisbane, Queensland, Australia; 136 questionnaires 'ASQ' were returned completed (81%) and were compared to formal psychometric assessment (Griffith Mental Development Scales for 12- and 24-months, Bayley Mental Development Intelligence Scale for 18-months, McCarthy General Cognitive Intelligence Scale for 18-months). Developmental delay was considered to be present if any of the above psychometric assessments fell below 1.0 standard deviations (SD). The ASQ cut-off used was 2.0 SD (US data derived means and SD). Results: Aggregate results for all age groups comparing ASQ to psychometric assessments as 'gold standards' found the ASQ to have the following test characteristics: sensitivity (90%); specificity (77%); positive predictive value (40%); negative predictive value (98%): % over-referred (20%); % under-referred (1%); % agreement (79%). likelihood ratio for children failing the ASQ was 3.8 and for passing the ASQ was 0.13. Twenty-one children with known disabilities were included in the study and in 14 of these, the ASQ overall score agreed with the psychometric assessment (67%). Conclusion: The high negative predictive value of the ASQ supports its use as a screening tool for cognitive and motor delays in the follow up of ex-premature infants. This would need to be combined with other strategies as part of a comprehensive follow up program for ex-premature infants.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Use of umbilical artery Doppler velocimetry in the monitoring of pregnancy in women with pre-existing diabetes

Background: The usefulness of umbilical artery Doppler velocimetry for the monitoring of diabetic pregnancies is controversial. The aim of the present study was to assess whether umbilical artery Doppler velocity waveform analysis can predict adverse perinatal outcomes for pregnancies complicated by pre-existing diabetes mellitus. Methods: All diabetic pregnancies (type 1 and 2) delivered at Mater Mothers' Hospital, Queensland, between 1 January 1995 and 31 December 1999 were included. All pregnant diabetic women were monitored with umbilical artery Doppler velocimetry at 28, 32, 36, and 38 weeks' gestation. Adverse perinatal outcome was defined as pregnancies with one or more of the following: small-for-gestational age, Caesarean section for non-reassuring cardiotocography, fetal acidaemia at delivery, 1-min Apgar of 3 or less, 5-min Apgar of less than 7, hypoxic ischaemic encephalopathy or perinatal death. Abnormal umbilical artery Doppler velocimetry was defined as a pulsatility index of 95th centile or higher for gestation. Results: One hundred and four pregnancies in women with pre-existing diabetes had umbilical arterial Doppler studies carried out during the study period. Twenty-three pregnancies (22.1%) had an elevated pulsatility index. If the scans were carried out within 2 weeks of delivery, 71% of pregnancies with abnormal umbilical Doppler had adverse outcomes (P < 0.01; likelihood ratio, 4.2). However, the sensitivity was 35%; specificity was 94%; positive predictive value was 80%; and negative predictive value was 68%. Only 30% of women with adverse perinatal outcomes had abnormal umbilical arterial Doppler flow. Conclusion: Umbilical artery Doppler velocimetry is not a good predictor of adverse perinatal outcomes in diabetic pregnancies.

Selection pressure-driven evolution of the Epstein-Barr virus-encoded oncogene LMP1 in virus isolates from southeast Asia

The geographically constrained distribution of Epstein-Barr virus (EBV)-associated nasopharyngeal carcinoma (NPC) in southeast Asian populations suggests that both viral and host genetics may influence disease risk. Although susceptibility loci have been mapped within the human genome, the role of viral genetics in the focal distribution of NPC remains an enigma. Here we report a molecular phylogenetic analysis of an NPC-associated viral oncogene, LMP1, in a large panel of EBV isolates from southeast Asia and from Papua New Guinea, Africa, and Australia, regions of the world where NPC is and is not endemic, respectively. This analysis revealed that LMP1 sequences show a distinct geographic structure, indicating that the southeast Asian isolates have evolved as a lineage distinct from those of Papua New Guinea, African, and Australian isolates. Furthermore, a likelihood ratio test revealed that the C termini of the LMP1 sequences of the southeast Asian lineage are under significant positive selection pressure, particularly at some sites within the C-terminal activator regions. We also present evidence that although the N terminus and transmembrane region of LMP1 have undergone recombination, the C-terminal region of the gene has evolved without any history of recombination. Based on these observations, we speculate that selection pressure may be driving the LMP1 sequences in virus isolates from southeast Asia towards a more malignant phenotype, thereby influencing the endemic distribution of NPC in this region.

Trade liberalisation and technical efficiency: Evidence from Bangladesh manufacturing industries

The paper investigates the effects of trade liberalisation on the technical efficiency of the Bangladesh manufacturing sector by estimating a combined stochastic frontier-inefficiency model using panel data for the period 197894 for 25 three-digit level industries. The results show that the overall technical efficiency of the manufacturing sector as well as the technical efficiencies of the majority of the individual industries has increased over time. The findings also clearly suggest that trade liberalisation, proxied by export orientation and capital deepening, has had significant impact on the reduction of the overall technical inefficiency. Similarly, the scale of operation and the proportion of non-production labour in total employment appear as important determinants of technical inefficiency. The evidence also indicates that both export-promoting and import-substituting industries have experienced rises in technical efficiencies over time. Besides, the results are suggestive of neutral technical change, although (at the 5 per cent level of significance) the empirical results indicate that there was no technical change in the manufacturing industries. Finally, the joint test based on the likelihood ratio (LR) test rejects the Cobb-Douglas production technology as description of the database given the specification of the translog production technology.

Association between polymorphisms in the progesterone receptor gene and endometriosis

The progesterone receptor (PR) is a candidate gene for the development of endometriosis, a complex disease with strong hormonal features, common in women of reproductive age. We typed the 306 base pair Alu insertion (AluIns) polymorphism in intron G of PR in 101 individuals, estimated linkage disequilibrium (LD) between five single-nucleotide polymorphisms (SNPs) across the PR locus in 980 Australian triads (endometriosis case and two parents) and used transmission disequilibrium testing (TDT) for association with endometriosis. The five SNPs showed strong pairwise LD, and the AluIns was highly correlated with proximal SNPs rs1042839 ({Delta}2 = 0.877, D9 = 1.00, P < 0.0001) and rs500760 ({Delta}2 = 0.438, D9 = 0.942, P < 0.0001). TDT showed weak evidence of allelic association between endometriosis and rs500760 (P = 0.027) but not in the expected direction. We identified a common susceptibility haplotype GGGCA across the five SNPs (P = 0.0167) in the whole sample, but likelihood ratio testing of haplotype transmission and non-transmission of the AluIns and flanking SNPs showed no significant pattern. Further, analysis of our results pooled with those from two previous studies suggested that neither the T2 allele of the AluIns nor the T1/T2 genotype was associated with endometriosis.

Detecting finite bandwidth periodic signals in stationary noise using the signal coherence spectrum

All signals that appear to be periodic have some sort of variability from period to period regardless of how stable they appear to be in a data plot. A true sinusoidal time series is a deterministic function of time that never changes and thus has zero bandwidth around the sinusoid's frequency. A zero bandwidth is impossible in nature since all signals have some intrinsic variability over time. Deterministic sinusoids are used to model cycles as a mathematical convenience. Hinich [IEEE J. Oceanic Eng. 25 (2) (2000) 256-261] introduced a parametric statistical model, called the randomly modulated periodicity (RMP) that allows one to capture the intrinsic variability of a cycle. As with a deterministic periodic signal the RMP can have a number of harmonics. The likelihood ratio test for this model when the amplitudes and phases are known is given in [M.J. Hinich, Signal Processing 83 (2003) 1349-13521. A method for detecting a RMP whose amplitudes and phases are unknown random process plus a stationary noise process is addressed in this paper. The only assumption on the additive noise is that it has finite dependence and finite moments. Using simulations based on a simple RMP model we show a case where the new method can detect the signal when the signal is not detectable in a standard waterfall spectrograrn display. (c) 2005 Elsevier B.V. All rights reserved.

Phase equilibria in high MgO ferro-manganese and silico-manganese smelting slags

Liquidus isotherms and phase equilibria have been determined experimentally for a pseudo-ternary section of the form MnO-(CaO+MgO)-(SiO2+Al2O3) with a fixed Al-2,O-3,/SiO2, weight ratio of 0.17 and MgO/CaO weight ratio of 0.17 for temperatures in the range 1473-1673 K. The primary phase fields present for the section investigated include manganosite (Mn,Mg,Ca)O; dicalcium silicate alpha-2(Ca,Mg,Mn)O (.) SiO2; merwinite 3CaO(.) ((Mg,Mn)O.2SiO(2); wollastonite [(Ca,Mg,Mn)(OSiO2)-Si-.]; ;tephroite [2(Mn,Mg)O.SiO2]; rhodonite [(Mn,Mg)O. diopside [(CaO,MgO,MnO,Al2O3)(SiO2)-Si-.]; tridymite (SiO2), SiO2] and melilite [2CaO (.) (MgO,MnO,Al2O3).2(SiO2,Al2O3)]. The liquidus temperatures relevant to ferro-manganese and silico-manganese smelting slags have been determined. The liquiclus temperature is shown to be principally dependent on the modified basicity weight ratio (CaO+Mgo)/(SiO2+Al2O3) at low MnO concentrations, and dependent on the mole ratio (CaO+ MgO+MnO)/(SiO2+Al2O3) at higher MnO concentrations.