Inverse probability weighting estimation of the volume under the ROC surface in the presence of verification bias

In diagnostic medicine, the volume under the receiver operating characteristic (ROC) surface (VUS) is a commonly used index to quantify the ability of a continuous diagnostic test to discriminate between three disease states. In practice, verification of the true disease status may be performed only for a subset of subjects under study since the verification procedure is invasive, risky, or expensive. The selection for disease examination might depend on the results of the diagnostic test and other clinical characteristics of the patients, which in turn can cause bias in estimates of the VUS. This bias is referred to as verification bias. Existing verification bias correction in three‐way ROC analysis focuses on ordinal tests. We propose verification bias‐correction methods to construct ROC surface and estimate the VUS for a continuous diagnostic test, based on inverse probability weighting. By applying U‐statistics theory, we develop asymptotic properties for the estimator. A Jackknife estimator of variance is also derived. Extensive simulation studies are performed to evaluate the performance of the new estimators in terms of bias correction and variance. The proposed methods are used to assess the ability of a biomarker to accurately identify stages of Alzheimer's disease.     

Statistical properties of population differentiation estimators under stepwise mutation in a finite island model

Microsatellite loci mutate at an extremely high rate and are generally thought to evolve through a stepwise mutation model. Several differentiation statistics taking into account the particular mutation scheme of the microsatellite have been proposed. The most commonly used is R(ST) which is independent of the mutation rate under a generalized stepwise mutation model. F(ST) and R(ST) are commonly reported in the literature, but often differ widely. Here we compare their statistical performances using individual-based simulations of a finite island model. The simulations were run under different levels of gene flow, mutation rates, population number and sizes. In addition to the per locus statistical properties, we compare two ways of combining R(ST) over loci. Our simulations show that even under a strict stepwise mutation model, no statistic is best overall. All estimators suffer to different extents from large bias and variance. While R(ST) better reflects population differentiation in populations characterized by very low gene-exchange, F(ST) gives better estimates in cases of high levels of gene flow. The number of loci sampled (12, 24, or 96) has only a minor effect on the relative performance of the estimators under study. For all estimators there is a striking effect of the number of samples, with the differentiation estimates showing very odd distributions for two samples.     

Overexpression of nPKC theta is permissive for myogenic differentiation

Although protein kinase C (PKC) has been shown to participate in skeletal myogenic differentiation, the functions of individual isoforms of PKC in myogenesis have not been completely elucidated. These studies focused on the role of nPKC straight theta, an isoform of the PKC family whose expression has been shown to be regulated by commitment to the myogenic lineage, myogenic differentiation and innervation. We used the myogenic cell line C(2)C(12) as a tissue culture model system to explore the role of nPKC straight theta in the formation of multinucleated myotubes. We examined endogenous levels of nPKC straight theta in C(2)C(12) cells and showed that it is expressed at low levels in myoblasts compared to mouse skeletal muscle and that expression is maintained in myotubes. We overexpressed nPKC straight theta in C(2)C(12) myoblasts and examined the ability of overexpressing cells to differentiate into myotubes. Using an nPKC straight theta - green fluorescent protein (GFP) chimera to detect transfected myoblasts, we showed that overexpressed nPKC straight theta-GFP translocates to the plasma membrane in response to phorbol ester treatment of myoblast cultures in situ. nPKC straight theta-GFP was found to be completely extracted into the detergent-soluble fraction of cell lysates and was stably expressed throughout the extent of differentiation into myotubes. No difference was seen in the ability of myoblasts either overexpressing nPKC straight theta - GFP or GFP alone to form myotubes. These studies demonstrate that overexpression of nPKC straight theta does not interfere with fusion of myoblasts into myotubes suggesting that nPKC straight theta activity is not inhibitory for myogenesis. These studies also demonstrate a method for transfecting myoblasts and identifying differentiated cells that overexpress nPKC straight theta-GFP for investigating the function of nPKC straight theta in living myotubes.     

Improving sandwich variance estimation for marginal Cox analysis of cluster randomized trials

Cluster randomized trials (CRTs) frequently recruit a small number of clusters, therefore necessitating the application of small-sample corrections for valid inference. A recent systematic review indicated that CRTs reporting right-censored, time-to-event outcomes are not uncommon and that the marginal Cox proportional hazards model is one of the common approaches used for primary analysis. While small-sample corrections have been studied under marginal models with continuous, binary, and count outcomes, no prior research has been devoted to the development and evaluation of bias-corrected sandwich variance estimators when clustered time-to-event outcomes are analyzed by the marginal Cox model. To improve current practice, we propose nine bias-corrected sandwich variance estimators for the analysis of CRTs using the marginal Cox model and report on a simulation study to evaluate their small-sample properties. Our results indicate that the optimal choice of bias-corrected sandwich variance estimator for CRTs with survival outcomes can depend on the variability of cluster sizes and can also slightly differ whether it is evaluated according to relative bias or type I error rate. Finally, we illustrate the new variance estimators in a real-world CRT where the conclusion about intervention effectiveness differs depending on the use of small-sample bias corrections. The proposed sandwich variance estimators are implemented in an R package CoxBcv .     

A Comparative Statistical Analysis of Genetic Distances. I - Estimation of Distances and of their Variances: Distribution of the Estimators

We present a Monte-Carlo simulation analysis of the statistical properties of absolute genetic distance and of Nei's minimum and standard genetic distances. The estimation of distances (bias) and of their variances is analysed as well as the distributions of distance and variance estimators, taking into account both gamete and locus samplings. Both of Nei's statistics are non-linear when distances are small and consequently the distributions of their estimators are extremely asymmetrical. It is difficult to find theoretical laws that fit such asymmetrical distributions. Absolute genetic distance is linear and its distributions are better fit by a normal distribution. When distances are medium or large, minimum distance and absolute distance distributions are close to a normal distribution, but those of the standard distance can never be considered as normal. For large distances the jack-knife estimator of the standard distance variance is bad; another standard distance estimator is suggested. Absolute distance, which has the best mathematical properties, is particularly interesting for small distances if the gamete sample size is large, even when the number of loci is small. When both distance and gamete sample size are small, this statistic is biased.     

Estimating the encounter rate variance in distance sampling

Summary .  The dominant source of variance in line transect sampling is usually the encounter rate variance. Systematic survey designs are often used to reduce the true variability among different realizations of the design, but estimating the variance is difficult and estimators typically approximate the variance by treating the design as a simple random sample of lines. We explore the properties of different encounter rate variance estimators under random and systematic designs. We show that a design-based variance estimator improves upon the model-based estimator of Buckland et al. (2001, Introduction to Distance Sampling. Oxford: Oxford University Press, p. 79) when transects are positioned at random. However, if populations exhibit strong spatial trends, both estimators can have substantial positive bias under systematic designs. We show that poststratification is effective in reducing this bias.     

Estimating effective population size or mutation rate with microsatellites

Microsatellites are short tandem repeats that are widely dispersed among eukaryotic genomes. Many of them are highly polymorphic; they have been used widely in genetic studies. Statistical properties of all measures of genetic variation at microsatellites critically depend upon the composite parameter theta = 4Nmicro, where N is the effective population size and micro is mutation rate per locus per generation. Since mutation leads to expansion or contraction of a repeat number in a stepwise fashion, the stepwise mutation model has been widely used to study the dynamics of these loci. We developed an estimator of theta, theta; (F), on the basis of sample homozygosity under the single-step stepwise mutation model. The estimator is unbiased and is much more efficient than the variance-based estimator under the single-step stepwise mutation model. It also has smaller bias and mean square error (MSE) than the variance-based estimator when the mutation follows the multistep generalized stepwise mutation model. Compared with the maximum-likelihood estimator theta; (L) by, theta; (F) has less bias and smaller MSE in general. theta; (L) has a slight advantage when theta is small, but in such a situation the bias in theta; (L) may be more of a concern.     

Ratio estimation with measurement error in the auxiliary variate

Summary .  With auxiliary information that is well correlated with the primary variable of interest, ratio estimation of the finite population total may be much more efficient than alternative estimators that do not make use of the auxiliary variate. The well-known properties of ratio estimators are perturbed when the auxiliary variate is measured with error. In this contribution we examine the effect of measurement error in the auxiliary variate on the design-based statistical properties of three common ratio estimators. We examine the case of systematic measurement error as well as measurement error that varies according to a fixed distribution. Aside from presenting expressions for the bias and variance of these estimators when they are contaminated with measurement error we provide numerical results based on a specific population. Under systematic measurement error, the biasing effect is asymmetric around zero, and precision may be improved or degraded depending on the magnitude of the error. Under variable measurement error, bias of the conventional ratio-of-means estimator increased slightly with increasing error dispersion, but far less than the increased bias of the conventional mean-of-ratios estimator. In similar fashion, the variance of the mean-of-ratios estimator incurs a greater loss of precision with increasing error dispersion compared with the other estimators we examine. Overall, the ratio-of-means estimator appears to be remarkably resistant to the effects of measurement error in the auxiliary variate.     

Linkage of low-density lipoprotein size to the lipoprotein lipase gene in heterozygous lipoprotein lipase deficiency.

Small low-density lipoprotein (LDL) particles are a genetically influenced coronary disease risk factor. Lipoprotein lipase (LpL) is a rate-limiting enzyme in the formation of LDL particles. The current study examined genetic linkage of LDL particle size to the LpL gene in five families with structural mutations in the LpL gene. LDL particle size was smaller among the heterozygous subjects, compared with controls. Among heterozygous subjects, 44% were classified as affected by LDL subclass phenotype B, compared with 8% of normal family members. Plasma triglyceride levels were significantly higher, and high-density lipoprotein cholesterol (HDL-C) levels were lower, in heterozygous subjects, compared with normal subjects, after age and sex adjustment. A highly significant LOD score of 6.24 at straight theta=0 was obtained for linkage of LDL particle size to the LpL gene, after adjustment of LDL particle size for within-genotype variance resulting from triglyceride and HDL-C. Failure to adjust for this variance led to only a modest positive LOD score of 1.54 at straight theta=0. Classifying small LDL particles as a qualitative trait (LDL subclass phenotype B) provided only suggestive evidence for linkage to the LpL gene (LOD=1. 65 at straight theta=0). Thus, use of the quantitative trait adjusted for within-genotype variance, resulting from physiologic covariates, was crucial for detection of significant evidence of linkage in this study. These results indicate that heterozygous LpL deficiency may be one cause of small LDL particles and may provide a potential mechanism for the increase in coronary disease seen in heterozygous LpL deficiency. This study also demonstrates a successful strategy of genotypic specific adjustment of complex traits in mapping a quantitative trait locus.     

Linkage mapping of highly informative DNA polymorphisms within the human interferon-alpha receptor gene on chromosome 21.

Two polymorphic loci within the interferon-alpha receptor (IFNAR) gene on human chromosome 21 have been identified and mapped by linkage analysis in 40 CEPH families. These markers are (1) a multiallelic RFLP with an observed heterozygosity of 0.72 and (2) a variable (AT3)n short sequence repeat at the poly(A) tail of an Alu sequence (AluVpA) with an observed heterozygosity of 0.83. This locus is close to D21S58 (theta = 0.02, zeta = 36.76) and D21S17 (theta = 0.02, Zeta = 21.76) with chromosomal band 21q22.1. Multipoint linkage analysis suggests the most likely locus order to be 21cen-D21S58-IFNAR-D21S17-21qter. Given its high heterozygosity, the IFNAR gene can be used as an index marker on human chromosome 21.     

The Exact Test for Cytonuclear Disequilibria

We extend the analysis of the statistical properties of cytonuclear disequilibria in two major ways. First, we develop the asymptotic sampling theory for the nonrandom associations between the alleles at a haploid cytoplasmic locus and the alleles and genotypes at a diploid nuclear locus, when there are an arbitrary number of alleles at each marker. This includes the derivation of the maximum likelihood estimators and their sampling variances for each disequilibrium measure, together with simple tests of the null hypothesis of no disequilibrium. In addition to these new asymptotic tests, we provide the first implementation of Fisher's exact test for the genotypic cytonuclear disequilibria and some approximations of the exact test. We also outline an exact test for allelic cytonuclear disequilibria in multiallelic systems. An exact test should be used for data sets when either the marginal frequencies are extreme or the sample size is small. The utility of this new sampling theory is illustrated through applications to recent nuclear-mtDNA and nuclear-cpDNA data sets. The results also apply to population surveys of nuclear loci in conjunction with markers in cytoplasmically inherited microorganisms.     

Bias correction in the hierarchical likelihood approach to the analysis of multivariate survival data

Frailty models are useful for measuring unobserved heterogeneity in risk of failures across clusters, providing cluster-specific risk prediction. In a frailty model, the latent frailties shared by members within a cluster are assumed to act multiplicatively on the hazard function. In order to obtain parameter and frailty variate estimates, we consider the hierarchical likelihood (H-likelihood) approach (Ha, Lee and Song, 2001. Hierarchical-likelihood approach for frailty models. Biometrika 88, 233-243) in which the latent frailties are treated as "parameters" and estimated jointly with other parameters of interest. We find that the H-likelihood estimators perform well when the censoring rate is low, however, they are substantially biased when the censoring rate is moderate to high. In this paper, we propose a simple and easy-to-implement bias correction method for the H-likelihood estimators under a shared frailty model. We also extend the method to a multivariate frailty model, which incorporates complex dependence structure within clusters. We conduct an extensive simulation study and show that the proposed approach performs very well for censoring rates as high as 80%. We also illustrate the method with a breast cancer data set. Since the H-likelihood is the same as the penalized likelihood function, the proposed bias correction method is also applicable to the penalized likelihood estimators.     

The dilemma of negative analysis of variance estimators of intraclass correlation

Summary At least two common practices exist when a negative variance component estimate is obtained, either setting it to zero or not reporting the estimate. The consequences of these practices are investigated in the context of the intraclass correlation estimation in terms of bias, variance and mean squared error (MSE). For the one-way analysis of variance random effects model and its extension to the common correlation model, we compare five estimators: analysis of variance (ANOVA), concentrated ANOVA, truncated ANOVA and two maximum likelihood-like (ML) estimators. For the balanced case, the exact bias and MSE are calculated via numerical integration of the exact sample distributions, while a Monte Carlo simulation study is conducted for the unbalanced case. The results indicate that the ANOVA estimator performs well except for designs with family size n = 2. The two ML estimators are generally poor, and the concentrated and truncated ANOVA estimators have some advantages over the ANOVA in terms of MSE. However, the large biases may make the concentrated and truncated ANOVA estimators objectionable when intraclass correlation () is small. Bias should be a concern when a pooled estimate is obtained from the literature since <0.05 in many genetic studies.     

Bias-corrected variance estimation and hypothesis testing for spatial point and marked point processes using subsampling

Summary We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate of n^?2 can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.     

Estimation of the coancestry coefficient: basis for a short-term genetic distance

A distance measure for populations diverging by drift only is based on the coancestry coefficient θ, and three estimators of the distance D = -ln(1 - θ) are constructed for multiallelic, multilocus data. Simulations of a monoecious population mating at random showed that a weighted ratio of single-locus estimators performed better than an unweighted average or a least squares estimator. Jackknifing over loci provided satisfactory variance estimates of distance values. In the drift situation, in which mutation is excluded, the weighted estimator of D appears to be a better measure of distance than others that have appeared in the literature.     

Inferring admixture proportions from molecular data

We derive here two new estimators of admixture proportions based on a coalescent approach that explicitly takes into account molecular information as well as gene frequencies. These estimators can be applied to any type of molecular data (such as DNA sequences, restriction fragment length polymorphisms [RFLPs], or microsatellite data) for which the extent of molecular diversity is related to coalescent times. Monte Carlo simulation studies are used to analyze the behavior of our estimators. We show that one of them (mY) appears suitable for estimating admixture from molecular data because of its absence of bias and relatively low variance. We then compare it to two conventional estimators that are based on gene frequencies. mY proves to be less biased than conventional estimators over a wide range of situations and especially for microsatellite data. However, its variance is larger than that of conventional estimators when parental populations are not very differentiated. The variance of mY becomes smaller than that of conventional estimators only if parental populations have been kept separated for about N generations and if the mutation rate is high. Simulations also show that several loci should always be studied to achieve a drastic reduction of variance and that, for microsatellite data, the mean square error of mY rapidly becomes smaller than that of conventional estimators if enough loci are surveyed. We apply our new estimator to the case of admixed wolflike Canid populations tested for microsatellite data.      

Dominant intermediate Charcot-Marie-Tooth neuropathy maps to chromosome 19p12-p13.2

The hereditary disorders of peripheral nerve form one of the most common groups of human genetic diseases, collectively called Charcot-Marie-Tooth (CMT) neuropathy. Using linkage analysis we have identified a new locus for a form of CMT that we have called "dominant intermediate CMT" (DI-CMT). A genomewide screen using 383 microsatellite markers showed strong linkage to the short arm of chromosome 19 (maximum LOD score 4.3, with a recombination fraction (straight theta) of 0, at D19S221 and maximum LOD score 5.28, straight theta=0, at D19S226). Haplotype analysis performed with 14 additional markers placed the DI-CMT locus within a 16.8-cM region flanked by the markers D19S586 and D19S546. Multipoint linkage analysis suggested the most likely location at D19S226 (maximum multipoint LOD score 6.77), within a 10-cM confidence interval. This study establishes the presence of a locus for DI-CMT on chromosome 19p12-p13.2.     

The haplotype-relative-risk (HRR) method for analysis of association in nuclear families.

One major problem in studying an association between a marker locus and a disease is the selection of an appropriate group of controls. However, this problem of population stratification can be circumvented in a quite elegant manner by family-based methods. The haplotype-relative-risk (HRR) method, which samples nuclear families with a single affected child and uses the parental haplotypes not transmitted to that child as a control individual, represents such a method for estimating the relative risk of a marker phenotype. In the special case of a recessive disease, it was already known that the equivalence of the HRR method with the classical relative risk (RR) obtained from independent samples holds only if the probability theta of a recombination between marker and disease locus is zero. We extend this result to an arbitrary mode of inheritance. Furthermore, we compare the distribution of the estimators for HRR and RR and show that, in the case of a positive linkage disequilibrium between a marker and disease allele, the distribution of the estimator for HRR is (stochastically) smaller than that for RR, irrespective of the recombination fraction. The practical implication of this result is that, for the HRR method, there is no tendency to give unduly high risk estimators, even for theta > 0. Finally, we give an expression for the standard error of the estimator for HRR by taking into account the nonindependence of transmitted and nontransmitted parental marker alleles in the case of theta > 0.     

A new locus on chromosome 12p13.3 for pseudohypoaldosteronism type II, an autosomal dominant form of hypertension

Pseudohypoaldosteronism type II (PHA2) is a rare autosomal dominant form of volume-dependent low-renin hypertension characterized by hyperkalemia and hyperchloremic acidosis but also by a normal glomerular filtration rate. These features, together with the correction of blood pressure and metabolic abnormalities by small doses of thiazide diuretics, suggest a primary renal tubular defect. Two loci have previously been mapped at low resolution to chromosome 1q31-42 (PHA2A) and 17p11-q21 (PHA2B). We have now analyzed a new, large French pedigree, in which 12 affected members over three generations confirmed the autosomal dominant inheritance. Affected subjects had hypertension together with long-term hyperkalemia (range 5.2-6.2 mmol/liter), hyperchloremia (range: 100-109 mmol/liter), normal plasma creatinine (range: 63-129 mmol/liter) and low renin levels. Genetic linkage was excluded for both PHA2A and PHA2B loci (all LOD scores Z<-3.2 at recombination fraction [theta] 0), as well as for the thiazide-sensitive sodium-chloride cotransporter gene. A genome-wide scan using 383 microsatellite markers showed a strong linkage with the chromosome 12p13 region (maximum LOD score Z=6.18, straight theta=0, at D12S99). Haplotype analysis using 10 additional polymorphic markers led to a minimum 13-cM interval flanked by D12S1652 and D12S336, thus defining a new PHA2C locus. Analysis of two obvious candidate genes (SCNN1A and GNb3) located within the interval showed no deleterious mutation. In conclusion, we hereby demonstrate further genetic heterogeneity of this Mendelian form of hypertension and identify a new PHA2C locus, the most compelling and precise linkage interval described to date.     

Multiallelic models of genetic effects and variance decomposition in non-equilibrium populations

Quantitative genetics stems from the theoretical models of genetic effects, which are re-parameterizations of the genotypic values into parameters of biological (genetic) relevance. Different formulations of genetic effects are adequate to address different subjects. We thus need to generalize and unify them under a common framework for enabling researchers to easily transform genetic effects between different biological meanings. The Natural and Orthogonal Interactions (NOIA) model of genetic effects has been developed to achieve this aim. Here, we further implement the statistical formulation of NOIA with multiple alleles under Hardy–Weinberg departures (HWD). We show that our developments are straightforwardly connected to the decomposition of the genetic variance and we point out several emergent properties of multiallelic quantitative genetic models, as compared to the biallelic ones. Further, NOIA entails a natural extension of one-locus developments to multiple epistatic loci under linkage equilibrium. Therefore, we present an extension of the orthogonal decomposition of the genetic variance to multiple epistatic, multiallelic loci under HWD. We illustrate this theory with a graphical interpretation and an analysis of published data on the human acid phosphatase (ACP1) polymorphism.