Tradeoff between no-call reduction in genotyping error rate and loss of sample size for genetic case/control association studies.

Single nucleotide polymorphisms (SNP) may be genotyped for use in case-control designs to test for association between a SNP marker and a disease using a 2 x 3 chi-squared test of independence. Genotyping is often based on underlying continuous measurements, which are classified into genotypes. A "no-call" procedure is sometimes used in which borderline observations are not classified. This procedure has the simultaneous effect of reducing the genotype error rate and the expected number of genotypes observed. Both quantities affect the power of the statistic. We develop methods for calculating the genotype error rate, the expected number of genotypes observed, and the expected power of the resulting test as a function of the no-call procedure. We examine the statistical properties of the chi-squared test using a no-call procedure when the underlying continuous measure of genotype classification is a three-component mixture of univariate normal distributions under a range of parameter specifications. The genotype error rate decreases as the no-call region is increased. The expected number of observations genotyped also decreases. Our key finding is that the expected power of the chi-squared test is not sensitive to the no-call procedure. That is, the benefits of reduced genotype error rate are almost exactly balanced by the losses due to reduced genotype observations. For an underlying univariate normal mixture of genotype classification to be analyzed with a 2 x 3 chi-squared test, there is little, if any, increase in power using a no-call procedure.

Errors and linkage disequilibrium interact multiplicatively when computing sample sizes for genetic case-control association studies.

Single nucleotide polymorphisms (SNP) may be used in case-control designs to test for association between a SNP marker and a disease. Such designs may assume that the genotype data are reported without error. Our goal is quantifying the effects that errors have on sample size for case-control studies with haplotypes formed by a disease locus and a SNP marker locus in the presence of linkage disequilibrium (LD). We consider the effects of a recently published error model on 2x3 chi-square analysis. We study the joint relation of LD and errors with sample size for three specific genetic disease models and two settings each of marker allele frequencies (total of 6 studies). Minimal sample size necessary for fixed asymptotic power is estimated as a 4th degree polynomial in the variables S (error) and D' (LD measure) via a backward step-wise regression. We find that increased error rates lower power. In all studies, we observe that LD and errors interact in a non-linear fashion. In particular, regression analyses shows that several higher order interaction terms have coefficients significantly different from 0 in each study, with fraction of variance explained greater than 0.9999. Finally, the increase in sample size necessary to maintain constant asymptotic power and level of significance as a function of S is smallest when D' = 1 (perfect LD). The increase grows monotonically as D' decreases to 0.5 for all studies.

Applying a novel statistical process control model to platelet quality monitoring.

BACKGROUND: Many countries are implementing universal WBC reduction of blood components Thus, manufacturing procedures must include QC techniques to detect units that fail to meet established standards. STUDY DESIGN AND METHODS: A statistical process control model, based on the exponentially weighted moving average of the cumulative distribution function (CDF-EWMA), was developed to detect shifts in a mean and/or variance of a process. The model's parameters (weights) were optimized to maximize detection of an out-of-control process while minimizing sensitivity to autocorrelation. Validation was performed using a retrospective set of WBC-reduction data obtained from a blood bank. The WBC-reduction process was considered in control when there was 95-percent confidence that more than 95 percent of platelet concentrates would contain less than 1 x 10(6) WBCs (6.0 log WBC) as required by European standards. A sentry setting of 5.7 log WBCs was used to allow earlier detection of an out-of-control process. RESULTS: Graphic output of the CDF-EWMA model provided a continuous update of the probability that a WBC-reduction process was in control. Using the validation data, the model showed that the process was in control until Observation 332, at which point residual WBCs per unit increased. However, the first platelet concentrate to exceed specified criteria (Observation 346) occurred after the model detected that the process was out of control, demonstrating the forecasting value of this model. This deviation corresponded to an equipment failure in a single apheresis instrument. The Shewhart and EWMA techniques were similarly able to detect when the process was out of control using the test data. CONCLUSION: As a statistical process control model, the CDF-EWMA provides real-time estimation of the fraction of components meeting a regulatory limit. It is capable of detecting developing QC problems before units fail to meet regulatory requirements and is a potential alternative to other QC techniques for monitoring WBC reduction of blood components.

Two approaches for consolidating results from genome scans of complex traits: selection methods and scan statistics.

This work has two purposes: (i) empirically selecting levels of significance that maximize the fraction of markers close to a gene (hit rate) when performing linkage analyses of simulated data and (ii) evaluating the utility of a previously reported scan statistic on the same data. Genotype data were simulated from a trait model of seven susceptibility genes. For purpose (i), five statistics were evaluated on all marker loci in fifty replicates; two-point lod and heterogeneity lod scores maximized over dominance (mlod, mhlod), a multi-allelic TDT test, an affected sib-pair test (ASP), and a model-free test on all sib-pairs (ALL_SIBS). Within each replicate the fraction of markers (hit rate) significant at specified levels of significance and also (a) within fifty markers of, or (b) on the same chromosome as a major gene was calculated. For purpose (ii), scan statistics of length 15 were calculated for each chromosome and their empirical significance levels estimated on the basis of 500 replicates generated under no linkage. The scan statistic was applied to the mhlod scores from one replicate (Replicate 5). Empirical p-values for the scan statistic were determined by computing mhlod scores on 500 replicates of simulated null data. For purpose (i), significance levels between 0.001 and 0.01 had the greatest hit rate for all five methods and both criteria. For criterion (a) at the 0.001 level of significance, both mlod and mhlod displayed the highest hit rates, approximately 0.4 for each. For criterion (b), all methods but ALL_SIBS and ASP had hit rates ranging between 0.4 and 0.5. For purpose (ii), the scan statistic proved equally or more powerful than the single-locus statistic for two of the seven susceptibility genes while the remaining five genes were not detected.

Application of a Bayesian method for optimal subset regression to linkage analysis of Q1 and Q2.

We explore an approach that allows us to consider a trait for which we wish to determine the optimal subset of markers out of a set of p > or = 3 candidate markers being considered in a linkage analysis. The most effective analysis would find the model that only includes the q markers closest to the q major genes which determine the trait. Finding this optimal model using classical "frequentist" multiple regression techniques would require consideration of all 2p possible subsets. We apply the work of George and McCulloch [J Am Stat Assoc 88:881-9, 1993], who have developed a Bayesian approach to optimal subset selection regression, to a modification of the Haseman-Elston linkage statistic [Elston et al., Genet Epidemiol 19:1-17, 2000] in the analysis of the two quantitative traits simulated in Problem 2. The results obtained using this Bayesian method are compared to those obtained using (1) multiple regression and (2) the modified Haseman-Elston method (single variable regression analysis). We note upon doing this that for both Q1 and Q2, (1) we have extremely low power with all methods using the samples as given and have to resort to combining several simulated samples in order to have power of 50%, (2) the multivariate analysis does not have greater power than the univariate analysis for these traits, and (3) the Bayesian approach identifies the correct model more frequently than the frequentist approaches but shows no clear advantage over the multivariate approach.

A study comparing precision of the maximum multipoint heterogeneity LOD statistic to three model-free multipoint linkage methods.

This study compared the performance of the maximum lod (MLOD), maximum heterogeneity lod (MHLOD), maximum non-parametric linkage score (MNPL), maximum Kong and Cox linear extension (MKC(lin)) of NPL, and maximum Kong and Cox exponential extension (MKC(exp)) of NPL as calculated in Genehunter 1.2 and Genehunter-Plus. Our performance measure was the distance between the marker with maximum value for each linkage statistic and the trait locus. We performed a simulation study considering: 1) four modes of transmission, 2) 100 replicates for each model, 3) 58 pedigrees (with 592 subjects) per replicate, 4) three linked marker loci each having three equally frequent alleles, and 5) either 0% unlinked families (linkage homogeneity) or 50% unlinked families (linkage heterogeneity). For each replicate, we obtained the Haldane map position of the location at which each of the five statistics is maximized. The MLOD and MHLOD were obtained by maximizing over penetrances, phenocopy rate, and risk-allele frequencies. For the models simulated, MHLOD appeared to be the best statistic both in terms of identifying a marker locus having the smallest mean distance from the trait locus and in terms of the strongest negative correlation between maximum linkage statistic and distance of the identified position and the trait locus. The marker loci with maximum value of the Kong and Cox extensions of the NPL statistic also were closer to the trait locus than the marker locus with maximum value of the NPL statistic.

Individual latent growth curves in the development of marijuana use from childhood to young adulthood.

The present study was designed to examine the relationship between unconventionality and marijuana use over time. The sample for this paper consisted of 532 male and female participants interviewed during early adolescence, late adolescence, their early twenties, and their late twenties. Latent growth modeling was used. The findings indicated that (1) the influence of initial unconventionality (T2) on initial marijuana use (T2) was stronger for males, (2) unconventionality at T2 was not significantly related to overall rate of growth in marijuana use, and (3) change in unconventionality was related to overall growth rate of marijuana use. The implications of the findings for prevention and treatment are discussed.

Comparison of empirical strategies to maximize GENEHUNTER lod scores.

We compare four strategies for finding the settings of genetic parameters that maximize the lod scores reported in GENEHUNTER 1.2. The four strategies are iterated complete factorial designs, iterated orthogonal Latin hypercubes, evolutionary operation, and numerical optimization. The genetic parameters that are set are the phenocopy rate, penetrance, and disease allele frequency; both recessive and dominant models are considered. We selected the optimization of a recessive model on the Collaborative Study on the Genetics of Alcoholism (COGA) data of chromosome 1 for complete analysis. Convergence to a setting producing a local maximum required the evaluation of over 100 settings (for a time budget of 800 minutes on a Pentium II 300 MHz PC). Two notable local maxima were detected, suggesting the need for a more extensive search before claiming that a global maximum had been found. The orthogonal Latin hypercube design was the best strategy for finding areas that produced high lod scores with small numbers of evaluations. Numerical optimization starting from a region producing high lod scores was the strategy that found the highest maximum observed.

Process control procedures to augment quality control of leukocyte-reduced red cell blood products.

Quality control of leukocyte-reduced packed red cell units (LRprc) produced in blood facilities must conform to regulatory criteria, which state that units may not contain more than 1 x 10(6) to 5 x 10(6) white blood cells (WBC) per unit. The post-filtration WBC content of a total of n = 386 LRprc units was counted with a Nageotte chamber to model the probability that a unit would not meet the regulatory criteria. The distribution of the residual leukocyte counts is close to a negative binomial distribution (NBD) and is independent of the packed red cell volume filtered. The observed probability that a unit of blood has a residual WBC greater than 5 x 10(6) is 2.6 +/- 2.6 x 10(-3). A power analysis of the two-sample Kolmogorov-Smirnov (KS) test in this application shows that a sample size of 20 is sufficient for determining that the process is in control when an out of control process has a k NBD parameter greater than or equal to that of the in control process. The three out of control processes observed to date appear to have this property. A sample of size 80 may be necessary for confirming that process validation data sets conform to the larger 'reference' database (n = 386) for processes that are out of control in such a way that their k NBD parameter is less than the k parameter of the in control process.

Comparing estimates of the effects of air pollution on human mortality obtained using different regression methodologies.

Studies using regression techniques report their results using a variety of statistics. Evaluation of the consistency of findings, such as in a metaanalysis, requires calculating the statistical estimates of the effect reported in each study in a comparable manner. In this paper, we consider multiple linear regression, multiple Poisson regression, and logistic regression estimates. We present results that are needed to calculate, on a common basis, the slope of the regression function at a specified value, the elasticity function of the regression function at a specified value, the relative risk at a specified value, and the odds ratio at a specified value. We apply these results to studies of the association of daily mortality in an area to the daily air pollution level of ozone and PM10. We calculate the estimated slope of the number of deaths per billion population associated with an increase of 1 ppb of ozone level in studies of daily mortality in three urban areas. These studies, in Los Angeles, New York, and St. Louis, produced very comparable results on a common basis, especially when compared to the coefficients as reported. We also calculated the estimated elasticity function of the daily mortality and daily PM10 level for eight areas and found that the elasticities varied within a factor of roughly two, much less than the variability in the coefficients as reported.

Association of posterior p-values of S.A.G.E. SIBPAL proportion-IBD and Haseman-Elston statistics for ACTHR112.

A common practice among researchers performing linkage studies is the use of equal allele frequencies as input when reporting p-values from computer linkage programs such as S.A.G.E. SIBPAL. Our results, using 5,000 sets from a uniform-prior distribution of allele frequencies, showed that such input may be problematic. Further, we found that the S.A.G.E. SIBPAL test for proportion of alleles shared identical by descent among concordantly affected sib pairs showed a greater percentage of significant p-values with decreasing parental genotype information (Table III), while the S.A.G.E. SIBPAL Haseman-Elston test produced significant p-values comparatively less frequently (Table IV).

Young adult drug use and delinquency: childhood antecedents and adolescent mediators.

OBJECTIVE: The aims of this study were (1) to examine the childhood, early adolescent, and late adolescent predictors of young adult drug use and delinquency; and (2) to explore the effects of drug use on delinquent behavior. METHOD: Data were gathered during the course of a 20-year longitudinal study of children representative of the Northeast. Data were gathered on childhood aggression, early and late adolescent drug use and delinquency, and young adult drug use and delinquency. RESULTS: Overall, the results were consistent with our proposed model. Childhood aggression had an adverse effect on young adult drug use and female deviant behavior. Drug use and delinquency during early and late adolescence served as the mediator between childhood aggression and young adult drug use. Moreover, adolescent drug use was associated with later delinquency. CONCLUSIONS: The findings indicated that childhood aggression was related to both young adult drug use and delinquency. Second, there was stability of drug use and delinquency between early adolescence and young adulthood. Third, drug use during early adolescence had an impact on delinquency not only in early adolescence, but also in late adolescence and young adulthood.

Gain in efficiency from using generalized least squares in the Haseman-Elston test.

Techniques that test for linkage between a marker and a trait locus based on the regression methods proposed by Haseman and Elston [1972] involve testing a null hypothesis of no linkage by examination of the regression coefficient. Modified Haseman-Elston methods accomplish this using ordinary least squares (OLS), weighted least squares (WLS), in which weights are reciprocals of estimated variances, and generalized estimating equations (GEE). Methods implementing the WLS and GEE currently use a diagonal covariance matrix, thus incorrectly treating the squared trait differences of two sib pairs within a family as uncorrelated. Correctly specifying the correlations between sib pairs in a family yields the best linear unbiased estimator of the regression coefficient [Scheffe, 1959]. This estimator will be referred to as the generalized least squares (GLS) estimator. We determined the null variance of the GLS estimator and the null variance of the WLS/OLS estimator. The correct null variance of the WLS/OLS estimate of the Haseman-Elston (H-E) regression coefficient may be either larger or smaller than the variance of the WLS/OLS estimate calculated assuming that the squared sib-pair differences are uncorrelated. For a fully informative marker locus, the gain in efficiency using GLS rather than WLS/OLS under the null hypothesis is approximately 11% in a large multifamily study with three siblings per family and 25% for families with four siblings each.

Testing the measurement properties of risk assessment instruments in child protective services.

This study examined a population of children alleged to be at risk of abuse and the adult allegedly abusing the child for the purpose of identifying variables that were predictive of the child's risk of being abused. The study population consisted of 72 Brooklyn, New York children and the alleged adult abuser. These cases were investigated in the Child Protective Services office in Bedford-Stuyvesant by 12 workers who volunteered to participate in the research effort. The worker assigned to a case filled out the standard New York City case recording instrument (called the Child Protective Services Review Document, CPSRD for short), the Magura-Moses Child Well-Being Scales, and the Beck and Jones List of Problems and Conditions. In addition, the worker also evaluated the degree of risk of abuse that the child was exposed to from the alleged abuser using a supplemental scale created for this study. Our hypotheses were that variables from each of the instruments would be predictive of the case decision-making by protective service workers regarding the abuse to which a child was exposed, that the data from the Magura-Moses scales would have predictive value for a minority population, and that the data from the CPSRD would reflect unique dimensions of this population. The data from the 72 cases supported each of these hypotheses.

Where is the likelihood ratio test powerful for detecting two component normal mixtures?

We compare the power of the likelihood ratio test, the Engelman-Hartigan test, two outlier tests, four goodness-of-fit tests, and eight tests of normality to detect a mixture consisting of two components that are normally distributed with different means but equal variances. We consider the entire range of mixing proportions pi, 0 < pi < 1. For pi > .85 or pi < .15, overall Fisher's skewness statistic is best with Filliben's probability plot correlation coefficient test somewhat less powerful. A combined skewness and kurtosis test, the Anderson-Darling test, and the likelihood ratio test are also competitive. For .35 < pi < .65, the Engelman-Hartigan test is best. For other mixing proportions, the likelihood ratio test is best. For situations in which the preferred test had power 50% or more, the power of the likelihood ratio test is also above 50% and within 15 percentage points of the preferred test.

Direct evidence for active metalloproteinases mediating matrix degradation in interleukin 1-stimulated human articular cartilage.

When adult human articular cartilage was maintained in organ culture in the presence of interleukin 1 beta, increased destruction of the extracellular matrix was observed, as judged by increased type II collagen degradation in situ determined immunohistochemically and the increased release of proteoglycan into the culture medium. Concomitant with these changes was the increased release of latent metalloproteinases into the culture medium. Culture of cartilage in the presence of a peptidylhydroxamate metalloproteinase inhibitor indicated a key role for the active forms of these enzymes in situ, since it produced a marked reduction in both proteoglycan release and collagen degradation. This compound had no detectable cytotoxic effects in organ culture and did not reduce the secretion of the metalloproteinases. The results of this study provide direct evidence that the latent metalloproteinase precursors, whose release is greatly stimulated by interleukin 1, are indeed activated to some degree and participate in cartilage matrix degradation.

LISREL modeling of high density lipoprotein cholesterol (HDL) levels in male twins.

Based on the LISREL modeling approach for data from monozygotic (MZ) and dizygotic (DZ) twins [Heath et al., 1989; Neale and Cardon, 1992], the hypothesized variance of the logarithm of high density lipoprotein cholesterol due to additive genetic factors was estimated to equal 19% for males. Unobserved common environment accounted for 32% of the variance of log HDL. Both estimates controlled for body mass, alcohol consumption, and smoking. The model had very strong goodness-of-fit indices.

Serving the urban poor: a study of child welfare preventive services.

This summary, for journal publication, of a study whose full details are being published in book form, brings the welfare field up-to-date on what began as a precedent-setting agency. The Lower East Side Family Union, in New York City, has provided many years of service, and has justifiably drawn national attention from its inception, when prevention was more talked about than funded. The lessons to be drawn from its work and the example it has set grow more timely every year.

Social indicators and the prediction of psychiatric inpatient service utilisation.

The relationship between social variables and psychiatric service use in Victoria was investigated using a social indicators approach. Indicators were developed separately for the urban and rural areas of the state using 1986 census data. Principal components analysis was employed to reduce the data. Simple, unit weight indicators were developed and explained a considerable proportion of the variation in the rate of persons admitted to psychiatric facilities, the rate of admission episodes and the rate of occupied bed days for urban areas; a moderate amount of variation for these measures was accounted for by indicators developed for rural areas. The findings were considered in relation to both methodological issues and the role of other factors (e.g., accessibility and availability of psychiatric services) which may contribute to service use.

The likelihood ratio test for the two-component normal mixture problem: power and sample size analysis.

We find, through simulation and modeling, an approximation to the alternative distribution of the likelihood ratio test for two-component mixtures in which the components have different means but equal variances. We consider the range of mixing proportions from 0.5 through .95. Our simulation results indicate a dependence of power on the mixing proportion when pi less than .2 and pi greater than .80. Our model results indicated that the alternative distribution is approximately noncentral chi-square, possibly with 2 degrees of freedom. Using this model, we estimate a sample of 40 is needed to have 50% power to detect a difference between means equal to 3.0 for mixing proportions between .2 and .8. The sample size increases to 50 when the mixing proportion is .90 (or .1) and 82 when the mixing proportion is .95 (or .05). This paper contains a complete table of sample sizes needed for 50%, 80%, and 90% power.