Discordant Sib Pairs Research Articles

A Novel Framework for Sib Pair Linkage Analysis

Sib pair linkage analysis of a dichotomous trait is a popular method for narrowing the search for genes that influence complex diseases. Although the pedigree structures are uncomplicated and the underlying genetic principles straightforward, a surprising degree of complexity is involved in implementing a sib pair study and interpreting the results. Ascertainment may be based on affected, discordant, or unaffected sib pairs, as well as on pairs defined by threshold values for quantitative traits, such as extreme discordant sib pairs. To optimize power, various domain restrictions and null hypotheses have been proposed for each of these designs, yielding a wide array of choices for the analyst. To begin, we systematically classify the major sources of discretion in sib pair linkage analysis. Then, we extend the work of Kruglyak and Lander (1995), to bring the various forms into a unified framework and to facilitate a more general approach to the analysis. Finally, we describe a new, freely available computer program, Splat (Sib Pair Linkage Analysis Testing), that can perform any sib pair statistical test currently in use, as well as any user-defined test yet to be proposed. Splat uses the expectation maximization algorithm to calculate maximum-likelihood estimates of sharing (subject to user-specified conditions) and then plots LOD scores versus chromosomal position. It includes a novel grid-scanning capability that enables simultaneous visualization of multiple test statistics. This can lead to further insight into the genetic basis of the disease process under consideration. In addition, phenotype definitions can be modified without the recalculation of inheritance vectors, thereby providing considerable flexibility for exploratory analysis. The application of Splat will be illustrated with data from studies on the genetics of diabetic nephropathy.

Practical Considerations on the Use of Extreme Sib-pairs for Obesity

The extreme sib-pair approach has been shown to be a powerful strategy to identify susceptibility loci linked to quantitative traits. The body mass index is the usually assessed trait in genetic studies on human obesity. Environmental factors clearly play an important role for this trait. We hypothesized that the low weight of most sibs who were seemingly discordant to the obese index proband was influenced by other environmental and/or genetic factors like restrained eating or psychiatric disorders. A screening questionnaire was sent to parents of all consecutively admitted patients three weeks prior to referral of index probands for inpatient treatment of obesity. The first 320 families were further investigated. Twenty-seven seemingly extremely discordant sib-pairs (ED) were identified and examined in detail. The low weight of most sibs who were seemingly discordant to the obese index proband was influenced by factors like restrained eating or psychiatric disorders. Only 20% of the interviewed ED could be considered as genuine ED. We conclude that extensive medical evaluation is necessary if the aim is to guarantee genuine ED in family studies for human obesity. Non-paternity deserves specific attention in ED studies.

A novel method to identify gene–gene effects in nuclear families: the MDR‐PDT

It is now well recognized that gene-gene and gene-environment interactions are important in complex diseases, and statistical methods to detect interactions are becoming widespread. Traditional parametric approaches are limited in their ability to detect high-order interactions and handle sparse data, and standard stepwise procedures may miss interactions that occur in the absence of detectable main effects. To address these limitations, the multifactor dimensionality reduction (MDR) method [Ritchie et al., 2001: Am J Hum Genet 69:138-147] was developed. The MDR is well-suited for examining high-order interactions and detecting interactions without main effects. The MDR was originally designed to analyze balanced case-control data. The analysis can use family data, but requires a single matched pair be selected from each family. This may be a discordant sib pair, or may be constructed from triad data when parents are available. To take advantage of additional affected and unaffected siblings requires a test statistic that measures the association of genotype with disease in general nuclear families. We have developed a novel test, the MDR-PDT, by merging the MDR method with the genotype-Pedigree Disequilibrium Test (geno-PDT)[Martin et al., 2003: Genet Epidemiol 25:203-213]. MDR-PDT allows identification of single-locus effects or joint effects of multiple loci in families of diverse structure. We present simulations to demonstrate the validity of the test and evaluate its power. To examine its applicability to real data, we applied the MDR-PDT to data from candidate genes for Alzheimer disease (AD) in a large family dataset. These results show the utility of the MDR-PDT for understanding the genetics of complex diseases.

Incorporating endophenotypes into allele‐sharing based linkage tests

For a genetic study in which there are concordant and discordant sibpairs for a complex disease trait and the measurements of other endophenotypes/intermediate phenotypes for each of the individuals are also available, we describe an allele-sharing based multipoint linkage test that utilizes nonparametrically the additional endophenotypes/intermediate phenotypes. The usefulness of this method is evaluated in simulation studies, which show that the gain in power is influenced by not only the endophenotypic value but also the correlation between the diagnosis-based phenotype and the endophenotype. In addition to reporting p values, our method also provides an index C(E), derived from the coefficients of the weight function associated with the endophenotype in the proposed statistic, to indicate the relevance of a specific endophenotype/intermediate phenotype in the genetic study. The simulation study indicates that a larger power, in general, corresponds to a larger value of the index C(E). The index C(E) is thus suggested as a quantity to be used in the choice of endophenotypes in linkage study. Data from the Stanford Asian Pacific Program in Hypertension and Insulin Resistance (SAPPHIRe) are used to illustrate the method.

Genotypic interaction between DRD4 and DAT1 loci is a high risk factor for attention‐deficit/hyperactivity disorder in Chilean families

Attention-deficit/hyperactivity disorder, ADHD [MIM 126452], is a common, highly heritable neurobiological disorder of childhood onset, characterized by hyperactivity, impulsiveness, and/or inattentiveness. As part of an ongoing study of ADHD, we carried out a family-based discordant sib-pair analysis to detect possible associations between dopamine receptor D4 (DRD4) and dopamine transporter 1 (DAT1) polymorphisms and ADHD in Chilean families. Both loci individually classified as homozygotes or heterozygotes for the DRD4 7-repeat and DAT1 10-repeat alleles, did not exhibit genotype frequency differences between affected children and their healthy siblings (Fisher's exact test P > 0.25 in both cases). However, the simultaneous presence of both DRD4 7-repeat heterozygosity and DAT1 10 allele homozygosity were significantly higher (34.6%) in cases (26), compared with their unaffected siblings (25) (4%; Fisher's exact test P = 0.0096; odds-ratio, OR = 12.71). Increased density of dopamine transporter in ADHD brains, along with abundance of 7-repeat D4 receptors in prefrontal cortex, which is impaired in ADHD patients, make the observed gene-gene interaction worthy of further incisive studies.

Multifactor-dimensionality reduction versus family-based association tests in detecting susceptibility loci in discordant sib-pair studies

Complex diseases are generally thought to be under the influence of multiple, and possibly interacting, genes. Many association methods have been developed to identify susceptibility genes assuming a single-gene disease model, referred to as single-locus methods. Multilocus methods consider joint effects of multiple genes and environmental factors. One commonly used method for family-based association analysis is implemented in FBAT. The multifactor-dimensionality reduction method (MDR) is a multilocus method, which identifies multiple genetic loci associated with the occurrence of complex disease. Many studies of late onset complex diseases employ a discordant sib pairs design. We compared the FBAT and MDR in their ability to detect susceptibility loci using a discordant sib-pair dataset generated from the simulated data made available to participants in the Genetic Analysis Workshop 14. Using FBAT, we were able to identify the effect of one susceptibility locus. However, the finding was not statistically significant. We were not able to detect any of the interactions using this method. This is probably because the FBAT test is designed to find loci with major effects, not interactions. Using MDR, the best result we obtained identified two interactions. However, neither of these reached a level of statistical significance. This is mainly due to the heterogeneity of the disease trait and noise in the data.

Linkage analysis of alcohol dependence using both affected and discordant sib pairs.

The basic idea of affected-sib-pair (ASP) linkage analysis is to test whether the inheritance pattern of a marker deviates from Mendelian expectation in a sample of ASPs. The test depends on an assumed Mendelian control distribution of the number of marker alleles shared identical by descent (IBD), i.e., 1/4, 1/2, and 1/4 for 2, 1, and 0 allele(s) IBD, respectively. However, Mendelian transmission may not always hold, for example because of inbreeding or meiotic drive at the marker or a nearby locus. A more robust and valid approach is to incorporate discordant-sib-pairs (DSPs) as controls to avoid possible false-positive results. To be robust to deviation from Mendelian transmission, here we analyzed Collaborative Study on the Genetics of Alcoholism data by modifying the ASP LOD score method to contrast the estimated distribution of the number of allele(s) shared IBD by ASPs with that by DSPs, instead of with the expected distribution under the Mendelian assumption. This strategy assesses the difference in IBD sharing between ASPs and the IBD sharing between DSPs. Further, it works better than the conventional LOD score ASP linkage method in these data in the sense of avoiding false-positive linkage evidence.

Assessing genetic susceptibility to diabetic nephropathy

Diabetic nephropathy is a serious complication of diabetes and the leading cause of end-stage renal disease. Studies indicate both environmental and genetic factors contribute to the development and progression of diabetic nephropathy. In particular, epidemiological evidence shows a familial clustering of nephropathy in siblings with diabetes, supporting an important role of genetic susceptibility in the pathogenesis of diabetic nephropathy. A common approach in genetic research is assessment of candidate gene polymorphisms using case-control analysis; a number of studies have evaluated predictable candidate genes for diabetic nephropathy. In contrast, only a few studies have used a whole genome approach, such as scanning of micro-satellite markers, in the assessment of genetic susceptibility to diabetic nephropathy. A whole genome linkage analysis using families of Pima Indians showed susceptibility loci for diabetic nephropathy on chromosome 3, 7, and 20. Another linkage analysis using discordant sib-pairs of Caucasian families with type 1 diabetes identified a critical area on chromosome 3q. However, these results have been inconclusive and further investigation is required. Recently, a genome-wide, case-control analysis identifying susceptibility genes for diabetic nephropathy was performed. As a result, a single nucleotide polymorphism in exon 23 of the solute carrier family 12 (sodium-chloride cotransporter) member 3 gene was found to be strongly associated with diabetic nephropathy. Although further assessment of this polymorphism is needed, this strategy offers great promise in the identification of genetic factors predisposing patients to diabetic nephropathy. Identification of genetic susceptibility markers may offer new hope in the diagnosis and treatment of diabetic nephropathy.

Meprin β metalloprotease gene polymorphisms associated with diabetic nephropathy in the Pima Indians

There is evidence that susceptibility to diabetic nephropathy has a significant genetic component. This investigation tested the hypothesis that variations in the structural or regulatory regions of the MEP1B gene are related to susceptibility to diabetic nephropathy in the Pima Indian population. The structure of the human MEP1B gene on chromosome 18 was determined by polymerase chain reaction (PCR) amplification. Samples from 154 diabetic individuals were analyzed for polymorphisms. These individuals belonged to 65 sibships with at least one sibling pair discordant for diabetic nephropathy. Approximately half of the individuals had diabetic nephropathy. Of the 154 samples, there were 91 discordant sibling pairs. Sequencing revealed 19 single nucleotide polymorphisms (SNPs) in the MEP1B gene. SNPs 1-5 were in the 5' region upstream of the start site for transcription; SNPs 6, 7, 9, 11-15, 17, and 19 were within introns; SNPs 8, 10, 16, and 18 were in exons 4, 9, 12, and 14. SNP 18 was the only one that results in an amino acid change (proline to leucine in the cytoplasmic tail). No overall associations were found for individual SNPs. Within-family association tests found significant results for SNPs 1, 3, 4, 5, 6, 9, 11, 18, and 19 such that the more common allele was more frequently observed in those with nephropathy than in their unaffected siblings. The present study demonstrates significant within-family association for SNPs in MEP1B gene with diabetic nephropathy. These results could be explained by functional effects of one or more of these SNPs or by linkage disequilibrium with a nearby functional locus.

Identifying Susceptibility Genes for Prostate Cancer—A Family-Based Association Study of Polymorphisms in CYP17, CYP19, CYP11A1, and LH-β

Polymorphisms in genes that code for enzymes or hormones involved in the synthesis and metabolism of androgens are compelling biological candidates for prostate cancer. Four such genes, CYP17, CYP19, CYP11A1, and LH-beta, are involved in the synthesis and conversion of testosterone to dihydrotestosterone and estradiol. In a study of 715 men with and without prostate cancer from 266 familial and early-onset prostate cancer families, we examined the association between prostate cancer susceptibility and common single-nucleotide polymorphisms in each of these four candidate genes. Family-based association tests revealed a significant association between prostate cancer and a common single-nucleotide polymorphism in CYP17 (P=0.004), with preferential transmission of the minor allele to unaffected men. Conditional logistic regression analysis of 461 discordant sibling pairs from these same families reaffirmed the association between the presence of the minor allele in CYP17 and prostate cancer risk (odds ratio, 0.51; 95% confidence interval, 0.28-0.92). These findings suggest that variation in or around CYP17 predicts susceptibility to prostate cancer. Family-based association tests may be especially valuable in studies of genetic variation and prostate cancer risk because this approach minimizes confounding due to population substructure, which is of particular concern for prostate cancer given the tremendous variation in the worldwide incidence of this disease.

Identification of functional candidate genes for body composition by expression analyses and evidencing impact by association analysis and mapping

This study aims to identify hepatic genes affecting traits related to muscularity and obesity by combining expression analyses, association studies, and gene mapping. Functional candidate genes with trait-associated expression were obtained by hybridising custom made application-specific cDNA microarrays with targets of discordant sib pairs of a porcine experimental population. Out of 238 genes addressed, nine genes were regulated by the factor ≥ 2 between the sib pairs. Differential gene expression was independently confirmed for selected genes by real time RT-PCR. Transcript levels of four genes (APOH, PEDF, SLCO1B3, TBG) were significantly different between the phenotype groups. Screening for trait associated markers within TBG and APOH by comparative sequencing of discordant sib pairs revealed a SNP at position nt 778 (A > C) (N229H) of TBG. No polymorphism in APOH was detected. Association analysis confirmed effects of TBG on carcass traits statistically. Allocating TBG to a QTL region on chromosome X revealed genetic evidence for the effect. Moreover, our results indicate that there are probably two polymorphisms segregating-one (N229H) altering binding capability of TBG and another still to be detected altering the transcription rate of TBG.

Brain MRI abnormalities in schizophrenia: same genes or same environment?

Structural brain volume abnormalities are among the most extensively studied endophenotypes in schizophrenia. Bivariate genetic model fitting (adjusted to account for selection) was used to quantify the genetic relationship between schizophrenia and brain volumes and to estimate the heritability of these volumes. We demonstrated by simulation that the adjusted genetic model produced unbiased estimates for endophenotype heritability and the genetic and environmental correlations. The model was applied to brain volumes (whole brain, hippocampus, third and lateral ventricles) in a sample of 14 monozygotic (MZ) twin pairs concordant for schizophrenia, 10 MZ discordant pairs, 17 MZ control pairs, 22 discordant sibling pairs, three concordant sibling pairs, and 114 healthy control subjects. Whole brain showed a substantial heritability (88%) and lateral ventricles substantial common environmental effects (67%). Whole brain showed a significant genetic correlation with schizophrenia, whereas lateral ventricles showed a significant individual specific correlation with schizophrenia. There were significant familial effects for hippocampus and third ventricle, but the analyses could not resolve whether these were genetic or environmental in origin (around 30%each). Using genetic model fitting on twin and sibling data we have demonstrated differential sources of covariation between schizophrenia and brain volumes, genetic in the case of whole brain volume and individual specific environment in the case of lateral ventricles.

Blood is thicker than water

Case-control studies are commonly used in clinical research to test the association of risk factors with diseases. Typically, the comparison subjects selected are unrelated to the cases. However, the use of unrelated controls may introduce bias when the studies are conducted in ethnically heterogeneous populations such as the United States.1 Specifically, disease and risk factor frequencies (genetic and environmental) may vary according to ethnicity. Unequal distributions of ethnic subgroups in case and unrelated control samples may therefore result in spurious association findings (population stratification bias). By contrast, in the absence of nonpaternity, case-unaffected sibling pairs are matched for ethnicity. Therefore, statistical methods have been developed to compare the frequency of risk factors in discordant sibling pairs (e.g., sibling transmission disequilibrium test).2 Although family-based association studies have been employed primarily for the study of genetic factors, the same design can be employed for the study of environmental factors.3 Indeed, in this issue of Neurology , Scott et al.3 report findings from a family-based case-control study of cigarette smoking and Parkinson disease (PD). They interviewed 143 PD cases and their 168 unaffected siblings …

Family-based case-control study of cigarette smoking and Parkinson disease

To determine whether people with Parkinson disease (PD) are less likely to report a history of cigarette smoking than their unaffected siblings. Previous studies reported that individuals with PD are half as likely to have smoked as those unaffected by PD. Other studies reported that smoking modified the risk of PD due to polymorphisms in the MAO-B and nNOS genes. Thus, genetic studies of PD should consider confounding or interaction with smoking history as well. The authors have collected detailed smoking histories on a family-based case-control sample ascertained for genetic studies of PD. In a matched case-control study of 140 sibships, individuals with PD (n = 143) were compared to sibling controls (n = 168). Cigarette smoking history was collected by a structured telephone interview. Conditional logistic regression was used to examine the relationship between smoking and PD while controlling for confounding by age and sex. Ever smoking, current smoking, and increasing duration (in years), dose (in packs/day), and intensity (in pack-years) of smoking were significantly inversely associated with PD (p < 0.05). The association was not modified by sex, age at onset, or recency of exposure. Consistent with previous studies, individuals with Parkinson disease are significantly less likely to have smoked regularly than their unaffected siblings. This association was detected even though discordant sibling pairs are more likely to be overmatched for environmental exposures than unmatched case and control groups.

QTL mapping with discordant and concordant sibling pairs: new statistics and new design strategies

The term "extreme discordant and concordant" (EDAC) sampling has been used to describe a variety of strategies for quantitative trait locus mapping using sibling pairs sampled from the corners of the bivariate trait distribution. The principle of the design is to gain efficiency by genotyping only the most informative of the available sibling pairs. EDAC-type designs have been studied in a number of papers, and have been applied in a few others. This literature is somewhat out of date, however, because there are many new statistics that are appropriate for EDAC data. With newer statistics, the power of EDAC designs can be improved. Moreover, the relative power of different designs must be re-evaluated, because the newer statistics improve the power of some designs more than others. That is, there is a circular relationship between design and statistic choices. In this report, we review a number of available design and statistic choices for EDAC studies, and use simulation to show what statistics are most powerful for each design. We then use those more powerful statistics to suggest strategies for making design choices among various EDAC and non-EDAC designs that use sibling pairs. We find that when genotyping must be minimized, an EDAC design with predominantly discordant pairs is the best choice, and when a balance of genotyping and phenotyping effort must be achieved, single proband ascertainment can do better. We also show that moderately selected samples (as opposed to very extreme samples) can be an efficient choice for many studies.

Familial cognitive deficits in schizophrenia

Susceptibility to schizophrenia is considered familial, but the mechanism for transmission has not been found. Since widespread cognitive deficits have been found in patients with schizophrenia, several of these have been proposed as candidate familial endophenotypes that may or may not be predictive of who develops the illness. The current study examines these candidates in individuals from 32 families with at least 2 members having the diagnosis of chronic schizophrenia and normal comparison subjects using an extensive neuropsychological battery. Consistent with previous literature, family members with schizophrenia were significantly impaired on all measures compared with controls. Well relatives demonstrated significantly worse performance on a measure of verbal learning, delayed visual recall, perceptual-motor, and pure motor speed. Expressive and receptive language, but not other functions, were highly correlated within both concordant for schizophrenia and discordant sibling pairs, suggesting that they are familial vulnerability endophenotypes, but not predictive of whom becomes ill. On the other hand, some measures of perceptual-motor, pure motor speed, and frontal/executive functioning were significantly correlated in concordant, but not discordant pairs. These latter correlations suggest that some cognitive measures may be genetically related to the illness.

Gene expression analysis of peripheral blood leukocytes from discordant sib-pairs with schizophrenia and bipolar disorder reveals points of convergence between genetic and functional genomic approaches

We performed global RNA transcript analysis and comprehensive gene group analysis of peripheral blood leukocyte (PBL) RNA from two groups of matched sib-pairs that were discordant for either schizophrenia (n = 33 sib-pairs) or bipolar disorder (n = 5 sib-pairs). The pairs chosen for these analyses were selected from families with known patterns of genetic linkage (5q for schizophrenia and 6q for bipolar disorder). At the single gene level, we obtained lists of the transcripts with the most significant changes in expression and from these lists determined those with the highest degree of predictive power for classifying subjects according to diagnosis in these samples. At the gene group level, we comprehensively analyzed pairwise expression changes of more than 4,000 functional groups and cytogenetic locations, and present a novel method of displaying these data that we term "cytogenomic" mapping. Verification of selected changes in expression was performed using quantitative real-time RT-PCR. Our results provide compelling evidence for the utility of analyzing PBL RNA for changes in expression in neuropsychiatric disorders.

A Discordant Sib-Pair Linkage Analysis of Age-Related Macular Degeneration

Background:Age-related macular degeneration (AMD) is the leading cause of visual impairment and blindness among older adults in the United States and throughout the developed world. Etiological research implicates both genetic and environmental components. Our prior genome scan in 511 affected sib-pairs and other relative pairs identified significant or suggestive linkage signals on chromosomes 1, 2, 3, 6, 8, 10, 12, 16, and 22. Purpose:To search for genetic loci for AMD using the extremely discordant sib-pair (EDSP) method of linkage analysis, which until now has never been applied to the study of AMD. Methods: The EDSP method is a more powerful approach than standard methods which rely on relative pairs selected at random or pairs concordant for the phenotype. The EDSP approach has also been characterized as the only design that is uniformly powerful in nearly all genetic situations. Thus, substantial reductions in sample size can be achieved. Study population:The study sample for analysis included 110 EDSPs from 40 families that comprise a subset of the 158 families studied in a prior genome-wide scan using affected relative pairs. Results: Evidence for linkage was found on chromosomes 1q, 2q, 6q, 19p, and 20q. The regions identified on chromosomes 1q and 2q were the same regions identified in our prior analysis, whereas the identified region on 6q was approximately 80 cM distal to our previous signal. Discussion: Within this study population, we have narrowed the focus to chromosomes 1q, 2q, 6q, 19p, and 20q in our search for AMD loci. However, given the fact that a gene was recently identified on chromosome 1q, future family- and population-based analyses should concentrate on testing for associations with candidate gene variants in the other identified chromosomal regions in searches for additional AMD loci.

Linkage mapping methods applied to the COGA data set: Presentation Group 4 of Genetic Analysis Workshop 14

Presentation Group 4 participants analyzed the Collaborative Study on the Genetics of Alcoholism data provided for Genetic Analysis Workshop 14. This group examined various aspects of linkage analysis and related issues. Seven papers included linkage analyses, while the eighth calculated identity-by-descent (IBD) probabilities. Six papers analyzed linkage to an alcoholism phenotype: ALDX1 (four papers), ALDX2 (one paper), or a combination both (one paper). Methods used included Bayesian variable selection coupled with Haseman-Elston regression, recursive partitioning to identify phenotype and covariate groupings that interact with evidence for linkage, nonparametric linkage regression modeling, affected sib-pair linkage analysis with discordant sib-pair controls, simulation-based homozygosity mapping in a single pedigree, and application of a propensity score to collapse covariates in a general conditional logistic model. Alcoholism linkage was found with > or =2 of these approaches on chromosomes 2, 4, 6, 7, 9, 14, and 21. The remaining linkage paper compared the utility of several single-nucleotide polymorphism (SNP) and microsatellite marker maps for Monte Carlo Markov chain combined oligogenic segregation and linkage analysis, and analyzed one of the electrophysiological endophenotypes, ttth1, on chromosome 7. Linkage was found with all marker sets. The last paper compared the multipoint IBD information content of several SNP sets and the microsatellite set, and found that while all SNP sets examined contained more information than the microsatellite set, most of the information contained in the SNP sets was captured by a subset of the SNP markers with approximately 1-cM marker spacing. From these papers, we highlight three points: a 1-cM SNP map seems to capture most of the linkage information, so denser maps do not appear necessary; careful and appropriate use of covariates can aid linkage analysis; and sources of increased gene-sharing between relatives should be accounted for in analyses.

A Powerful and Robust New Linkage Statistic for Discordant Sibling Pairs

Previously, Szatkiewicz and colleagues evaluated the performance of a wide variety of statistics for quantitative-trait-locus linkage, using discordant sibling pairs. They found that the most powerful statistics, in general, were a score statistic and a "composite statistic." However, whereas these two statistics have equal power under ideal conditions, each has limitations that reduce its power in certain circumstances. The score statistic depends on estimates of trait parameters and can lose a lot of power if those estimates are incorrect. The composite statistic is not sensitive to trait-parameter estimates but does depend on arbitrary weights that must be chosen on the basis of the ascertainment scheme. In this report, we elucidate the algebraic relationship between the score and composite statistics and then use that relationship to suggest a new statistic that combines the best properties of both. We call our new statistic the "robust discordant pair" (RDP) statistic. We report simulation studies to show that the RDP statistic does, indeed, have all of the strengths and none of the weaknesses of the score and composite statistics.