Implications of the Co-Dominance Model for Hardy-Weinberg Testing in Genetic Association Studies.

INTRODUCTION: The standard way of using tests for compatibility of genetic markers with the Hardy-Weinberg equilibrium (HWE) assumptionvas a means of quality control in genetic association studies (GAS) is to vcarry out this step of preliminary data analysis with the sample of non-diseased vindividuals only. We show that this strategy has no rational basis whenever the genotype--phenotype relation for avmarker under consideration satisfies the assumption of co-dominance. METHODS/RESULTS: The justification of this statement is the fact rigorously shown here that under co-dominance, the genotype distribution of a diallelic marker is in HWE among the controls if and only if the same holds true for the cases. CONCLUSION: The major practical consequence of that theoretical result is that under the co-dominance model, testing for HWE should be done both for cases and controls aiming to establish the combined (intersection) hypothesis of compatibility of both underlying genotype distributions with the HWE assumption. A particularly useful procedure serving this purpose is obtained through applying the confidence-interval inclusion rule derived by Wellek, Goddard and Ziegler (Biom J. 2010; 52:253-270) to both samples separately and combining these two tests by means of the intersection-union principle.

Normal Fetal Growth Profile at 10-41 Weeks of Gestation - An Update Based on 10225 Normal Singleton Pregnancies and Measurement of the Fetal Parameters Using 3D Ultrasound.

OBJECTIVE: To construct new growth charts and tables for the following fetal growth parameters: biparietal diameter (BPD), occipitofrontal diameter (OFD), head circumference (HC), abdominal transverse diameter (ATD), abdominal sagittal diameter (ASD), abdominal circumference (AC), femur length (Fe), tibia length (Ti), fibula length (Fi), humerus length (Hu), radius length (Ra), and ulna length (Ul). PATIENTS AND METHODS: This prospective study was conducted at a level III ultrasound center as a population-based cross-sectional study on 10 225 normal singleton pregnancies with a gestational age between 10 and 41 completed weeks. Gestational age was confirmed in all cases by an ultrasound examination with crown-rump measurement before 10 weeks of gestation. All examinations were performed with 3 D probes. BPD, OFD, ATD, and ASD were measured as outer-to-outer measurements (skin-to-skin) after identifying the exact biometric planes by 3 D multiplanar display. HC was computed using the formula . For AC the approximate elliptical formula AC = (ATD+ASD)/2 × 3.142 was used. Measurements of the limb bones included the entire ossified shaft. RESULTS: Based on a nonlinear regression model for the age-specific mean values, distribution-free reference ranges were calculated for the parameters BPD, OFD, HC, ATD, ASD, AC, Fe, Ti, Fi, Hu, Ra and Ul. The new reference ranges were compared with our reference ranges published in 1996 as well as with different reference charts published by other authors. CONCLUSION: 3 D ultrasound allows a controlled demonstration of all fetal planes required for exact biometric measurements. The fetal growth profile including the 12 biometric parameters gives a precise overview of normal or abnormal fetal growth.

Termination rates and histological reclassification of active surveillance patients with low- and early intermediate-risk prostate cancer: results of the PREFERE trial.

PURPOSE: Active surveillance (AS) strategies for patients with low- and early intermediate-risk prostate cancer are still not consistently defined. Within a controlled randomized trial, active surveillance was compared to other treatment options for patients with prostate cancer. Aim of this analysis was to report on termination rates of patients treated with AS including different grade groups. METHODS: A randomized trial comparing radical prostatectomy, active surveillance, external beam radiotherapy and brachytherapy was performed from 2013 to 2016 and included 345 patients with low- and early intermediate-risk prostate cancer (ISUP grade groups 1 and 2). The trial was prematurely stopped due to slow accrual. A total of 130 patients were treated with active surveillance. Among them, 42 patients were diagnosed with intermediate-risk PCA. Reference pathology and AS quality control were performed throughout. RESULTS: After a median follow-up time of 18.8 months, 73 out of the 130 patients (56%) terminated active surveillance. Of these, 56 (77%) patients were histologically reclassified at the time of rebiopsy, including 35% and 60% of the grade group 1 and 2 patients, respectively. No patients who underwent radical prostatectomy at the time of reclassification had radical prostatectomy specimens ≥ grade group 3. CONCLUSION: In this prospectively analyzed subcohort of patients with AS and conventional staging within a randomized trial, the 2-year histological reclassification rates were higher than those previously reported. Active surveillance may not be based on conventional staging alone, and patients with grade group 2 cancers may be recommended for active surveillance in carefully controlled trials only.

Sample size planning of two-arm superiority and noninferiority survival studies with discrete follow-up.

In clinical trials using lifetime as primary outcome variable, it is more the rule than the exception that even for patients who are failing in the course of the study, survival time does not become known exactly since follow-up takes place according to a restricted schedule with fixed, possibly long intervals between successive visits. In practice, the discreteness of the data obtained under such circumstances is plainly ignored both in data analysis and in sample size planning of survival time studies. As a framework for analyzing the impact of making no difference between continuous and discrete recording of failure times, we use a scenario in which the partially observed times are assigned to the points of the grid of inspection times in the natural way. Evaluating the treatment effect in a two-arm trial fitting into this framework by means of ordinary methods based on Cox's relative risk model is shown to produce biased estimates and/or confidence bounds whose actual coverage exhibits marked discrepancies from the nominal confidence level. Not surprisingly, the amount of these distorting effects turns out to be the larger the coarser the grid of inspection times has been chosen. As a promising approach to correctly analyzing and planning studies generating discretely recorded failure times, we use large-sample likelihood theory for parametric models accommodating the key features of the scenario under consideration. The main result is an easily implementable representation of the expected information and hence of the asymptotic covariance matrix of the maximum likelihood estimators of all parameters contained in such a model. In two real examples of large-scale clinical trials, sample size calculation based on this result is contrasted with the traditional approach, which consists of applying the usual methods for exactly observed failure times. Copyright © 2017 John Wiley & Sons, Ltd.

A U-statistics based approach to sample size planning of two-arm trials with discrete outcome criterion aiming to establish either superiority or noninferiority.

In current practice, the most frequently applied approach to the handling of ties in the Mann-Whitney-Wilcoxon (MWW) test is based on the conditional distribution of the sum of mid-ranks, given the observed pattern of ties. Starting from this conditional version of the testing procedure, a sample size formula was derived and investigated by Zhao et al. (Stat Med 2008). In contrast, the approach we pursue here is a nonconditional one exploiting explicit representations for the variances of and the covariance between the two U-statistics estimators involved in the Mann-Whitney form of the test statistic. The accuracy of both ways of approximating the sample sizes required for attaining a prespecified level of power in the MWW test for superiority with arbitrarily tied data is comparatively evaluated by means of simulation. The key qualitative conclusions to be drawn from these numerical comparisons are as follows: With the sample sizes calculated by means of the respective formula, both versions of the test maintain the level and the prespecified power with about the same degree of accuracy. Despite the equivalence in terms of accuracy, the sample size estimates obtained by means of the new formula are in many cases markedly lower than that calculated for the conditional test. Perhaps, a still more important advantage of the nonconditional approach based on U-statistics is that it can be also adopted for noninferiority trials. Copyright © 2016 John Wiley & Sons, Ltd.

A critical evaluation of the current "p-value controversy".

This article has been triggered by the initiative launched in March 2016 by the Board of Directors of the American Statistical Association (ASA) to counteract the current p-value focus of statistical research practices that allegedly "have contributed to a reproducibility crisis in science." It is pointed out that in the very wide field of statistics applied to medicine, many of the problems raised in the ASA statement are not as severe as in the areas the authors may have primarily in mind, although several of them are well-known experts in biostatistics and epidemiology. This is mainly due to the fact that a large proportion of medical research falls under the realm of a well developed body of regulatory rules banning the most frequently occurring misuses of p-values. Furthermore, it is argued that reducing the statistical hypotheses tests nowadays available to the class of procedures based on p-values calculated under a traditional one-point null hypothesis amounts to ignoring important developments having taken place and going on within the statistical sciences. Although hypotheses testing is still an indispensable part of the statistical methodology required in medical and other areas of empirical research, there is a large repertoire of methods based on different paradigms of inference that provide ample options for supplementing and enhancing the methods of data analysis blamed in the ASA statement for causing a crisis.

Multivariate equivalence tests for use in pharmaceutical development.

Statistical equivalence analyses are well-established parts of many studies in the biomedical sciences. Also in pharmaceutical development and manufacturing equivalence testing methods are required in order to statistically establish similarities between machines, process components, or complete processes. This article presents a choice of multivariate equivalence testing procedures for normally distributed data as generalizations of existing univariate methods. In all derived methods, variability is interpreted as nuisance parameter. The use of the proposed methods in pharmaceutical development is demonstrated with a comparative analysis of dissolution profiles.

Determination of reference limits: statistical concepts and tools for sample size calculation.

Reference limits are estimators for 'extreme' percentiles of the distribution of a quantitative diagnostic marker in the healthy population. In most cases, interest will be in the 90% or 95% reference intervals. The standard parametric method of determining reference limits consists of computing quantities of the form X̅±c·S. The proportion of covered values in the underlying population coincides with the specificity obtained when a measurement value falling outside the corresponding reference region is classified as diagnostically suspect. Nonparametrically, reference limits are estimated by means of so-called order statistics. In both approaches, the precision of the estimate depends on the sample size. We present computational procedures for calculating minimally required numbers of subjects to be enrolled in a reference study. The much more sophisticated concept of reference bands replacing statistical reference intervals in case of age-dependent diagnostic markers is also discussed.

Results of a double-blind, placebo-controlled pharmacotherapy trial in alcoholism conducted in Germany and comparison with the US COMBINE study.

The results of placebo-controlled trials (RCTs) with acamprosate or naltrexone vary substantially. Those differences have been attributed to differing patient characteristics, recruitment strategies, treatment settings and remuneration systems. We tested these assumptions by comparing a new double-blind, placebo-controlled randomized trial conducted in Germany (called PREDICT Study) with data from the US COMBINE Study. PREDICT was designed according to the protocol of the COMBINE Study. A total of 426 alcohol-dependent patients were compared to 459 COMBINE Study patients corresponding to the treatment cells in PREDICT. All patients received acamprosate, naltrexone or placebo for 3 months (PREDICT) or 4 months (COMBINE). Biweekly manualized 'medical management' to enhance compliance was delivered in both studies. Time until the first occurrence of heavy drinking was the main outcome measure. PREDICT found neither acamprosate nor naltrexone to supply any additional benefit compared with placebo, which is at variance with a positive naltrexone effect being reported in the COMBINE Study. A secondary comparison between both studies showed better overall treatment outcomes in PREDICT, although these patients had been more severely affected than their COMBINE counterparts. The divergence in results may be attributable to basic differences in the treatment environments (such as in-patient pre-treatment versus primary outpatient care). We suggest that identically designed RCTs conducted in different parts of the world may help improve the external validity of RCTs. This approach could be called 'comparative efficacy research'.

Cochran-Armitage test versus logistic regression in the analysis of genetic association studies.

OBJECTIVE: The Cochran-Armitage trend test based on the linear regression model has become a standard procedure for association testing in case-control studies. In contrast, the logistic regression model is generally used for estimating effect sizes. The aim of this paper is to propose an approach that allows for association testing and parameter estimation by means of the same statistic. METHODS/RESULTS: The trend test is recommendable as a test of no association between genotype and risk of disease. It is a two-sample test for differences between cases and controls with respect to the average number of risk alleles occurring in the genotype of an individual. We argue that this difference is not of primary interest in genetic association studies. It should be replaced with the disease odds ratio, which can be assessed under both cohort sampling and case-control sampling. CONCLUSION: The Cochran-Armitage trend test should be replaced by the Wald statistic from a logistic regression model for hypothesis testing and estimation in genetic association studies.

Adjuvant vs. progression-triggered treatment with gemcitabine in platinum-ineligible high-risk bladder cancer patients: Long-term follow-up of a randomized phase 3 trial.

BACKGROUND: Cisplatin-based chemotherapy (ChT) is the preferred perioperative treatment in muscle-invasive urothelial carcinoma of the urinary bladder (UCUB). Nevertheless, a certain number of patients are ineligible for platinum-based ChT. This trial compared immediate adjuvant vs. delayed gemcitabine ChT at progression in platinum-ineligible patients with high-risk UCUB. METHODS: High-risk platinum-ineligible UCUB patients (n = 115) were randomized 1:1 to adjuvant gemcitabine (n = 59) or gemcitabine at progression (n = 56). Overall survival was analyzed. Additionally, we analyzed progression-free survival (PFS), toxicity and quality of life (QoL). RESULTS: After a median follow-up of 3.0 years (inter quartile range [IQR]: 1.3-11.6), adjuvant ChT did not significantly prolong overall survival (OS) (HR: 0.84; 95% CI: 0.57-1.24; P = 0.375), with 5-year OS of 44.1% (95% CI: 31.2-56.2) and 30.4% (95% CI: 19.0-42.5), respectively. We noted no significant difference in PFS (HR: 0.76; 95% CI: 0.49-1.18; P = 0.218), with 5-year PFS of 36.2% (95% CI: 22.8-49.7) in the adjuvant group and 22.2% (95% CI: 11.5%-35.1%) when treated at progression. Patients with adjuvant treatment showed a significantly worse QoL. The trial was prematurely closed after recruitment of 115 of the planned 178 patients. CONCLUSIONS: There was no statistically significant difference in terms of OS and PFS for patients with platinum-ineligible high-risk UCUB receiving adjuvant gemcitabine compared to patients treated at progression. These findings underline the importance of implementing and developing new perioperative treatments for platinum-ineligible UCUB patients.

Allowing for stratification in sample size planning of two-arm trials with continuous or binary outcome: Overview and tutorial.

More often than not, clinical trials and even nonclinical medical experiments have to be run with observational units sampled from populations to be assumed heterogeneous with respect to covariates associated with the outcome. Relevant covariates which are known prior to randomization are usually categorical in type, and the corresponding subpopulations are called strata. In contrast to randomization which in most cases is performed in a way ensuring approximately constant sample size ratios across the strata, sample size planning is rarely done taking stratification into account. This holds true although the statistical literature provides a reasonably rich repertoire of testing procedures for stratified comparisons between two treatments in a parallel group design. For all of them, at least approximate methods of power calculation are available from which algorithms or even closed-form formulae for required sample sizes can be derived. The objective of this tutorial is to give a systematic review of the most frequently applicable of these methods and to compare them in terms of their efficiency under standard settings. Based on the results, recommendations for the sample size planning of stratified two-arm trials are given.

Investigating Hardy-Weinberg equilibrium in case-control or cohort studies or meta-analysis.

Yu et al. (Breast Cancer Res Treat 117:675-677, 2009) recently stated that testing for deviation from Hardy-Weinberg equilibrium (HWE) is necessary to identify systematic genotyping errors in case-control studies. They criticized a meta-analytic study for the deviation from HWE in the case group of one study. The aim of this article is twofold. First, we derive recommendations on how to test for deviations from HWE in different study designs. Second, we develop a meta-analytic framework for assessing compatibility with HWE or measuring deviation from HWE. The authors sketch the possible reasons behind deviation from HWE and provide guidelines for proper investigation of HWE deviations in different study designs. The authors argue that the standard HWE χ² lack of fit test is logically flawed and provide a logically unflawed approach for measuring deviation from HWE using confidence intervals. The proposed method is applicable to meta-analyses of both case-control or cohort association studies. The proposed approach is illustrated using the meta-analysis criticized by Yu et al. Heterogeneity between studies can be assessed. The critique of Yu et al. to the article of Frank et al. (Breast Cancer Res Treat 111:139-144, 2008) can be refuted. Even more, validity of HWE can be proven for the pooled control sample. The authors advocate the use of a confidence interval-based approach to assess HWE. The latter should only be investigated in control populations. In multicenter studies or meta-analysis, deviation from HWE should be analyzed using a meta-analytic approach.

On easily interpretable multivariate reference regions of rectangular shape.

Till now, multivariate reference regions have played only a marginal role in the practice of clinical chemistry and laboratory medicine. The major reason for this fact is that such regions are traditionally determined by means of concentration ellipsoids of multidimensional Gaussian distributions yielding reference limits which do not allow statements about possible outlyingness of measurements taken in specific diagnostic tests from a given patient or subject. As a promising way around this difficulty we propose to construct multivariate reference regions as p-dimensional rectangles or (in the one-sided case) rectangular half-spaces whose edges determine univariate percentile ranges of the same probability content in each marginal distribution. In a first step, the corresponding notion of a quantile of a p-dimensional probability distribution of any type and shape is made mathematically precise. Subsequently, both parametric and nonparametric procedures of estimating such a quantile are described. Furthermore, results on sample-size calculation for reference-centile studies based on the proposed definition of multivariate quantiles are presented generalizing the approach of Jennen-Steinmetz and Wellek.

Testing for goodness rather than lack of fit of continuous probability distributions.

The vast majority of testing procedures presented in the literature as goodness-of-fit tests fail to accomplish what the term is promising. Actually, a significant result of such a test indicates that the true distribution underlying the data differs substantially from the assumed model, whereas the true objective is usually to establish that the model fits the data sufficiently well. Meeting that objective requires to carry out a testing procedure for a problem in which the statement that the deviations between model and true distribution are small, plays the role of the alternative hypothesis. Testing procedures of this kind, for which the term tests for equivalence has been coined in statistical usage, are available for establishing goodness-of-fit of discrete distributions. We show how this methodology can be extended to settings where interest is in establishing goodness-of-fit of distributions of the continuous type.

Results of a randomized trial of treatment modalities in patients with low or early-intermediate risk prostate cancer (PREFERE trial).

PURPOSE: The optimal treatment for patients with low to early-intermediate risk prostate cancer (PCa) remains to be defined. The randomized PREFERE trial (DRKS00004405) aimed to assess noninferiority of active surveillance (AS), external-beam radiotherapy (EBRT), or brachytherapy by permanent seed implantation (PSI) vs. radical prostatectomy (RP) for these patients. METHODS: PREFERE was planned to enroll 7600 patients. The primary endpoint was disease specific survival. Patients with PCa stage ≤ cT2a, cN0/X, M0, PSA ≤ 10 ng/ml and Gleason-Score ≤ 3 + 4 at reference pathology were eligible. Patients were allowed to exclude one or two of the four modalities, which yielded eleven combinations for randomization. Sixty-nine German study centers were engaged in PREFERE. RESULTS: Of 2251 patients prescreened between 2012 and 2016, 459 agreed to participate in PREFERE. Due to this poor accrual, the trial was stopped. In 345 patients reference pathology confirmed inclusion criteria. Sixty-nine men were assigned to RP, 53 to EBRT, 93 to PSI, and 130 to AS. Forty patients changed treatment shortly after randomization, 21 to AS. Forty-eight AS patients with follow-up received radical treatment. Median follow-up was 19 months. Five patients died, none due to PCa; 8 had biochemical progression after radical therapy. Treatment-related acute grade 3 toxicity was reported in 3 RP patients and 2 PSI patients. CONCLUSIONS: In this prematurely closed trial, we observed an unexpected high rate of termination of AS and an increased toxicity related to PSI. Patients hesitated to be randomized in a multi-arm trial. The optimal treatment of low and early-intermediate risk PCa remains unclear.

Adapting the logical basis of tests for Hardy-Weinberg Equilibrium to the real needs of association studies in human and medical genetics.

The standard procedure to assess genetic equilibrium is a chi(2) test of goodness-of-fit. As is the case with any statistical procedure of that type, the null hypothesis is that the distribution underlying the data is in agreement with the model. Thus, a significant result indicates incompatibility of the observed data with the model, which is clearly at variance with the aim in the majority of applications: to exclude the existence of gross violations of the equilibrium condition. In current practice, we try to avoid this basic logical difficulty by increasing the significance bound to the P-value (e.g. from 5 to 10%) and inferring compatibility of the data with Hardy Weinberg Equilibrium (HWE) from an insignificant result. Unfortunately, such direct inversion of a statistical testing procedure fails to produce a valid test of the hypothesis of interest, namely, that the data are in sufficiently good agreement with the model under which the P-value is calculated. We present a logically unflawed solution to the problem of establishing (approximate) compatibility of an observed genotype distribution with HWE. The test is available in one- and two-sided versions. For both versions, we provide tools for exact power calculation. We demonstrate the merits of the new approach through comparison with the traditional chi(2) goodness-of-fit test in 2x60 genotype distributions from 43 published genetic studies of complex diseases where departure from HWE was noted in either the case or control sample. In addition, we show that the new test is useful for the analysis of genome-wide association studies.

A genotype-based approach to assessing the association between single nucleotide polymorphisms.

Measuring the extent of linkage disequilibrium (LD) between single nucleotide polymorphisms (SNPs) is of considerable importance, and many different between SNP association measures including Lewontin's D' and Pearson's correlation coefficient rho have been proposed. The vast majority of these association measures are based on haplotypes instead of genotypes. If no family data are available, the required additional haplotype estimation step is based on the assumption of Hardy-Weinberg equilibrium (HWE). In this paper we propose to estimate the extent of LD by using a genotype- rather than haplotype-based measure. Furthermore, we require of an appropriate measure of LD that it should remain invariant under the transition from haplotypes to diploid genotypes if HWE holds. We show that Pearson's rhofulfills this invariance property in contrast to a variety of different LD measures including D'. We derive the asymptotic distribution of the empirical product-moment correlation R for counting variables and construct asymptotically valid confidence intervals using Fisher's z-transformation. We demonstrate the validity of our approach by a numerical study of the coverage properties. We show that the loss in precision encountered by using genotype rather than haplotype data for estimating the association between SNPs is negligible for practical purposes. We finally illustrate our approach with data from an association study of IL-4 associated phenotypes and polymorphisms from the human IL-4 receptor alpha chain gene (IL4R).

A confidence-limit-based approach to the assessment of Hardy-Weinberg equilibrium.

The classical chi(2)-procedure for the assessment of Hardy-Weinberg equilibrium (HWE) is tailored for detecting violations of HWE. However, many applications in genetic epidemiology require approximate compatibility with HWE. In a previous contribution to the field (Wellek, S. (2004). Biometrics, 60, 694-703), the methodology of statistical equivalence testing was exploited for the construction of tests for problems in which the assumption of approximate compatibility of a given genotype distribution with HWE plays the role of the alternative hypothesis one aims to establish. In this article, we propose a procedure serving the same purpose but relying on confidence limits rather than critical bounds of a significance test. Interval estimation relates to essentially the same parametric function that was previously chosen as the target parameter for constructing an exact conditional UMPU test for equivalence with a HWE conforming genotype distribution. This population parameter is shown to have a direct genetic interpretation as a measure of relative excess heterozygosity. Confidence limits are constructed using both asymptotic and exact methods. The new approach is illustrated by reanalyzing genotype distributions obtained from published genetic association studies, and detailed guidance for choosing the equivalence margin is provided. The methods have been implemented in freely available SAS macros.