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.

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.

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.

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.

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.

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.

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.

On powerful exact nonrandomized tests for the Poisson two-sample setting.

In the case of two independent samples from Poisson distributions, the natural target parameter for hypothesis testing is the ratio of the two population means. The conditional tests which have been derived for this class of problems already in the 1940s are well known to be optimal in terms of power only when randomized decisions between hypotheses are admitted at the boundary of the respective rejection regions. The major objective of this contribution is to show how the approach used by Boschloo in 1970 for constructing a powerful nonrandomized version of Fisher's exact test for hypotheses about the odds ratio between two binomial parameters can successfully be adapted for the Poisson case. The resulting procedure, which we propose to term Poisson-Boschloo test, depends on some cutoff for the observed total number of events, the variable upon which conditioning has to be done. We show that for any fixed specific alternative, this cutoff can be chosen in such a way that the resulting nonrandomized test falls short in power of the randomized UMPU test only by a negligible amount. Thus, sample size calculation for the Poisson-Boschloo test can be carried out nearly exactly by means of the same computational procedure as has to be used for the randomized UMPU test. Since the power of the latter is accessible to elementary computational tools, this result makes approximate methods of sample size calculation for the Poisson-Boschloo test dispensable. It is furthermore shown how the construction of a Poisson-Boschloo type test extends to the case that interest is in establishing equivalence in the strict, two-sided sense rather than noninferiority. Although proceeding to two-sided equivalence considerably complicates the construction, comparing the resulting test procedure in terms of power with the exact randomized UMPU test leads essentially to the same conclusions as in the noninferiority case.

Planning and Analysis of Trials Using a Stepped Wedge Design.

BACKGROUND: The stepped-wedge design (SWD) of clinical trials has become very popular in recent years, particularly in health services research. Typically, study participants are randomly allotted in clusters to the different treatment options. METHODS: The basic principles of the stepped wedge design and related statistical techniques are described here on the basis of pertinent publications retrieved by a selective search in PubMed and in the CIS statistical literature database. RESULTS: In a typical SWD trial, the intervention is begun at a time point that varies from cluster to cluster. Until this time point is reached, all participants in the cluster belong to the control arm of the trial. Once the intervention is begun, it is continued with- out change until the end of the trial period. The starting time for the intervention in each cluster is determined by randomization. At the first time point of measurement, no intervention has yet begun in any cluster; at the last one, the intervention is in prog- ress in all clusters. The treatment effect can be optimally assessed under the assumption of an identical correlation at all time points. A method is available to calculate the power and the number of clusters that would be necessary in order to achieve statistical significance by the appropriate type of significance test. All of the statistical techniques presented here are based on the assumptions of a normal distribution of cluster means and of a constant intervention effect across all time points of measure- ment. CONCLUSION: The necessary statistical tools for the planning and evaluation of SWD trials now stand at our disposal. Such trials nevertheless are subject to major risks, as valid results can be obtained only if the far-reaching assumptions of the model are, in fact, justified.

Testing for goodness rather than lack of fit of an X-chromosomal SNP to the Hardy-Weinberg model.

The problem of checking the genotype distribution obtained for some diallelic marker for compatibility with the Hardy-Weinberg equilibrium (HWE) condition arises also for loci on the X chromosome. The possible genotypes depend on the sex of the individual in this case: for females, the genotype distribution is trinomial, as in the case of an autosomal locus, whereas a binomial proportion is observed for males. Like in genetic association studies with autosomal SNPs, interest is typically in establishing approximate compatibility of the observed genotype frequencies with HWE. This requires to replace traditional methods tailored for detecting lack of fit to the model with an equivalence testing procedure to be derived by treating approximate compatibility with the model as the alternative hypothesis. The test constructed here is based on an upper confidence bound and a simple to interpret combined measure of distance between true and HWE conforming genotype distributions in female and male subjects. A particular focus of the paper is on the derivation of the asymptotic distribution of the test statistic under null alternatives which is not of the usual Gaussian form. A closed sample size formula is also provided and shown to behave satisfactorily in terms of the approximation error.

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 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.

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.

[PREFERE - Study on the rise]. / PREFERE-Studie im Aufwind.

The PREFERE study, which compares the treatment options for prostate cancer with low and early intermediate risk, has recorded a noticeable upswing in recruitment since mid-2015. Responsible for this are the revised inclusion criteria and the wide support for this study in Germany. The inclusion criteria opened the study to the use of imaging techniques (MRI, C­Trus / Anna) and the inclusion of all Gleason 3 + 3 = 6 cancers, regardless of tumor extent. In addition, patients can now be included who, for example due to the size of the prostate or existing obstructive micturition disorders, had a contraindication to percutaneous radiotherapy or brachytherapy - these can now be randomized between active surveillance and radical prostatectomy. With the increased recruitment numbers, it seems realistic that the required milestones in recruiting will be achieved.

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.