Nonparametric Methods in Crossover Trials

The crossover design is often used in biomedical trials since it eliminates between subject variability. This paper is concerned with the statistical analysis of data arising from such trials when assumptions like normality do not necessarily apply. Nonparametric analysis of the two-period, two-treatment design was first described by Koch in a paper 1972. The purpose of this paper is to study nonparametric methods in crossover designs with three or more treatments and an equal number of periods. The proposed test for direct treatment effects is based on within subject comparisons after removing a possible period effect. With only two treatments this test reduces to the twosided Wilcoxon signed rank test. By simulation experiments the validity of the significance level of the test when using the asymptotic distribution of the test statistic are manifested and the power against different alternatives illustrated. A test for first order carryover effects can be constructed by a straightforward generalization of the test proposed by Koch in 1972. However, since this test is based on between subject comparisons its power will be low. Our recommendation is to consider the crossover design rather than the parallel group design if the carryover effects are assumed to be neglible or positive and smaller then the direct treatment effects.     

Utilities of the P‐value Distribution Associated with Effect Size in Clinical Trials

The P‐value, which is widely used for assessing statistical evidence in randomized comparative clinical trials, is a function of the observed effect size of the experimental treatment relative to the control treatment. The relationship of the P‐value with the observed effect size at study completion and the effect size anticipated at the design stage has potential usefulness in providing guidance for planning and interpretation of a clinical trial. The post‐trial power associated with a statistically significant P‐value from a completed study is also a random variable and its use may assist in planning a follow‐up trial to confirm the statistically significant findings in an initial study. A measure of robustness is explored to quantify the degree of sensitivity of the observed P‐value to potential bias that may be contained in the observed effect size.     

Detecting Change in Biological Rhythms: A Multivariate Permutation Test Approach to Fourier‐Transformed Data

Treatment‐related changes in neurobiological rhythms are of increasing interest to psychologists, psychiatrists, and biological rhythms researchers. New methods for analyzing change in rhythms are needed, as most common methods disregard the rich complexity of biological processes. Large time series data sets reflect the intricacies of underlying neurobiological processes, but can be difficult to analyze. We propose the use of Fourier methods with multivariate permutation test (MPT) methods for analyzing change in rhythms from time series data. To validate the use of MPT for Fourier‐transformed data, we performed Monte Carlo simulations and compared statistical power and family‐wise error for MPT to Bonferroni‐corrected and uncorrected methods. Results show that MPT provides greater statistical power than Bonferroni‐corrected tests, while appropriately controlling family‐wise error. We applied this method to human, pre‐ and post‐treatment, serially‐sampled neurotransmitter data to confirm the utility of this method using real data. Together, Fourier with MPT methods provides a statistically powerful approach for detecting change in biological rhythms from time series data.     

The best warm-up for the vertical jump in college-age athletic men

The purpose of this study was to determine the effectiveness of specific and nonspecific warm-ups on the vertical jump test performed by athletic men. Twenty-nine men (18-23 years) in athletics (speed positions in football) performed vertical jump tests on 4 separate days after completing 4 different warm-up protocols. The 4 warm-up protocols were (a) submaximal jump warm-up, (b) weighted jump warm-up, (c) stretching warm-up, and (d) no warm-up. The weighted jump warm-up protocol required 5 countermovement jumps onto a box, with the athletes holding dumbbells equaling 10% of their body weight. The submaximal jump warm-up protocol required the athletes to perform 5 countermovement jumps at 75% intensity of their past maximum vertical jump score. The stretching warm-up protocol required the athletes to perform 14 different stretches, each held for 20 seconds. The no warm-up protocol required the athletes to perform no activity prior to being tested. Three vertical jumps were measured following each warm-up; the score for analysis was the best jump. The data were analyzed with a repeated measures analysis of variance and Bonferroni post hoc tests. The Bonferroni post hoc tests showed a significant difference (p < 0.001) between the weighted jump warm-up and all other warm-ups. The effect size was 0.380 and the power was 1.00 for the statistical analyses. We concluded that utilizing a weighted resistance warm-up would produce the greatest benefit when performing the vertical jump test.     

The effect of acute stretching on agility performance

Static stretching (SS) has shown decreases in many areas including strength, anaerobic power, and sprinting time. Dynamic stretching (DS) has shown increases in anaerobic power and decreases in sprinting time. Research on the effects of stretching on agility performance is limited. The purpose of this study was to determine the effect of SS and DS on performance time of a sport agility test. Sixty male subjects consisting of collegiate (n = 18) and recreational (n = 42) basketball athletes volunteered for the study. Subjects were randomly assigned to 1 of 3 intervention groups: SS, DS, or no stretching (NS). All groups completed a 10-minute warm-up jog followed by a 3-minute rest. The SS and DS groups then completed an 8.5-minute stretching intervention. Next, all subjects completed 3 trials of the 505 agility test with 2-5 minutes of rest between trials. A 2-way repeated-measure analysis of variance (Stretch group, athlete category, group × athlete interaction) was used to determine statistical significance (p < 0.05). A Tukey post hoc test was performed to determine differences between groups. For all athletes, the DS group produced significantly faster times on the agility test (2.22 ± 0.12 seconds, mean ± SD) in comparison to both the SS group (2.33 ± 0.15 seconds, p = 0.013) and NS group (2.32 ± 0.12 seconds, p = 0.026). Differences between the SS and NS groups revealed no significance (p = 0.962). There was a significant difference in mean times for the type of athlete (p = 0.002); however, interaction between the type of athlete and stretching group was not significant (p = 0.520). These results indicate that in comparison to SS or NS, DS significantly improves performance on closed agility skills involving a 180° change of direction.     

Retinoic acid treatment partially rescues failed septation in rats and in mice

Pulmonary alveoli are formed in part by subdivision (septation) of the gas-exchange saccules of the immature lung. Septation results in smaller, more numerous structures (alveoli) and is developmentally regulated in mammals including humans, rats, and mice; if it fails to occur at the appropriate time, there is no spontaneous post hoc septation nor has there been a means of inducing septation after it has failed to occur. We measured lung volume, the volume of individual alveoli, and alveolar surface area and calculated alveolar number in neonatal rats in which septation had been blocked by treatment with a glucocorticosteroid hormone and in adult tight-skin mice that have a genetic failure of septation. We tested the hypothesis that treatment with all-trans retinoic acid induces post hoc septation. In both models of failed septation, hence in two species, and in immature and adult animals, treatment with all-trans retinoic acid induced post hoc septation, offering the possibility of a similar effect in premature infants.     

On the use of comparison regions in visualizing stochastic uncertainty in some two-parameter estimation problems

When considering simultaneous inference for two parameters, it is very common to visualize stochastic uncertainty by plotting two-dimensional confidence regions. This allows us to test post hoc null hypotheses about a single point in a simple manner. However, in some applications the interest is not in rejecting hypotheses on single points, but in demonstrating evidence for the two parameters to be in a convex subset of the parameter space. The specific convex subset to be considered may vary from one post hoc analysis to another. Then it is of interest to have a visualization allowing to perform corresponding analyses. We suggest comparison regions as a simple tool for this task.     

Confidence in results of beta-blocker postinfarction trials.

Seventeen published trials of beta-blockers in myocardial infarction were scrutinised for the 95% confidence limits for the reported treatment effects. All the trials were prospective, randomised, and (except when treatment was given intravenously) placebo controlled. For analysis of pooled results the trials were divided arbitrarily according to whether treatment had been given "early" or "late" after the onset of pain. All trials were consistent with a treatment effect of just over 20%, but benefit was more apparent in trials using late intervention with beta-blockers. The pooled results of trials using early intervention showed a positive effect of 8%, whereas those using late intervention showed a 26% reduction in mortality and confidence limits of 17-35%. The results confirm that late intervention with beta-blockers after myocardial infarction reduces mortality but show that the effect of early intervention remains to be determined.     

Statistical considerations of optimal study design for human plasma proteomics and biomarker discovery

A mass spectrometry-based plasma biomarker discovery workflow was developed to facilitate biomarker discovery. Plasma from either healthy volunteers or patients with pancreatic cancer was 8-plex iTRAQ labeled, fractionated by 2-dimensional reversed phase chromatography and subjected to MALDI ToF/ToF mass spectrometry. Data were processed using a q-value based statistical approach to maximize protein quantification and identification. Technical (between duplicate samples) and biological variance (between and within individuals) were calculated and power analysis was thereby enabled. An a priori power analysis was carried out using samples from healthy volunteers to define sample sizes required for robust biomarker identification. The result was subsequently validated with a post hoc power analysis using a real clinical setting involving pancreatic cancer patients. This demonstrated that six samples per group (e.g., pre- vs post-treatment) may provide sufficient statistical power for most proteins with changes>2 fold. A reference standard allowed direct comparison of protein expression changes between multiple experiments. Analysis of patient plasma prior to treatment identified 29 proteins with significant changes within individual patient. Changes in Peroxiredoxin II levels were confirmed by Western blot. This q-value based statistical approach in combination with reference standard samples can be applied with confidence in the design and execution of clinical studies for predictive, prognostic, and/or pharmacodynamic biomarker discovery. The power analysis provides information required prior to study initiation.     

Clinical trials of investigational agents for IPF: a review of a Cochrane report

The magnitude of treatment effect can be assessed by a number of methods. One reliable method of collectively analysing data from randomised clinical trials is that used in Cochrane reviews. These systematic reviews identify and analyse the available evidence using the reliable method of meta-analysis. These often combine data from studies to provide robust evaluations of overall treatment effects. In 2003, a review of data from studies of corticosteroid use in IPF patients found no evidence of a treatment effect. Similarly, very little evidence was found to support the use of immunomodulatory agents. A recent update of these Cochrane reviews failed to identify any new evidence supporting the use of corticosteroids in IPF. However, a review of non-steroid agents for the treatment of IPF identified data from 15 RCTs that was suitable for analysis. Two trials of interferon gamma-1b were pooled and analysed, but no treatment effect was observed in terms of survival. Meta-analysis of three Phase III studies of pirfenidone treatment in IPF patients suggested that progression-free survival was significantly increased by 30%, demonstrating a reduction in the decline of lung function in IPF patients. In addition, there are numerous ongoing trials investigating potential therapeutic agents which provides hope for IPF patients and their doctors.     

Prevention of Chronic Kidney Disease and Subsequent Effect on Mortality: A Systematic Review and Meta-Analysis

Objectives

To perform a systematic review of randomized controlled trials to determine whether prevention or slowing of progression of chronic kidney disease would translate into improved mortality, and if so, the attributable risk due to CKD itself on mortality.

Background

CKD is associated with increased mortality. This association is largely based on evidence from the observational studies and evidence from randomized controlled trials is lacking.

Methods

We searched Ovid, Medline and Embase for RCTs in which an intervention was given to prevent or slow the progression of CKD and mortality was reported as primary, secondary or adverse outcomes were eligible and selected. For the first phase, pooled relative risks for renal endpoints were assessed. For the second phase, we assessed the effect on mortality in trials of interventions that definitively reduced CKD endpoints.

Results

Among 52 studies selected in first phase, only renin-angiotensin-aldosterone-system blockade vs. placebo (n = 18 trials, 32,557 participants) met the efficacy criteria for further analysis in the second phase by reducing renal endpoints 15 to 27% compared to placebo. There was no difference in all-cause mortality (RR 0.99, 95% CI 0.92 to 1.08) or CV death (RR 0.97, 95% CI 0.78 to 1.21) between the treatment and control groups in these trials. There was sufficient statistical power to detect a 9% relative risk reduction in all-cause mortality and a 14% relative risk reduction in cardiovascular mortality.

Conclusions

Firm evidence is lacking that prevention of CKD translates into reductions in mortality. Larger trials with longer follow-up time are needed to determine the benefit of CKD prevention on survival.     

Tests for density dependence revisited

We have examined a number of statistical issues associated with methods for evaluating different tests of density dependence. The lack of definitive standards and benchmarks for conducting simulation studies makes it difficult to assess the performance of various tests. The biological researcher has a bewildering choice of statistical tests for testing density dependence and the list is growing. The most recent additions have been based on computationally intensive methods such as permutation tests and boot-strapping. We believe the computational effort and time involved will preclude their widespread adoption until: (1) these methods have been fully explored under a wide range of conditions and shown to be demonstrably superior than other, simpler methods, and (2) general purpose software is made available for performing the calculations. We have advocated the use of Bulmer's (first) test as a de facto standard for comparative studies on the grounds of its simplicity, applicability, and satisfactory performance under a variety of conditions. We show that, in terms of power, Bulmer's test is robust to certain departures from normality although, as noted by other authors, it is affected by temporal trends in the data. We are not convinced that the reported differences in power between Bulmer's test and the randomisation test of Pollard et al. (1987) justifies the adoption of the latter. Nor do we believe a compelling case has been established for the parametric bootstrap likelihood ratio test of Dennis and Taper (1994). Bulmer's test is essentially a test of the serial correlation in the (log) abundance data and is affected by the presence of autocorrelated errors. In such cases the test cannot distinguish between the autoregressive effect in the errors and a true density dependent effect in the time series data. We suspect other tests may be similarly affected, although this is an area for further research. We have also noted that in the presence of autocorrelation, the type I error rates can be substantially different from the assumed level of significance, implying that in such cases the test is based on a faulty significance region. We have indicated both qualitatively and quantitatively how autoregressive error terms can affect the power of Bulmer's test, although we suggest that more work is required in this area. These apparent inadequacies of Bulmer's test should not be interpreted as a failure of the statistical procedure since the test was not intended to be used with autocorrelated error terms.     

No evidence for long‐term effects of reproductive effort on parasite prevalence in great tits Parus major

Allocation of resources between the life history traits reproduction and parasite defence are expected because both are energetically costly. Experimental evidence for such allocation has been found in short‐term effects of reproduction on parasite prevalence or immune function. However, there is increasing evidence for long‐term negative effects of reproductive effort on individuals. This study investigates whether long‐term effects of reproductive effort on parasite prevalence exist. Brood sizes of great tits Parus major were experimentally altered in one breeding season and in the subsequent breeding season the prevalence of three parasites types (blood parasites, ticks and fleas) on the surviving parents were investigated. We detected no long‐term effects of brood size manipulation on the prevalence of parasites in the next year and therefore provide no evidence for inter‐seasonal effects of reproductive effort on parasite prevalence. The post hoc level of statistical power was reasonable for effects on blood parasite and flea prevalence, but low for effects on tick prevalence.     

Sequential monitoring of randomization tests: stratified randomization

In many clinical trials, it is desirable to establish a sequential monitoring plan, whereby the test statistic is computed at an interim point or points in the trial and a decision is made whether to stop early due to evidence of treatment efficacy. In this article, we will set up a sequential monitoring plan for randomization-based inference under the permuted block design, stratified block design, and stratified urn design. We will also propose a definition of information fraction in these settings and discuss its calculation under these different designs.     

Debate: A subversive view of subsets - a dissident clinician's opinion

Clinical trialists and statisticians are very wary of subgroup analysis, for good reasons. Clinicians have to deal with situations in which subgroups of patients differ widely from one another in their prognosis and response to treatment. Few trials are large enough to demonstrate convincingly these differences in outcome, but often provide suggestive evidence. Should we ignore this and treat all patients as the same, or should we allow dubious statistical evidence to buttress biological plausibility in making clinical decisions?     

Incongruence in molecular species delimitation schemes: What to do when adding more data is difficult

Using multiple, independent approaches to molecular species delimitation is advocated to accommodate limitations and assumptions of a single approach. Incongruence in delimitation schemes is a potential by‐product of employing multiple methods on the same data, and little attention has been paid to its reconciliation. Instead, a particular scheme is prioritized, and/or molecular delimitations are coupled with additional, independent lines of evidence that mitigate incongruence. We advocate that incongruence within a line of evidence should be accounted for before comparing across lines of evidence that can themselves be incongruent. Additionally, it is not uncommon for empiricists working in nonmodel systems to be data‐limited, generating some concern for the adequacy of available data to address the question of interest. With conservation and management decisions often hinging on the status of species, it seems prudent to understand the capabilities of approaches we use given the data we have. Here, we apply two molecular species delimitation approaches, spedeSTEM and BPP, to the Castilleja ambigua (Orobanchaceae) species complex, a relatively young plant lineage in western North America. Upon finding incongruence in our delimitation, we employed a post hoc simulation study to examine the power of these approaches to delimit species. Given the data we collected, we find that spedeSTEM lacks the power to delimit while BPP is capable, thus allowing us to address incongruence before proceeding in delimitation. We suggest post hoc simulation studies like this compliment empirical delimitation and serve as a means of exploring conflict within a line of evidence and dealing with it appropriately.     

Health-related quality of life in ADHD: a pooled analysis of gender differences in five atomoxetine trials

Attention-deficit/hyperactivity disorder (ADHD) is associated with considerable impairment in health-related quality of life (HR-QoL). Atomoxetine has been found to improve HR-QoL in both children and adolescents. However, there is scarcity of data on gender differences in treatment responses to ADHD medications. This pooled analysis of five atomoxetine trials aimed to evaluate treatment differences with respect to HR-QoL and ADHD symptoms across genders. Data from 5 clinical atomoxetine trials (4 from Europe and 1 from Canada) with similar inclusion and exclusion criteria and similar durations (8- to 12-week follow-up) were included in the pooled analysis. All studies included the Child Health and Illness Profile-Child Edition (CHIP-CE) Parent Report Form. In addition, correlations between HR-QoL and ADHD core symptoms were compared between girls and boys. Data from 136 girls and 658 boys (mean age: 9.6 and 9.7 years, respectively) were pooled. Boys and girls were similarly impaired at baseline with minor differences in some of the subdomains. Treatment effect of atomoxetine was significant in both groups for the Risk Avoidance domain and its subdomains. No gender effect with both clinical and statistical significance was found for treatment outcome. Correlations between ADHD Rating Scale and CHIP-CE scores were similar in both genders and were generally low at baseline and moderate at endpoint and for the change from baseline to endpoint. Atomoxetine was effective in improving some aspects of HR-QoL in both genders without any significant differences across genders. Correlations between core symptoms of ADHD and HR-QoL were low to moderate in both boys and girls.