Power Calculations for Preclinical Studies Using a K-Sample Rank Test and the Lehmann Alternative Hypothesis

Power calculations in a small sample comparative study, with a continuous outcome measure, are typically undertaken using the asymptotic distribution of the test statistic. When the sample size is small, this asymptotic result can be a poor approximation. An alternative approach, using a rank based test statistic, is an exact power calculation. When the number of groups is greater than two, the number of calculations required to perform an exact power calculation is prohibitive. To reduce the computational burden, a Monte Carlo resampling procedure is used to approximate the exact power function of a k-sample rank test statistic under the family of Lehmann alternative hypotheses. The motivating example for this approach is the design of animal studies, where the number of animals per group is typically small.

Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

A SIMULATION STUDY OF THE SIZE AND POWER OF SOME TWO-SAMPLE TESTS FOR UNEQUALLY CENSORED SURVIVAL DATA (RANK TESTS, LOGRANK, PROPORTIONAL HAZARDS, WILCOXON TESTS, EXPONENTIAL DISTRIBUTION)

Sizes and power of selected two-sample tests of the equality of survival distributions are compared by simulation for small samples from unequally, randomly-censored exponential distributions. The tests investigated include parametric tests (F, Score, Likelihood, Asymptotic), logrank tests (Mantel, Peto-Peto), and Wilcoxon-Type tests (Gehan, Prentice). Equal sized samples, n = 18, 16, 32 with 1000 (size) and 500 (power) simulation trials, are compared for 16 combinations of the censoring proportions 0%, 20%, 40%, and 60%. For n = 8 and 16, the Asymptotic, Peto-Peto, and Wilcoxon tests perform at nominal 5% size expectations, but the F, Score and Mantel tests exceeded 5% size confidence limits for 1/3 of the censoring combinations. For n = 32, all tests showed proper size, with the Peto-Peto test most conservative in the presence of unequal censoring. Powers of all tests are compared for exponential hazard ratios of 1.4 and 2.0. There is little difference in power characteristics of the tests within the classes of tests considered. The Mantel test showed 90% to 95% power efficiency relative to parametric tests. Wilcoxon-type tests have the lowest relative power but are robust to differential censoring patterns. A modified Peto-Peto test shows power comparable to the Mantel test. For n = 32, a specific Weibull-exponential comparison of crossing survival curves suggests that the relative powers of logrank and Wilcoxon-type tests are dependent on the scale parameter of the Weibull distribution. Wilcoxon-type tests appear more powerful than logrank tests in the case of late-crossing and less powerful for early-crossing survival curves. Guidelines for the appropriate selection of two-sample tests are given. ^

An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov–Smirnov two-sample test

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the Kolmogorov–Smirnov two sample statistic. This test is able to detect differences in position, dispersion or shape of the c.p.d.f.’s. In our context, this statistic allows us to cluster the recorded data with a homogeneity criterion based on the whole distribution of each data set, and to decide whether it is necessary to add more clusters or not. In this sense, the proposed algorithm is adaptive as it automatically increases the number of clusters only as necessary; therefore, there is no need to fix in advance the number of clusters. The output of the algorithm are the common c.p.d.f. of all observed data in the cluster (the centroid) and, for each cluster, the Kolmogorov–Smirnov statistic between the centroid and the most distant c.p.d.f. The proposed algorithm has been used for a large data set of solar global irradiation spectra distributions. The results obtained enable to reduce all the information of more than 270,000 c.p.d.f.’s in only 6 different clusters that correspond to 6 different c.p.d.f.’s.

Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

Effect of tin-chloride pretreatment on bond strength of two adhesive systems to dentin

OBJECTIVES: To determine the effect on resin composite-to-dentin bond strength of incorporation of an acidic tin-chloride pretreatment in two adhesive systems. MATERIALS AND METHODS: Human molars were ground to expose mid-coronal dentin. For microtensile bond strength (μTBS) testing, dentin was treated with Optibond FL or Clearfil SE according to one of six protocols (n = 22/group). Group 1: Phosphoric acid etching, Optibond FL Prime, Optibond FL Adhesive (manufacturer's instructions; control); Group 2: Tin-chloride pretreatment, Optibond FL Prime, Optibond FL Adhesive; Group 3: Phosphoric acid etching, tin-chloride pretreatment, Optibond FL Prime, Optibond FL Adhesive; Group 4: Clearfil SE Primer, Clearfil SE Bond (manufacturer's instructions; control); Group 5: Phosphoric acid etching, Clearfil SE Primer, Clearfil SE Bond; and Group 6: Tin-chloride pretreatment, Clearfil SE Primer, Clearfil SE Bond. The molars were then built up with resin composite (Clearfil Majesty Esthetic). After storage (1 week, 100  % humidity, 37 °C) the μTBS was measured and failure mode was determined. Additionally, pretreated dentin surfaces were evaluated using SEM and EDX. The μTBS results were analyzed statistically by a Welch Two Sample t-test and a Kruskal-Wallis test followed by exact Wilcoxon rank sum tests with Bonferroni-Holm adjustment for multiple testing (α = 0.05). RESULTS: When Optibond FL was used, partial or total replacement of phosphoric acid with tin-chloride decreased μTBS significantly. In contrast, when Clearfil SE was used, inclusion of a tin-chloride pretreatment in the adhesive procedure increased μTBS significantly. CONCLUSIONS: Tin-chloride pretreatment had a beneficial influence on the bond promoting capacity of the MDP-containing adhesive system Clearfil SE.

Effect of patient accrual patterns on power and size of log-rank test for time-to-event outcome in clinical trials

The determination of size as well as power of a test is a vital part of a Clinical Trial Design. This research focuses on the simulation of clinical trial data with time-to-event as the primary outcome. It investigates the impact of different recruitment patterns, and time dependent hazard structures on size and power of the log-rank test. A non-homogeneous Poisson process is used to simulate entry times according to the different accrual patterns. A Weibull distribution is employed to simulate survival times according to the different hazard structures. The current study utilizes simulation methods to evaluate the effect of different recruitment patterns on size and power estimates of the log-rank test. The size of the log-rank test is estimated by simulating survival times with identical hazard rates between the treatment and the control arm of the study resulting in a hazard ratio of one. Powers of the log-rank test at specific values of hazard ratio (≠1) are estimated by simulating survival times with different, but proportional hazard rates for the two arms of the study. Different shapes (constant, decreasing, or increasing) of the hazard function of the Weibull distribution are also considered to assess the effect of hazard structure on the size and power of the log-rank test. ^

Pyramid Multi-resolution Scanning for Two-sample Comparison

Testing for two-sample differences is challenging when the differences are local and only involve a small portion of the data. To solve this problem, we apply a multi- resolution scanning framework that performs dependent local tests on subsets of the sample space. We use a nested dyadic partition of the sample space to get a collection of windows and test for sample differences within each window. We put a joint prior on the states of local hypotheses that allows both vertical and horizontal message passing among the partition tree to reflect the spatial dependency features among windows. This information passing framework is critical to detect local sample differences. We use both the loopy belief propagation algorithm and MCMC to get the posterior null probability on each window. These probabilities are then used to report sample differences based on decision procedures. Simulation studies are conducted to illustrate the performance. Multiple testing adjustment and convergence of the algorithms are also discussed.

Abnormal EEG Synchronization Correlates with Demyelination in Alzheimer's Disease

Introduction : The pathological processes caused by Alzheimer's disease (AD) supposedly disrupt communication between and within the distributed cortical networks due to the dysfunction/loss of synapses and myelination breakdown. Indeed, recently (Knyazeva et al. 2008), we have revealed the whole-head topography of EEG synchronization specific to AD. Here we analyze whether and how these abnormalities of synchronization are related to the demyelination of cortico-cortical fibers. Methods : Fifteen newly diagnosed AD patients (CDR 0.5-1) and 15 controls matched for age, participated in the study. Their multichannel (128) EEGs were recorded during 3-5 min at rest. They were submitted to the multivariate phase synchronization (MPS) analysis for mapping regional synchronization. To obtain individual whole-head maps, the MPS was computed for each sensor considering its 2nd nearest topographical neighbors. Separate calculations were performed for the delta, theta, alpha-1/−2, and beta-1/−2 EEG bands. The same subjects were scanned on a 3 Tesla Philips scanner. The protocol included a high-resolution T1-weighted sequence and a Magnetization Transfer Imaging (MTI) acquisition. For each subject, we defined a 3mm thick layer of white matter exactly below the cortical gray matter. The magnetization transfer ratio (MTR) - an estimator of myelination - was calculated for this layer in 39 Brodmann-defined ROIs per hemisphere. To assess the between-group differences, we used a permutation version of Hotelling's T2 test or two-sample T-test (Pcorrected <0.05). For correlation analysis, Spearman Rank Correlation was calculated. Results : In AD patients, we have found an abnormal landscape of synchronization characterized by a decrease in MPS over the fronto-temporal region of the left hemisphere and an increase over the temporo-parieto-occipital regions bilaterally. Also, we have shown a widespread decrease in regional MTR in the AD patients for all the areas excluding motor, premotor, and primary sensory ones. Assuming that AD-related changes in synchronization are associated with demyelination, we hypothesized a correlation between the regional MTR values and MPS values in the hypo- and hyper-synchronized clusters. We found that MPS in the left fronto-temporal hypo-synchronized cluster directly correlates with myelination in BA42-46 of the left hemisphere: the lower the myelination in individual patients, the lower the EEG synchronization. By contrast, in the posterior hyper-synchronized cluster, MPS inversely correlated with myelination, i.e., the lower the myelination, the higher the synchronization. This posterior hyper-synchronization, more characteristic for early-onset AD, probably, results from the initial effect of the disease on cortical inhibition, reducing cortical capacity for decoupling irrelevant connections. Remarkably, it showed different topography of correlations in early- vs. late-onset patients. In the early-onset patients, hyper-synchronization was mainly related to demyelination in posterior BAs, the effect being significant in all the EEG frequency bands. In the late-onset patients, widely distributed correlations were significant for the EEG delta band, suggesting an interaction between the cerebral manifestations of AD and the age of its onset, i.e., topographically selective impairment of cortical inhibition in early-onset AD vs. its wide-spread weakening in old age. Conclusions : Overall, our results document that the degradation of white matter is a significant factor of AD pathogenesis leading to functional dysconnection, the latter being reflected in EEG synchronization abnormalities.

Surgical outcomes of Baerveldt aqueous shunt implantation versus combined phacoemulsification and Baerveldt aqueous shunt implantation

Purpose: To examine the efficacy and safety of Baerveldt shunt (BS) implantation compared to combined phacoemulsification and Baerveldt shunt implantation (PBS). This study was designed to detect a difference in IOP reduction of 20% (~4mmHg) between groups with 90% power. Methods: Sixty patients with medically uncontrolled glaucoma, prospectively underwent either or BS implantation with phacoemulsification (Group PBS; n=30) or BS implantation alone (group BS; n=30, pseudophakic eyes only). Groups were matched for age, glaucoma subtype and length of follow-up. Pre and post-operative measures recorded included patient demographics, visual acuity, IOP, number of glaucoma medications (GMs) and all complications. Success was defined as IOP≤21mmHg and 20% reduction in IOP from baseline with or without GMs. Results: Age of PBS and BS groups was 61 vs 62 years respectively (p=0.72*). There were no significant differences in preoperative baseline characteristics: PBS vs PB, mean IOP =25.5mmHg (standard deviation (SD); ±10.3mmHg) vs 26.1mmHg (SD ±10.6mmHg), p=0.81*; mean GMs=3.0 (SD ±1.1) vs 3.1 (SD ±1.0), p=0.83*; mean VA=0.3 vs 0.3, p=0.89*. At year one there were no significant differences observed between groups in post-operative IOP, GMs or VA, mean IOP =14.1mmHg (SD ±5.4mmHg) vs 11.5 mmHg (SD ±4.2mmHg), p=0.12*; mean GMs=1.6 (SD ±1.4) vs 1.1 (SD ±1.1), p=0.23*; mean VA=0.5 vs 0.4, p=0.46*. Complication rates were similar between the two groups (7% vs 14%). Success rate was lower in eyes with PBS (71%) than with BS (88%), however this did not reach statistical significance (p=0.95, log-rank test). * two-sample t-test Conclusions: There were no significant differences at year one in success or complication rates between PBS and BS groups suggesting that simultaneous phacoemulsification does not have a marked (difference of >4mmHg) effect on tube function. IOP reduction and success were less in the PBS group, a larger sample (n=120) would be required to investigate if there is a 10% difference in IOP reduction between groups, however it is unclear if this would be a clinically significant difference to justify separate surgeries.

Surgical outcomes of deep sclerectomy versus Baerveldt aqueous shunt implantation following initial failed deep sclerectomy

Purpose: To examine the efficacy and safety of repeat deep sclerectomy (DS) versus Baerveldt shunt (BS) implantation as second line surgery following failed primary DS. Methods: Fifty one patients were prospectively recruited to undergo BS implantation following failed DS and 51 patients underwent repeat DS, for which data was collected retrospectively. All eyes had at least one failed DS. Surgical success was defined as IOP≤21mmHg and 20% reduction in IOP from baseline. Success rates, number of glaucoma medications (GMs), IOP, and complication rates were compared between the two groups at year 1, post-operatively. Results: Mean age, sex and the proportion of glaucoma subtypes were similar between groups. Preoperatively IOP was significantly lower in DS group vs BS group (18.8mmHg vs 23.8mmHg, p<0.01, two sample t-test). Postoperatively IOP was significantly higher in DS group than BS group (14.6mmHg vs 12.0mmHg, p<0.01, two-sample t-test). In the DS group, 47% of eyes did not achieve 20% reduction in IOP from baseline, as a result the success rates were significantly lower in eyes with DS (51%) than in eyes with BS (88%) (p=0.02, log-rank test). Preoperatively the number of GMs used in DS and BS groups were similar (2.2 vs 2.7 p=0.02, two sample t-test). Postoperatively there remained no significant difference in GMs between groups (0.9 vs 1.1, p= 0.58, two sample t-test). Complication rates were similar between the two groups (12% vs 10%). Conclusions: Baerveldt tube implantation was more effective in lowering IOP than repeat deep sclerectomy in eyes with failed primary DS, at year one. Complications were minor and infrequent in both groups

Equilibrium curves and growth models to deal with forests in transition to uneven-aged structure : application in two sample stands

Abstract

A comparative study on the effects of the benzodiazepine midazolam and the dopamine agents, apomorphine and sulpiride, on rat behavior in the two-way avoidance test

In recent years. studies in behavioral pharmacology have shown the involvement of dopaminergic mechanisms in avoidance behavior as assessed by the two-way active avoidance test (CAR). Changes in dopaminergic transmission also occur in response to particularly threatening challenges. However, studies on the effects of benzodiazepine (BZD) drugs ill this test are still unclear. Given the interplay of dopamine and other neurotransmitters in the neurobiology of anxiety and schizophrenia the aim of this work was to evaluate the effects of systemic administration of midazolam, the dopaminergic agonist apomorphine, and the D(2) receptor antagonist sulpiride using the CAR, a test that shows good sensitivity to typical neuroleptic drugs. Whereas midazolam did not alter the avoidance response. apomorphine increased and sulpiride reduced them in this test. Escape was not affected by any drug treatments. Heightened avoidance was not associated with the increased motor activity caused by apomorphine. In contrast with the benzodiazepine midazolam, activation of post-synaptic D(2) receptors with apomorphine facilitates, whereas the D(2) receptor antagonism with sulpiride inhibited the acquisition of the avoidance behavior. Together, these results bring additional evidence for a role of D(2) mechanisms in the acquisition of the active avoidance. (C) 2009 Elsevier Inc. All rights reserved.

The Synthetic Control Chart Based on Two Sample Variances for Monitoring the Covariance Matrix

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)