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1.  Nonparametric tests for right-censored data with biased sampling 
Summary
Testing the equality of two survival distributions can be difficult in a prevalent cohort study when non random sampling of subjects is involved. Due to the biased sampling scheme, independent censoring assumption is often violated. Although the issues about biased inference caused by length-biased sampling have been widely recognized in statistical, epidemiological and economical literature, there is no satisfactory solution for efficient two-sample testing. We propose an asymptotic most efficient nonparametric test by properly adjusting for length-biased sampling. The test statistic is derived from a full likelihood function, and can be generalized from the two-sample test to a k-sample test. The asymptotic properties of the test statistic under the null hypothesis are derived using its asymptotic independent and identically distributed representation. We conduct extensive Monte Carlo simulations to evaluate the performance of the proposed test statistics and compare them with the conditional test and the standard logrank test for different biased sampling schemes and right-censoring mechanisms. For length-biased data, empirical studies demonstrated that the proposed test is substantially more powerful than the existing methods. For general left-truncated data, the proposed test is robust, still maintains accurate control of type I error rate, and is also more powerful than the existing methods, if the truncation patterns and right-censoring patterns are the same between the groups. We illustrate the methods using two real data examples.
doi:10.1111/j.1467-9868.2010.00742.x
PMCID: PMC2963462  PMID: 21031144
2.  Variable Selection in Semiparametric Regression Modeling1 
Annals of statistics  2008;36(1):261-286.
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and select significant variables for parametric portion. Thus, it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel. This leads to very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. The newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously. This allows us to establish the sampling properties of the resulting estimate. We first establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we then establish the asymptotic normality of the resulting estimate, and further demonstrate that the proposed procedures perform as well as an oracle procedure. Semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component. We investigate the asymptotic behavior of the proposed test and demonstrate its limiting null distribution follows a chi-squared distribution, which is independent of the nuisance parameters. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures.
doi:10.1214/009053607000000604
PMCID: PMC2605629  PMID: 19122808
Nonconcave penalized likelihood; SCAD; efficient score; local linear regression; partially linear model; varying coefficient models
3.  Differential gene expression in Lin-/VEGF-R2+ bone marrow-derived endothelial progenitor cells isolated from diabetic mice 
Background
Diabetes is known to impair the number and function of endothelial progenitor cells in the circulation, causing structural and functional alterations in the micro- and macro-vasculature. The aim of this study was to identify early diabetes-related changes in the expression of genes that have been reported to be closely involved in endothelial progenitor cell migration and function.
Methods
Based on review of current literature, this study examined the expression level of 35 genes that are known to be involved in endothelial progenitor cell migration and function in magnetically sorted Lin-/VEGF-R2+ endothelial progenitor cells obtained from the bone marrow of Akita mice in the early stages of diabetes (18 weeks) using RT-PCR and Western blotting. We used the Shapiro-Wilk and D’Agostino & Pearson Omnibus tests to assess normality. Differences between groups were evaluated by Student’s t-test for normally distributed data (including Welch correction in cases of unequal variances) or Mann–Whitney test for not normally distributed data.
Results
We observed a significant increase in the number of Lin-/VEGF-R2+ endothelial progenitor cells within the bone marrow in diabetic mice compared with non-diabetic mice. Two genes, SDF-1 and SELE, were significantly differentially expressed in diabetic Lin-/VEGF-R2+ endothelial progenitor cells and six other genes, CAV1, eNOS, CLDN5, NANOG, OCLN and BDNF, showed very low levels of expression in diabetic Lin-/VEGF-R2+ progenitor cells.
Conclusion
Low SDF-1 expression may contribute to the dysfunctional mobilization of bone marrow Lin-/VEGF-R2+ endothelial progenitor cells, which may contribute to microvascular injury in early diabetes.
doi:10.1186/1475-2840-13-42
PMCID: PMC3926942  PMID: 24521356
Diabetes; Endothelial progenitor cells; Diabetic vasculopathies; Molecular pathology; SDF-1; Lin-/VEGF-R2+ EPCs; Cardiovascular pathology; Retinopathy
4.  The Uptake and Accuracy of Oral Kits for HIV Self-Testing in High HIV Prevalence Setting: A Cross-Sectional Feasibility Study in Blantyre, Malawi 
PLoS Medicine  2011;8(10):e1001102.
Augustine Choko and colleagues assess the uptake and acceptability of home-based supervised oral HIV self-testing in Malawi, demonstrating the feasibility of this approach in a high-prevalence, low-income environment.
Background
Although HIV testing and counseling (HTC) uptake has increased dramatically in Africa, facility-based services are unlikely to ever meet ongoing need to the full. A major constraint in scaling up community and home-based HTC services is the unacceptability of receiving HTC from a provider known personally to prospective clients. We investigated the potential of supervised oral HIV self-testing from this perspective.
Methods and Findings
Adult members of 60 households and 72 members of community peer groups in urban Blantyre, Malawi, were selected using population-weighted random cluster sampling. Participants were offered self-testing plus confirmatory HTC (parallel testing with two rapid finger-prick blood tests), standard HTC alone, or no testing. 283 (95.6%) of 298 selected adults participated, including 136 (48.0%) men. 175 (61.8%) had previously tested (19 known HIV positive), although only 64 (21.5%) within the last year. HIV prevalence was 18.5%. Among 260 (91.9%) who opted to self-test after brief demonstration and illustrated instructions, accuracy was 99.2% (two false negatives). Although 98.5% rated the test “not hard at all to do,” 10.0% made minor procedural errors, and 10.0% required extra help. Most participants indicated willingness to accept self-test kits, but not HTC, from a neighbor (acceptability 94.5% versus 46.8%, p = 0.001).
Conclusions
Oral supervised self-testing was highly acceptable and accurate, although minor errors and need for supervisory support were common. This novel option has potential for high uptake at local community level if it can be supervised and safely linked to counseling and care.
Please see later in the article for the Editors' Summary
Editors' Summary
Background
According to the World Health Organization, despite the dramatic increase in the acceptability of HIV testing, more than 60% of people living with HIV do not know their status—a factor that is seriously hampering the global response to the HIV epidemic. The inconvenience and cost involved in visiting services in addition to a general aversion to visiting health facilities appear to be major barriers. Home-based HIV-testing services bypass these obstacles and are being adopted as national policy in a number of countries. However, given the tension between confidentiality and convenience, many people do not want to be counseled and tested by someone they know well, thus creating logistical difficulties and added costs to the provision of home-based testing services.
Why Was This Study Done?
Self-testing in private has considerable potential to contribute to first-time and repeat HIV testing but raises a number of issues, such as accuracy, the potential for adverse psychological reactions in the absence of face-to-face counseling, and the difficulty in organizing subsequent links to HIV/AIDS care. Self-testing has been used for over a decade in the US, but given the need to further scale up HIV testing and counseling in Africa, and to encourage regular repeat testing, the researchers conducted a mixed quantitative and qualitative study of self-testing for HIV using oral test kits to test whether supervised oral self-testing could yield accurate results. The researchers also wanted to explore reasons for accepting self-testing and respondents' preferences for HIV testing.
What Did the Researchers Do and Find?
The researchers conducted their study in four community health worker catchment areas in three high-density residential suburbs of Blantyre, Malawi. Between March and July 2010, the researchers randomly selected two groups of participants from within these catchment areas and all adults were then invited to participate in interview and optional HIV testing and counseling carried out in their home. Participants were offered the choice between self-test for HIV followed by standard voluntary counseling and testing, standard voluntary counseling and testing only, and no HIV testing or counseling. Pre-and post-test counseling was provided to all participants and after self-testing, a counselor reread the self-test kit, completed a checklist of potential errors and confirmed the result using two rapid HIV test kits run in parallel from a finger-prick blood specimen. All participants testing positive were referred to the nearest primary health center.
All 260 participants who consented to voluntary counseling and testing also opted to self-test, with the remaining 23 (8.1%) choosing not to test. HIV prevalence was 18.5% (48 of 260) and HIV prevalence among participants who had previously tested HIV-negative or not tested at all was 12.0% (29 of 241 participants) meaning that less than half of HIV-infected participants were previously diagnosed, and just over half of undiagnosed HIV infections were in individuals who had previously tested HIV negative. The researchers found self-testing to be highly accurate, with clear and concordant results for 256 (99.2%) of 258 participants with both self-test and blood results. Overall sensitivity for self-test self-read was 97.9% with specificity of 100%. At exit interview, 256 (98.5%) of participants rated self-testing as “very easy” to do but additional help was requested by 26 (10%) of self test participants and procedural errors were identified for 26 participants (10%). Importantly, self-testing was the preferred option for future HIV tests for 56.4% of participants and the most common choice for both men and women.
What Do These Findings Mean?
The findings of this study show that self-testing for HIV (after a brief demonstration and illustrated instructions) is highly accurate and is widely accepted by the community, indicating that there is strong community readiness to adopt self-testing alongside other HIV counseling and testing strategies in high HIV prevalence settings in urban Africa. Self-testing may prove especially valuable for encouraging regular repeat testing, couple testing, and first-time testing in otherwise hard-to-reach groups such as men and older individuals. Finally, given the accuracy achieved and strong preferences around future testing, further exploration of self-testing options could help to make progress towards meeting universal access goals.
Additional Information
Please access these Web sites via the online version of this summary at http://dx.doi.org/10.1371/journal.pmed.1001102.
This study is further discussed in a PLoS Medicine Perspective by Walensky and Bassett
Recently published WHO Guidelines explain the principles and processes of adapting HIV guidelines into national programs
The U.S. Centers for Disease Control's initiative Act against AIDS has some user-friendly information on the different types of HIV tests available
A WHO document discusses existing practices and surrounding issues related with HIV self-testing among health workers in sub-Saharan Africa
doi:10.1371/journal.pmed.1001102
PMCID: PMC3186813  PMID: 21990966
5.  Monte Carlo Validation of the Dorfman-Berbaum-Metz Method Using Normalized Pseudovalues and Less Data-Based Model Simplification 
Academic radiology  2005;12(12):1534-1541.
Rationale and Objectives
Two problems of the Dorfman-Berbaum-Metz (DBM) method for analyzing multireader ROC studies are that it tends to be conservative and can produce AUC estimates outside the parameter space – i.e., greater than one or less than zero. Recently it has been shown that the problem of AUC (or other accuracy) estimates outside the parameter space can be eliminated by using normalized pseudovalues, and it has been suggested that less data-based model simplification be used. Our purpose is to empirically investigate if these two modifications – normalized pseudovalues and less data-based model simplification – result in improved performance.
Materials and Methods
We examine the performance of the DBM procedure using the two proposed modifications for discrete and continuous ratings in a null simulation study comparing modalities with respect to the ROC area. The simulation study includes 144 different combinations of reader and case sample sizes, normal/abnormal case sample ratios, and variance components. The ROC area is estimated using parametric and nonparametric estimation.
Results
The DBM procedure with both modifications performs better than either the original DBM procedure or the DBM procedure with only one of the modifications. For parametric estimation with discrete rating data, use of both modifications resulted in the mean type I error (0.043) closest to the nominal .05 level and the smallest range (0.050) and standard deviation (0.0108) across the 144 type I error rates.
Conclusions
We recommend that normalized pseudovalues and less data-based model simplification be used with the DBM procedure.
doi:10.1016/j.acra.2005.07.012
PMCID: PMC1550352  PMID: 16321742
receiver operating characteristic (ROC) curve; DBM; diagnostic radiology; corrected F
6.  Elderly quality of life impacted by traditional chinese medicine techniques 
Background:
The shift in age structure is having a profound impact, suggesting that the aged should be consulted as reporters on the quality of their own lives.
Objectives:
The aim of this research was to establish the possible impact of traditional Chinese medicine (TCM) techniques on the quality of life (QOL) of the elderly.
Sample:
Two non-selected, volunteer groups of Rio de Janeiro municipality inhabitants: a control group (36 individuals), not using TCM, and an experimental group (28 individuals), using TCM at ABACO/Sohaku-in Institute, Brazil.
Methods:
A questionnaire on elderly QOL devised by the World Health Organization, the WHOQOL-Old, was adopted and descriptive statistical techniques were used: mean and standard deviation. The Shapiro–Wilk test checked the normality of the distribution. Furthermore, based on its normality distribution for the intergroup comparison, the Student t test was applied to facets 2, 4, 5, 6, and total score, and the Mann–Whitney U rank test to facets 1 and 3, both tests aiming to analyze the P value between experimental and control groups. The significance level utilized was 95% (P < 0.05).
Results:
The experimental group reported the highest QOL for every facet and the total score.
Conclusions:
The results suggest that TCM raises the level of QOL.
doi:10.2147/CIA.S10615
PMCID: PMC2981102  PMID: 21103400
quality of life; traditional chinese medicine; east-west medicine; WHOQOL-Old; elderly
7.  Tests of homoscedasticity, normality, and missing completely at random for incomplete multivariate data 
Psychometrika  2010;75(4):649-674.
Test of homogeneity of covariances (or homoscedasticity) among several groups has many applications in statistical analysis. In the context of incomplete data analysis, tests of homoscedasticity among groups of cases with identical missing data patterns have been proposed to test whether data are missing completely at random (MCAR). These tests of MCAR require large sample sizes n and/or large group sample sizes ni, and they usually fail when applied to non-normal data. Hawkins (1981) proposed a test of multivariate normality and homoscedasticity that is an exact test for complete data when ni are small. This paper proposes a modification of this test for complete data to improve its performance, and extends its application to test of homoscedasticity and MCAR when data are multivariate normal and incomplete. Moreover, it is shown that the statistic used in the Hawkins test in conjunction with a nonparametric k-sample test can be used to obtain a nonparametric test of homoscedasticity that works well for both normal and non-normal data. It is explained how a combination of the proposed normal-theory Hawkins test and the nonparametric test can be employed to test for homoscedasticity, MCAR, and multivariate normality. Simulation studies show that the newly proposed tests generally outperform their existing competitors in terms of Type I error rejection rates. Also, a power study of the proposed tests indicates good power. The proposed methods use appropriate missing data imputations to impute missing data. Methods of multiple imputation are described and one of the methods is employed to confirm the result of our single imputation methods. Examples are provided where multiple imputation enables one to identify a group or groups whose covariance matrices differ from the majority of other groups.
doi:10.1007/s11336-010-9175-3
PMCID: PMC3124223  PMID: 21720450
Covariance Structures; k-Sample Test; Missing Data; Multiple Imputation; Non-parametric Test; Structural Equations; Test of Homogeneity of Covariances
8.  Assessment of the effect of phenytoin on cutaneous healing from excision of melanocytic nevi on the face and on the back 
BMC Dermatology  2010;10:7.
Background
Topical phenytoin is a powerful skin wounds healing and it may be useful in clinical practice. The purpose of this study was to evaluate the effect of topical phenytoin 0.5%, by comparing it with cream (control) in wounds resulting from excision of two melanocytic nevi in the same patient. Our purpose was also to assess if phenytoin had better therapeutic and cosmetic outcomes when compared with cream (control).
Methods
This study evaluated 100 patients with skin wounds from excision of melanocytic nevi. 50 patients with lesions on the face and 50 patients with lesions on the back, totalizing 200 lesions excised with modified punch. The resulting superficial skin wounds had the same diameter and depth, and second intention healing followed.
Patients were followed for 60 days. Student's t-test, Mann Whitney nonparametric test, analysis of variance, LSD test, Shapiro-Wilks test and Fisher test were used to analyze the results, depending on the nature of the variables being studied.
Results
Phenytoin showed better therapeutic and cosmetic results, by healing faster, with more intense epithelization in wounds in comparison with cream (control). Phenytoin showed a statistically significant difference regarding the following parameters (p < 0.05): wounded area and healing time. Phenytoin application resulted in a smaller area and a shorter healing time. Also the intensity of exudates, bleeding, and the epithelization were more intense in phenytoin-treated wounds. Regarding the shape and thickness of the scar, injuries treated with phenytoin had round and flat shaped scars in most of the cases. Considering patient's gender and phototype, female patients presented smaller wounds and scar areas; and phototype I had the largest scar areas. Contact eczema was an adverse reaction in 7 injuries located on the back caused by cream (control) and hypoallergenic tape.
Conclusions
Phenytoin showed better therapeutic and cosmetic results compared with cream (control). Phenytoin is a low cost drug, which accelerates skin wounds healing in human patients. Trial registration: ISRCTN96539803
doi:10.1186/1471-5945-10-7
PMCID: PMC2936357  PMID: 20731878
9.  On Bootstrap Tests of Symmetry About an Unknown Median 
Journal of data science : JDS  2010;8(3):413-427.
It is important to examine the symmetry of an underlying distribution before applying some statistical procedures to a data set. For example, in the Zuni School District case, a formula originally developed by the Department of Education trimmed 5% of the data symmetrically from each end. The validity of this procedure was questioned at the hearing by Chief Justice Roberts. Most tests of symmetry (even nonparametric ones) are not distribution free in finite sample sizes. Hence, using asymptotic distribution may not yield an accurate type I error rate or/and loss of power in small samples. Bootstrap resampling from a symmetric empirical distribution function fitted to the data is proposed to improve the accuracy of the calculated p-value of several tests of symmetry. The results show that the bootstrap method is superior to previously used approaches relying on the asymptotic distribution of the tests that assumed the data come from a normal distribution. Incorporating the bootstrap estimate in a recently proposed test due to Miao, Gel and Gastwirth (2006) preserved its level and shows it has reasonable power properties on the family of distribution evaluated.
PMCID: PMC2907265  PMID: 20664754
Parametric bootstrap; Resampling; Testing symmetry about an unknown center; Zuni school district case
10.  The ChQoL questionnaire: an Italian translation with preliminary psychometric results for female oncological patients 
Background
in Occidental languages, no widely accepted questionnaire is available which deals with health related quality of life from the specific point of view of Traditional Chinese Medicine (TCM). Some psychometric tools of this kind are available in Chinese. One of them is the Chinese Quality of Life questionnaire (ChQoL). It comprises 50 items, subdivided in 3 Domains and 13 Facets. The ChQoL was built from scratch on the basis of TCM theory. It is therefore specifically valuable for the TCM practitioner. This paper describes our translation into Italian of the ChQoL, its first application to Occidental oncological patients, and some of its psychometric properties.
Methods
a translation scheme, originally inspired by the TRAPD procedure, is developed. This scheme focuses on comprehensibility and clinical usefulness more than on linguistic issues alone. The translated questionnaire is tested on a sample of 203 consecutive female patients with breast cancer. Shapiro-Wilk normality tests, Fligner-Killeen median tests, exploratory Two-step Cluster Analysis, and Tukey's test for non-additivity are applied to study the outcomes.
Results
an Italian translation is proposed. It retains the TCM characteristics of the original ChQoL, it is intelligible to Occidental patients who have no previous knowledge of TCM, and it is useful for daily clinical practice. The score distribution is not Normal, and there are floor and ceiling effects. A Visual Analogue Scale is identified as a suitable choice. A 3-point Likert scale can also efficiently describe the data pattern. The original scales show non-additivity, but an Anscombe-Tukey transformation with γ = 1.5 recovers additivity at the Domain level. Additivity is enhanced if different γ are adopted for different Facets, except in one case.
Conclusions
the translated questionnaire can be adopted both as a filing system based on TCM and as a source of outcomes for clinical trials. A Visual Analogue Scale is recommended, but a simpler 3-point Likert scale also suitably fits data. When estimating missing data, and when grouping items within Domain in order to build a summary Domain index, an Anscombe-Tukey transformation should be applied to the raw scores.
doi:10.1186/1477-7525-8-106
PMCID: PMC2958157  PMID: 20868514
11.  POWER-ENHANCED MULTIPLE DECISION FUNCTIONS CONTROLLING FAMILY-WISE ERROR AND FALSE DISCOVERY RATES 
Annals of statistics  2011;39(1):556-583.
Improved procedures, in terms of smaller missed discovery rates (MDR), for performing multiple hypotheses testing with weak and strong control of the family-wise error rate (FWER) or the false discovery rate (FDR) are developed and studied. The improvement over existing procedures such as the Šidák procedure for FWER control and the Benjamini–Hochberg (BH) procedure for FDR control is achieved by exploiting possible differences in the powers of the individual tests. Results signal the need to take into account the powers of the individual tests and to have multiple hypotheses decision functions which are not limited to simply using the individual p-values, as is the case, for example, with the Šidák, Bonferroni, or BH procedures. They also enhance understanding of the role of the powers of individual tests, or more precisely the receiver operating characteristic (ROC) functions of decision processes, in the search for better multiple hypotheses testing procedures. A decision-theoretic framework is utilized, and through auxiliary randomizers the procedures could be used with discrete or mixed-type data or with rank-based nonparametric tests. This is in contrast to existing p-value based procedures whose theoretical validity is contingent on each of these p-value statistics being stochastically equal to or greater than a standard uniform variable under the null hypothesis. Proposed procedures are relevant in the analysis of high-dimensional “large M, small n” data sets arising in the natural, physical, medical, economic and social sciences, whose generation and creation is accelerated by advances in high-throughput technology, notably, but not limited to, microarray technology.
PMCID: PMC4091923  PMID: 25018568
Benjamini–Hochberg procedure; Bonferroni procedure; decision process; false discovery rate (FDR); family wise error rate (FWER); Lagrangian optimization; Neyman–Pearson most powerful test; microarray analysis; reverse martingale; missed discovery rate (MDR); multiple decision function and process; multiple hypotheses testing; optional sampling theorem; power function; randomized p-values; generalized multiple decision p-values; ROC function; Šidák procedure
12.  A Bayesian approach to efficient differential allocation for resampling-based significance testing 
BMC Bioinformatics  2009;10:198.
Background
Large-scale statistical analyses have become hallmarks of post-genomic era biological research due to advances in high-throughput assays and the integration of large biological databases. One accompanying issue is the simultaneous estimation of p-values for a large number of hypothesis tests. In many applications, a parametric assumption in the null distribution such as normality may be unreasonable, and resampling-based p-values are the preferred procedure for establishing statistical significance. Using resampling-based procedures for multiple testing is computationally intensive and typically requires large numbers of resamples.
Results
We present a new approach to more efficiently assign resamples (such as bootstrap samples or permutations) within a nonparametric multiple testing framework. We formulated a Bayesian-inspired approach to this problem, and devised an algorithm that adapts the assignment of resamples iteratively with negligible space and running time overhead. In two experimental studies, a breast cancer microarray dataset and a genome wide association study dataset for Parkinson's disease, we demonstrated that our differential allocation procedure is substantially more accurate compared to the traditional uniform resample allocation.
Conclusion
Our experiments demonstrate that using a more sophisticated allocation strategy can improve our inference for hypothesis testing without a drastic increase in the amount of computation on randomized data. Moreover, we gain more improvement in efficiency when the number of tests is large. R code for our algorithm and the shortcut method are available at .
doi:10.1186/1471-2105-10-198
PMCID: PMC2718927  PMID: 19558706
13.  Validation of drop plate technique for bacterial enumeration by parametric and nonparametric tests 
Veterinary Research Forum  2013;4(3):179-183.
Drop plate technique has a priority and preference compared with the spread plate procedure, because of less time, quantity of media, effort requirement, little incubator space, and less labor intensive. The objective of this research was to compare the accuracy and fidelity of drop plate method vs. spread plate method by parametric and nonparametric statistical tests. For bacterial enumeration by drop and spread plate methods, successive dilutions of second subculture of Lactobacillus casei and Salmonella Typhimurium were transferred to selective agar. The correlation of agreement between both methods was evaluated by using statistical proofs. Results showed that mean value (parametric unpaired t-test) comparison at 95 percent confidence level did not reject null hypothesis, which it meant that the equality of the mean data could not be ruled out. Nonparametric method was used because of approximately Gaussian pattern of data distribution. For this purpose, Mann-Whitney test (equivalent nonparametric t-test) was used. It meant that the equality of medians obtained from two methods were similar. Spearman’s rho correlation coefficient (r) via both methods due to data distribution patterns for enumeration of S. Typhimurium and L. casei were 0.62 and 0.87, respectively; which represented moderately strong and strong relationship between two methods, respectively. Besides, there was a significant and strong positive correlation (p < 0.001) between spread and drop plate procedures. Because of aforementioned reasons, the spread plate method can be replaced by drop plate method.
PMCID: PMC4312378
Drop plate; Lactobacillus casei; Parametric and nonparametric tests; Salmonella Typhimurium; Spread plate
14.  Early Termination of a Two-Stage Study to Develop and Validate a Panel of Biomarkers 
Statistics in medicine  2012;32(6):1027-1037.
Two-stage designs to develop and validate a panel of biomarkers present a natural setting for the inclusion of stopping rules for futility in the event of poor preliminary estimates of performance. We consider the design of a two-stage study to develop and validate a panel of biomarkers where a predictive model is developed using a subset of the samples in stage 1 and the model is validated using the remainder of the samples in stage 2. First, we illustrate how a stopping rule for futility can be implemented in a standard, two-stage study for developing and validating a predictive model where samples are separated into a training and validation sample. Simulation results indicate that our design has similar type-I error rate and power to the fixed-sample design but with a substantially reduced sample size under the null hypothesis. We then illustrate how additional interim analyses can be included in stage 2 by applying existing group sequential methodology, which results in even greater savings in the number of samples required under both the null and alternative. Our simulation results also illustrate that the operating characteristics of our design are robust to changes in the underlying marker distribution.
doi:10.1002/sim.5622
PMCID: PMC3888241  PMID: 23413213
Group Sequential Design; Biomarker Panel; ROC Curve
15.  Using Parametric Multipoint Lods and Mods for Linkage Analysis Requires a Shift in Statistical Thinking 
Human Heredity  2011;72(4):264-275.
Multipoint (MP) linkage analysis represents a valuable tool for whole-genome studies but suffers from the disadvantage that its probability distribution is unknown and varies as a function of marker information and density, genetic model, number and structure of pedigrees, and the affection status distribution [Xing and Elston: Genet Epidemiol 2006;30:447–458; Hodge et al.: Genet Epidemiol 2008;32:800–815]. This implies that the MP significance criterion can differ for each marker and each dataset, and this fact makes planning and evaluation of MP linkage studies difficult. One way to circumvent this difficulty is to use simulations or permutation testing. Another approach is to use an alternative statistical paradigm to assess the statistical evidence for linkage, one that does not require computation of a p value. Here we show how to use the evidential statistical paradigm for planning, conducting, and interpreting MP linkage studies when the disease model is known (lod analysis) or unknown (mod analysis). As a key feature, the evidential paradigm decouples uncertainty (i.e. error probabilities) from statistical evidence. In the planning stage, the user calculates error probabilities, as functions of one's design choices (sample size, choice of alternative hypothesis, choice of likelihood ratio (LR) criterion k) in order to ensure a reliable study design. In the data analysis stage one no longer pays attention to those error probabilities. In this stage, one calculates the LR for two simple hypotheses (i.e. trait locus is unlinked vs. trait locus is located at a particular position) as a function of the parameter of interest (position). The LR directly measures the strength of evidence for linkage in a given data set and remains completely divorced from the error probabilities calculated in the planning stage. An important consequence of this procedure is that one can use the same criterion k for all analyses. This contrasts with the situation described above, in which the value one uses to conclude significance may differ for each marker and each dataset in order to accommodate a fixed test size, α. In this study we accomplish two goals that lead to a general algorithm for conducting evidential MP linkage studies. (1) We provide two theoretical results that translate into guidelines for investigators conducting evidential MP linkage: (a) Comparing mods to lods, error rates (including probabilities of weak evidence) are generally higher for mods when the null hypothesis is true, but lower for mods in the presence of true linkage. Royall [J Am Stat Assoc 2000;95:760–780] has shown that errors based on lods are bounded and generally small. Therefore when the true disease model is unknown and one chooses to use mods, one needs to control misleading evidence rates only under the null hypothesis; (b) for any given pair of contiguous marker loci, error rates under the null are greatest at the midpoint between the markers spaced furthest apart, which provides an obvious simple alternative hypothesis to specify for planning MP linkage studies. (2) We demonstrate through extensive simulation that this evidential approach can yield low error rates under the null and alternative hypotheses for both lods and mods, despite the fact that mod scores are not true LRs. Using these results we provide a coherent approach to implement a MP linkage study using the evidential paradigm.
doi:10.1159/000331463
PMCID: PMC3267993  PMID: 22189469
Evidential paradigm; Likelihood; Parametric linkage; Complex disease
16.  Reproducibility of an aerobic endurance test for nonexpert swimmers 
Background:
This study aimed to verify the reproduction of an aerobic test to determine nonexpert swimmers’ resistance.
Methods:
The sample consisted of 24 male swimmers (age: 22.79 ± 3.90 years; weight: 74.72 ± 11.44 kg; height: 172.58 ± 4.99 cm; and fat percentage: 15.19% ± 3.21%), who swim for 1 hour three times a week. A new instrument was used in this study (a Progressive Swim Test): the swimmer wore an underwater MP3 player and increased their swimming speed on hearing a beep after every 25 meters. Each swimmer’s heart rate was recorded before the test (BHR) and again after the test (AHR). The rate of perceived exertion (RPE) and the number of laps performed (NLP) were also recorded. The sample size was estimated using G*Power software (v 3.0.10; Franz Faul, Kiel University, Kiel, Germany). The descriptive values were expressed as mean and standard deviation. After confirming the normality of the data using both the Shapiro–Wilk and Levene tests, a paired t-test was performed to compare the data. The Pearson’s linear correlation (r) and intraclass coefficient correlation (ICC) tests were used to determine relative reproducibility. The standard error of measurement (SEM) and the coefficient of variation (CV) were used to determine absolute reproducibility. The limits of agreement and the bias of the absolute and relative values between days were determined by Bland–Altman plots. All values had a significance level of P < 0.05.
Results:
There were significant differences in AHR (P = 0.03) and NLP (P = 0.01) between the 2 days of testing. The obtained values were r > 0.50 and ICC > 0.66. The SEM had a variation of ±2% and the CV was <10%. Most cases were within the upper and lower limits of Bland–Altman plots, suggesting correlation of the results. The applicability of NLP showed greater robustness (r and ICC > 0.90; SEM < 1%; CV < 3%), indicating that the other variables can be used to predict incremental changes in the physiological condition of swimmers.
Conclusion:
The Progressive Swim Test for nonexpert swimmers produces comparable results for noncompetitive swimmers with a favorable degree of reproducibility, thus presenting possible applications for researching the physiological performance of nonexpert swimmers.
Video abstract
doi:10.2147/JMDH.S34447
PMCID: PMC3460665  PMID: 23055740
swimming; physical evaluation; resistance training; health
17.  Supervised and Unsupervised Self-Testing for HIV in High- and Low-Risk Populations: A Systematic Review 
PLoS Medicine  2013;10(4):e1001414.
By systematically reviewing the literature, Nitika Pant Pai and colleagues assess the evidence base for HIV self tests both with and without supervision.
Background
Stigma, discrimination, lack of privacy, and long waiting times partly explain why six out of ten individuals living with HIV do not access facility-based testing. By circumventing these barriers, self-testing offers potential for more people to know their sero-status. Recent approval of an in-home HIV self test in the US has sparked self-testing initiatives, yet data on acceptability, feasibility, and linkages to care are limited. We systematically reviewed evidence on supervised (self-testing and counselling aided by a health care professional) and unsupervised (performed by self-tester with access to phone/internet counselling) self-testing strategies.
Methods and Findings
Seven databases (Medline [via PubMed], Biosis, PsycINFO, Cinahl, African Medicus, LILACS, and EMBASE) and conference abstracts of six major HIV/sexually transmitted infections conferences were searched from 1st January 2000–30th October 2012. 1,221 citations were identified and 21 studies included for review. Seven studies evaluated an unsupervised strategy and 14 evaluated a supervised strategy. For both strategies, data on acceptability (range: 74%–96%), preference (range: 61%–91%), and partner self-testing (range: 80%–97%) were high. A high specificity (range: 99.8%–100%) was observed for both strategies, while a lower sensitivity was reported in the unsupervised (range: 92.9%–100%; one study) versus supervised (range: 97.4%–97.9%; three studies) strategy. Regarding feasibility of linkage to counselling and care, 96% (n = 102/106) of individuals testing positive for HIV stated they would seek post-test counselling (unsupervised strategy, one study). No extreme adverse events were noted. The majority of data (n = 11,019/12,402 individuals, 89%) were from high-income settings and 71% (n = 15/21) of studies were cross-sectional in design, thus limiting our analysis.
Conclusions
Both supervised and unsupervised testing strategies were highly acceptable, preferred, and more likely to result in partner self-testing. However, no studies evaluated post-test linkage with counselling and treatment outcomes and reporting quality was poor. Thus, controlled trials of high quality from diverse settings are warranted to confirm and extend these findings.
Please see later in the article for the Editors' Summary
Editors' Summary
Background
About 34 million people (most living in resource-limited countries) are currently infected with HIV, the virus that causes AIDS, and about 2.5 million people become infected with HIV every year. HIV is usually transmitted through unprotected sex with an infected partner. HIV infection is usually diagnosed by looking for antibodies to HIV in blood or saliva. Early during infection, the immune system responds to HIV by beginning to make antibodies that recognize the virus and target it for destruction. “Seroconversion”—the presence of detectable amounts of antibody in the blood or saliva—usually takes 6–12 weeks. Rapid antibody-based tests, which do not require laboratory facilities, can provide a preliminary result about an individual's HIV status from a simple oral swab or finger stick sample within 20 minutes. However preliminary rapid positive results have to be confirmed in a laboratory, which may take a few days or weeks. If positive, HIV infection can be controlled but not cured by taking a daily cocktail of powerful antiretroviral drugs throughout life.
Why Was This Study Done?
To reduce the spread of HIV, it is essential that HIV-positive individuals get tested, change behaviors avoid transmitting the virus to other people by, for example, always using a condom during sex, and if positive get on to treatment that is available worldwide. Treatment also reduces transmission of virus to the partner and controls the virus in the community. However, only half the people currently living with HIV know their HIV status, a state of affairs that increases the possibility of further HIV transmission to their partners and children. HIV positive individuals are diagnosed late with advanced HIV infection that costs health care services. Although health care facility-based HIV testing has been available for decades, people worry about stigma, visibility, and social discrimination. They also dislike the lack of privacy and do not like having to wait for their test results. Self-testing (i.e., self-test conduct and interpretation) might alleviate some of these barriers to testing by allowing individuals to determine their HIV status in the privacy of their home and could, therefore, increase the number of individuals aware of their HIV status. This could possibly reduce transmission and, through seeking linkages to care, bring HIV under control in communities. In some communities and countries, stigma of HIV prevents people from taking action about their HIV status. Indeed, an oral (saliva-based) HIV self-test kit is now available in the US. But how acceptable, feasible, and accurate is self-testing by lay people, and will people who find themselves self-test positive seek counseling and treatment? In this systematic review (a study that uses pre-defined criteria to identify all the research on a given topic), the researchers examine these issues by analyzing data from studies that have evaluated supervised self-testing (self-testing and counseling aided by a health-care professional) and unsupervised self-testing (self-testing performed without any help but with counseling available by phone or internet).
What Did the Researchers Do and Find?
The researchers identified 21 eligible studies, two-thirds of which evaluated oral self-testing and a third of which evaluated blood-based self-testing. Seven studies evaluated an unsupervised self-testing strategy and 14 evaluated a supervised strategy. Most of the data (89%) came from studies undertaken in high-income settings. The study populations varied from those at high risk of HIV infection to low-risk general populations. Across the studies, acceptability (defined as the number of people who actually self-tested divided by the number who consented to self-test) ranged from 74% to 96%. With both strategies, the specificity of self-testing (the chance of an HIV-negative person receiving a negative test result is true negative) was high but the sensitivity of self-testing (the chance of an HIV-positive person receiving a positive test result is indeed a true positive) was higher for supervised than for unsupervised testing. The researchers also found evidence that people preferred self-testing to facility-based testing and oral self-testing to blood-based self testing and, in one study, 96% of participants who self-tested positive sought post-testing counseling.
What Do These Findings Mean?
These findings provide new but limited information about the feasibility, acceptability, and accuracy of HIV self-testing. They suggest that it is feasible to implement both supervised and unsupervised self-testing, that both strategies are preferred to facility-based testing, but that the accuracy of self-testing is variable. However, most of the evidence considered by the researchers came from high-income countries and from observational studies of varying quality, and data on whether people self-testing positive sought post-testing counseling (linkage to care) were only available from one evaluation of unsupervised self-testing in the US. Consequently, although these findings suggest that self-testing could engage individuals in finding our their HIV status and thereby help modify behavior thus, reduce HIV transmission in the community, by increasing the proportion of people living with HIV who know their HIV status. The researchers suggested that more data from diverse settings and preferably from controlled randomized trials must be collected before any initiatives for global scale-up of self-testing for HIV infection are implemented.
Additional Information
Please access these Web sites via the online version of this summary at http://dx.doi.org/10.1371/journal.pmed.1001414.
Information is available from the US National Institute of Allergy and Infectious Diseases on HIV infection and AIDS
NAM/aidsmap provides basic information about HIV/AIDS and summaries of recent research findings on HIV care and treatment
Information is available from Avert, an international AIDS charity on many aspects of HIV/AIDS, including information on HIV testing, and on HIV transmission and testing (in English and Spanish)
The UK National Health Service Choices website provides information about all aspects of HIV and AIDS; a “behind the headlines” article provides details about the 2012 US approval for an over-the-counter HIV home-use test
The 2012 World AIDS Day Report provides information about the percentage of people living with HIV who are aware of their HIV status in various African countries, as well as up-to-date information about the AIDS epidemic
Patient stories about living with HIV/AIDS are available through Avert; the nonprofit website Healthtalkonline also provides personal stories about living with HIV, including stories about getting a diagnosis
doi:10.1371/journal.pmed.1001414
PMCID: PMC3614510  PMID: 23565066
18.  Paravertebral block is a proper alternative anesthesia for outpatient lithotripsy 
Context:
This study evaluated the effectiveness of paravertebral block as an alternative anesthetic technique for extracorporeal shock wave lithotripsy (ESWL) procedure. A total of 50 patients with renal stones, aged 20-60 years, were randomly allocated into two groups; 25 patients in group P; received unilateral paravertebral block from T8 through L1 with injection of 5 mL 0.5% bupivacaine and 25 patients in group L; received local infiltration by bupivacaine 0.25% (2 mg/kg) into the 30 cm2 area after localizing the stones site, 10 min before the session. A total of 10 mm visual analogue scale (VAS) was used to evaluate pain every 10 min during the session. At the end of the procedure, total doses of rescue analgesia, the number of shockwaves, their power, and the total duration of shockwave treatment were recorded. After completion of the procedure, the patient was assessed for pain and nausea in the postanesthesia care unit (PACU) using the VAS. Patient's satisfaction and time needed to discharge patients to home also were recorded. Time to do the anesthetic technique was significantly higher (P < 0.001) in group-P than group-L, it was 12.7 ± 2.3 min versus 6.9 ± 1.9 min, respectively; intraoperative rescue analgesia by fentanyl was lesser (P < 0.001) in group-P than group-L, 26.7 ± 6.32 mcg versus 78.6 ± 5.41 mcg, respectively, also time interval between ends of the procedure till discharge to home was significantly higher (P < 0.001) in group-P than group-L, it was 99 ± 17 min versus 133 ± 31 min, respectively. VAS was not significant difference between both groups either intraoperative or postoperative in first hour. Patient's satisfaction was significantly higher (P < 0.05) in group-P than group-L, it was 8.8 ± 1.1 versus 6.1 ± 0.6, respectively. Adverse events were lesser, but not significant in group-P than in group-L. Two patients (8%) in group-L and one patient (4%) in the group-P experienced episodes of postoperative nausea and vomiting (PONV).
Paravertebral block is an effective alternative anesthesia for outpatient lithotripsy; multiple level paravertebral blocks provide an optimal anesthetic condition, with acceptable adverse events for ESWL. And, providing proper analgesia during the procedure and in first hour after finishing of the procedure, early discharge to home and providing better patient's satisfactions.
Aims:
This study evaluated the effectiveness of paravertebral block as an alternative anesthetic technique for ESWL procedure.
Settings and Design:
Prospective open label study.
Subject and Methods:
A total of 50 patients with renal stones, aged 20-60 years, were randomly allocated into two groups; 25 patients in group P; received unilateral paravertebral block from T8 through L1 with injection of 5mL 0.5% bupivacaine and 25 patients in group L; received local infiltration by bupivacaine 0.25% (2 mg/kg) into the 30 cm2 area after localizing the stones site, 10 min before the session. A total of 10 mm VAS was used to evaluate pain every 10 min during the session. At the end of the procedure, total doses of rescue analgesia, the number of shockwaves, their power, and the total duration of shockwave treatment were recorded. After completion of the procedure, the patient was assessed for pain and nausea in the PACU using the VAS. Patient's satisfaction and time needed to discharge patients to home also were recorded.
Statistical Analysis:
The findings of the two groups were statistically compared using SPSS version 12 (SPSS Inc., Chicago, IL). Data were expressed as mean ± standard deviation, number, and percentage. Nominal nonparametric data were analyzed using Chi-square test. Parametric data were compared using unpaired t-test. Ordinal nonparametric data were analyzed using Mann-Whitney U-test.
Results:
Time to do the anesthetic technique was significantly higher (P < 0.001) in group-P than group-L, it was 12.7 ± 2.3 min versus 6.9 ± 1.9 min, respectively; intraoperative rescue analgesia by fentanyl was lesser (P < 0.001) in group-P than group-L, 26.7 ± 6.32 mcg versus 78.6 ± 5.41 mcg, respectively, also time interval between ends of the procedure till discharge to home was significantly higher (P < 0.001) in group-P than group-L, it was 99 ± 17 min versus 133 ± 31 min, respectively. VAS was not significant difference between both groups either intraoperative or postoperative in first hour. Patient's satisfaction was significantly higher (P < 0.05) in group-P than group-L, it was 8.8 ± 1.1 versus 6.1 ± 0.6, respectively. Adverse events were lesser, but not significant in group-P than in group-L. Two patients (8%) in group-L and one patient (4%) in the group-P experienced episodes of PONV.
Conclusions:
Paravertebral block is an effective alternative anesthesia for outpatient lithotripsy; multiple level paravertebral blocks provide an optimal anesthetic condition, with acceptable adverse events for ESWL. And providing proper analgesia during the procedure and in first hour after finishing of the procedure, early discharge to home and providing better patient's satisfactions.
doi:10.4103/0259-1162.123238
PMCID: PMC4173548
Extracorporeal shock wave lithotripsy; local anesthetic; paravertebral block
19.  Testing for differentially expressed genes with microarray data 
Nucleic Acids Research  2003;31(9):e52.
This paper compares the type I error and power of the one- and two-sample t-tests, and the one- and two-sample permutation tests for detecting differences in gene expression between two microarray samples with replicates using Monte Carlo simulations. When data are generated from a normal distribution, type I errors and powers of the one-sample parametric t-test and one-sample permutation test are very close, as are the two-sample t-test and two-sample permutation test, provided that the number of replicates is adequate. When data are generated from a t-distribution, the permutation tests outperform the corresponding parametric tests if the number of replicates is at least five. For data from a two-color dye swap experiment, the one-sample test appears to perform better than the two-sample test since expression measurements for control and treatment samples from the same spot are correlated. For data from independent samples, such as the one-channel array or two-channel array experiment using reference design, the two-sample t-tests appear more powerful than the one-sample t-tests.
PMCID: PMC154240  PMID: 12711697
20.  Nonparametric Covariate-Adjusted Association Tests Based on the Generalized Kendall’s Tau* 
Identifying the risk factors for comorbidity is important in psychiatric research. Empirically, studies have shown that testing multiple, correlated traits simultaneously is more powerful than testing a single trait at a time in association analysis. Furthermore, for complex diseases, especially mental illnesses and behavioral disorders, the traits are often recorded in different scales such as dichotomous, ordinal and quantitative. In the absence of covariates, nonparametric association tests have been developed for multiple complex traits to study comorbidity. However, genetic studies generally contain measurements of some covariates that may affect the relationship between the risk factors of major interest (such as genes) and the outcomes. While it is relatively easy to adjust these covariates in a parametric model for quantitative traits, it is challenging for multiple complex traits with possibly different scales. In this article, we propose a nonparametric test for multiple complex traits that can adjust for covariate effects. The test aims to achieve an optimal scheme of adjustment by using a maximum statistic calculated from multiple adjusted test statistics. We derive the asymptotic null distribution of the maximum test statistic, and also propose a resampling approach, both of which can be used to assess the significance of our test. Simulations are conducted to compare the type I error and power of the nonparametric adjusted test to the unadjusted test and other existing adjusted tests. The empirical results suggest that our proposed test increases the power through adjustment for covariates when there exist environmental effects, and is more robust to model misspecifications than some existing parametric adjusted tests. We further demonstrate the advantage of our test by analyzing a data set on genetics of alcoholism.
doi:10.1080/01621459.2011.643707
PMCID: PMC3381868  PMID: 22745516
Comorbidity; Environmental factor; Family-based association test; Maximum test statistic; Multiple traits; Ordinal traits
21.  Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods 
PLoS ONE  2015;10(1):e0116774.
A common problem that is encountered in medical applications is the overall homogeneity of survival distributions when two survival curves cross each other. A survey demonstrated that under this condition, which was an obvious violation of the assumption of proportional hazard rates, the log-rank test was still used in 70% of studies. Several statistical methods have been proposed to solve this problem. However, in many applications, it is difficult to specify the types of survival differences and choose an appropriate method prior to analysis. Thus, we conducted an extensive series of Monte Carlo simulations to investigate the power and type I error rate of these procedures under various patterns of crossing survival curves with different censoring rates and distribution parameters. Our objective was to evaluate the strengths and weaknesses of tests in different situations and for various censoring rates and to recommend an appropriate test that will not fail for a wide range of applications. Simulation studies demonstrated that adaptive Neyman’s smooth tests and the two-stage procedure offer higher power and greater stability than other methods when the survival distributions cross at early, middle or late times. Even for proportional hazards, both methods maintain acceptable power compared with the log-rank test. In terms of the type I error rate, Renyi and Cramér—von Mises tests are relatively conservative, whereas the statistics of the Lin-Xu test exhibit apparent inflation as the censoring rate increases. Other tests produce results close to the nominal 0.05 level. In conclusion, adaptive Neyman’s smooth tests and the two-stage procedure are found to be the most stable and feasible approaches for a variety of situations and censoring rates. Therefore, they are applicable to a wider spectrum of alternatives compared with other tests.
doi:10.1371/journal.pone.0116774
PMCID: PMC4304842  PMID: 25615624
22.  A simple powerful bivariate test for two sample location problems in experimental and observational studies 
Background
In many areas of medical research, a bivariate analysis is desirable because it simultaneously tests two response variables that are of equal interest and importance in two populations. Several parametric and nonparametric bivariate procedures are available for the location problem but each of them requires a series of stringent assumptions such as specific distribution, affine-invariance or elliptical symmetry.
The aim of this study is to propose a powerful test statistic that requires none of the aforementioned assumptions. We have reduced the bivariate problem to the univariate problem of sum or subtraction of measurements. A simple bivariate test for the difference in location between two populations is proposed.
Method
In this study the proposed test is compared with Hotelling's T2 test, two sample Rank test, Cramer test for multivariate two sample problem and Mathur's test using Monte Carlo simulation techniques. The power study shows that the proposed test performs better than any of its competitors for most of the populations considered and is equivalent to the Rank test in specific distributions.
Conclusions
Using simulation studies, we show that the proposed test will perform much better under different conditions of underlying population distribution such as normality or non-normality, skewed or symmetric, medium tailed or heavy tailed. The test is therefore recommended for practical applications because it is more powerful than any of the alternatives compared in this paper for almost all the shifts in location and in any direction.
doi:10.1186/1742-4682-7-13
PMCID: PMC2880022  PMID: 20459659
23.  Model error in covariance structure models: Some implications for power and Type I error 
The present study investigated the degree to which violation of the parameter drift assumption affects the Type I error rate for the test of close fit and power analysis procedures proposed by MacCallum, Browne, and Sugawara (1996) for both the test of close fit and the test of exact fit. The parameter drift assumption states that as sample size increases both sampling error and model error (i.e. the degree to which the model is an approximation in the population) decrease. Model error was introduced using a procedure proposed by Cudeck and Browne (1992). The empirical power for both the test of close fit, in which the null hypothesis specifies that the Root Mean Square Error of Approximation (RMSEA) ≤ .05, and the test of exact fit, in which the null hypothesis specifies that RMSEA = 0, is compared with the theoretical power computed using the MacCallum et al. (1996) procedure. The empirical power and theoretical power for both the test of close fit and the test of exact fit are nearly identical under violations of the assumption. The results also indicated that the test of close fit maintains the nominal Type I error rate under violations of the assumption.
doi:10.1027/1614-2241.4.4.159
PMCID: PMC3039454  PMID: 21331302
24.  Resampling-Based Empirical Bayes Multiple Testing Procedures for Controlling Generalized Tail Probability and Expected Value Error Rates: Focus on the False Discovery Rate and Simulation Study 
Summary
This article proposes resampling-based empirical Bayes multiple testing procedures for controlling a broad class of Type I error rates, defined as generalized tail probability (gTP) error rates, gTP(q, g) = Pr(g(Vn, Sn) > q), and generalized expected value (gEV) error rates, gEV(g) = E[g(Vn, Sn)], for arbitrary functions g(Vn, Sn) of the numbers of false positives Vn and true positives Sn. Of particular interest are error rates based on the proportion g(Vn, Sn) = Vn/(Vn + Sn) of Type I errors among the rejected hypotheses, such as the false discovery rate (FDR), FDR = E[Vn/(Vn + Sn)]. The proposed procedures offer several advantages over existing methods. They provide Type I error control for general data generating distributions, with arbitrary dependence structures among variables. Gains in power are achieved by deriving rejection regions based on guessed sets of true null hypotheses and null test statistics randomly sampled from joint distributions that account for the dependence structure of the data. The Type I error and power properties of an FDR-controlling version of the resampling-based empirical Bayes approach are investigated and compared to those of widely-used FDR-controlling linear step-up procedures in a simulation study. The Type I error and power trade-off achieved by the empirical Bayes procedures under a variety of testing scenarios allows this approach to be competitive with or outperform the Storey and Tibshirani (2003) linear step-up procedure, as an alternative to the classical Benjamini and Hochberg (1995) procedure.
doi:10.1002/bimj.200710473
PMCID: PMC4130579  PMID: 18932138
Adaptive; Adjusted p-value; Alternative hypothesis; Bootstrap; Correlation; Cut-off; Empirical Bayes; False discovery rate; Generalized expected value error rate; Generalized tail probability error rate; Joint distribution; Linear step-up procedure; Marginal procedure; Mixture model; Multiple hypothesis testing; Non-parametric; Null distribution; Null hypothesis; Posterior probability; Power; Prior probability; Proportion of true null hypotheses; q-value; R package; Receiver operator characteristic curve; Rejection region; Resampling; Simulation study; Software; t-statistic; Test statistic; Type I error rate
25.  Time that tells: critical clock-drawing errors for dementia screening 
Background
Clock-drawing tests are popular components of dementia screens but no single scoring system has been universally accepted. We sought to identify an optimal subset of clock errors for dementia screening and compare them with three other systems representative of the existing wide variations in approach (Shulman, Mendez, Wolf-Klein), as well as with the CDT system used in the Mini-Cog, which combines clock drawing with delayed recall.
Methods
The clock drawings of an ethnolinguistically and educationally diverse sample (N = 536) were analyzed for the association of 24 different errors with the presence and severity of dementia defined by independent research criteria. The final sample included 364 subjects with ≥5 years of education, as preliminary examination suggested different error patterns in subjects with 0–4 years of education and inadequate numbers of normal controls for reliable analysis.
Results
Eleven of 24 errors were significantly associated with dementia in subjects with ≥5 years of education, and six were combined to identify dementia with 88% specificity and 71% sensitivity: inaccurate time setting, no hands, missing numbers, number substitutions or repetitions, or refusal to attempt clock drawing. Time setting was the most prevalent error at all dementia stages, refusal occurred only in moderate and severe dementia; and ethnicity and language of administration had no effect. All critical errors increased in frequency with dementia stage. This simplified scoring system had much better specificity than two other systems (88% vs 39% for Mendez’s system –63% for Shulman’s) and much better sensitivity than Wolf-Klein’s (71% vs 51%). Stepwise logistic regression found the simplified system to be more strongly predictive of dementia than the three other CDT systems of dementia. Substituting the new CDT algorithm for that used in the original CDT Mini-Cog improved the Mini-Cog’s specificity from 89 to 93% with minimal change in sensitivity.
Conclusions
Only six errors need be assessed to capture most of the power of clock drawing to discriminate between people with dementia and normal subjects, and improves specificity over older systems in subjects with ≥5 years of education. These errors require minimal conceptual classification and are easily detected and scored by non-specialists.
doi:10.1017/S1041610207006035
PMCID: PMC2704110  PMID: 17908348
ethnicity; language; neuropsychology; dementia; geriatrics; neurodegenerative disease; Mini-Cog

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