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1.  Diagnostic, prognostic and predictive value of MicroRNA-21 in breast cancer patients, their daughters and healthy individuals 
American Journal of Cancer Research  2015;5(8):2484-2490.
MicroRNA-21 (miR-21) located on 17q23.1 expressed in breast cancer has anti-apoptotic ability and causes tumor cell growth. It is also involved in functions such as signal transduction pathways effecting normal cell growth and differentiation. The primary objective of the study was to identify presence of miR-21 in the serum levels of stage III invasive ductal carcinoma patients and compare its expression with age matched healthy individuals and daughters of index cases. The secondary objective was to evaluate the significance of serum miR-21 gene expression with histologically proven estrogen receptor (ER), progesterone receptor (PR) and human epidermal growth factor receptor 2 (HER2) proteins. A total of 132 subjects were recruited: 50 (cases) of stage III invasive ductal carcinoma patients who had not undergone any chemotherapy or surgery were randomly picked with exclusion of females with other types of breast carcinoma. Age-matched, 50 healthy individuals (control A) were selected by purposive sampling after confirmation of no palpable lump/s in their breasts together with 32 daughters of index cases (control B). Serum tests were run on Real Time quantitative Reverse Transcription PCR, threshold cycle was determined and fold change calculated.Normality of continuous variables was assessed by Shapiro-Wilk’s test, groups compared by student t-test, Mann-Whitney test and Fisher exact test, P-value ≤ 0.05 was considered significant. We observed that miR-21 was significantly higher in cases as compared to control A and B (P = 0.001) however control B showed significant gene expression as compared to control A (P = 0.001). The cases were also divided as positive or negative for ER, PR and HER2. High expression of miR-21 in females with stage III invasive ductal carcinoma had been calculated as compared to its age matched healthy subjects. It was observed that triple negative cases showed a greater expression of gene as compared to other groups (P = 0.001). Expression of miR-21 in daughters of the cases was significantly higher as compared to healthy controls but lesser than females with invasive intraductal carcinoma. This result strengthens the concept of inheritability of disease with prediction of miR-21 as a potentially strong diagnostic and prognostic biomarker of breast cancer.
PMCID: PMC4568784  PMID: 26396924
miR-21; breast cancer; ER; PR and HER-2
2.  Nonparametric tests for right-censored data with biased sampling 
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.
PMCID: PMC2963462  PMID: 21031144
3.  Simultaneous Statistical Inference for Epigenetic Data 
PLoS ONE  2015;10(5):e0125587.
Epigenetic research leads to complex data structures. Since parametric model assumptions for the distribution of epigenetic data are hard to verify we introduce in the present work a nonparametric statistical framework for two-group comparisons. Furthermore, epigenetic analyses are often performed at various genetic loci simultaneously. Hence, in order to be able to draw valid conclusions for specific loci, an appropriate multiple testing correction is necessary. Finally, with technologies available for the simultaneous assessment of many interrelated biological parameters (such as gene arrays), statistical approaches also need to deal with a possibly unknown dependency structure in the data. Our statistical approach to the nonparametric comparison of two samples with independent multivariate observables is based on recently developed multivariate multiple permutation tests. We adapt their theory in order to cope with families of hypotheses regarding relative effects. Our results indicate that the multivariate multiple permutation test keeps the pre-assigned type I error level for the global null hypothesis. In combination with the closure principle, the family-wise error rate for the simultaneous test of the corresponding locus/parameter-specific null hypotheses can be controlled. In applications we demonstrate that group differences in epigenetic data can be detected reliably with our methodology.
PMCID: PMC4428829  PMID: 25965389
4.  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.
PMCID: PMC2605629  PMID: 19122808
Nonconcave penalized likelihood; SCAD; efficient score; local linear regression; partially linear model; varying coefficient models
5.  Differential gene expression in Lin-/VEGF-R2+ bone marrow-derived endothelial progenitor cells isolated from diabetic mice 
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.
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.
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.
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.
PMCID: PMC3926942  PMID: 24521356
Diabetes; Endothelial progenitor cells; Diabetic vasculopathies; Molecular pathology; SDF-1; Lin-/VEGF-R2+ EPCs; Cardiovascular pathology; Retinopathy
6.  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.
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).
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.
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.
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
PMCID: PMC2936357  PMID: 20731878
7.  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.
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.
We recommend that normalized pseudovalues and less data-based model simplification be used with the DBM procedure.
PMCID: PMC1550352  PMID: 16321742
receiver operating characteristic (ROC) curve; DBM; diagnostic radiology; corrected F
8.  Elderly quality of life impacted by traditional chinese medicine techniques 
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.
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.
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.
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).
The experimental group reported the highest QOL for every facet and the total score.
The results suggest that TCM raises the level of QOL.
PMCID: PMC2981102  PMID: 21103400
quality of life; traditional chinese medicine; east-west medicine; WHOQOL-Old; elderly
9.  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.
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).
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
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
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
PMCID: PMC3186813  PMID: 21990966
10.  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.
PMCID: PMC3124223  PMID: 21720450
Covariance Structures; k-Sample Test; Missing Data; Multiple Imputation; Non-parametric Test; Structural Equations; Test of Homogeneity of Covariances
11.  The ChQoL questionnaire: an Italian translation with preliminary psychometric results for female oncological patients 
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.
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.
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.
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.
PMCID: PMC2958157  PMID: 20868514
12.  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
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
14.  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  PMID: 25653794
Drop plate; Lactobacillus casei; Parametric and nonparametric tests; Salmonella Typhimurium; Spread plate
15.  Reproducibility of an aerobic endurance test for nonexpert swimmers 
This study aimed to verify the reproduction of an aerobic test to determine nonexpert swimmers’ resistance.
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.
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.
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
PMCID: PMC3460665  PMID: 23055740
swimming; physical evaluation; resistance training; health
16.  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.
PMCID: PMC3888241  PMID: 23413213
Group Sequential Design; Biomarker Panel; ROC Curve
17.  Normal Distribution of CD8+ T-Cell-Derived ELISPOT Counts within Replicates Justifies the Reliance on Parametric Statistics for Identifying Positive Responses 
Cells  2015;4(1):96-111.
Accurate assessment of positive ELISPOT responses for low frequencies of antigen-specific T-cells is controversial. In particular, it is still unknown whether ELISPOT counts within replicate wells follow a theoretical distribution function, and thus whether high power parametric statistics can be used to discriminate between positive and negative wells. We studied experimental distributions of spot counts for up to 120 replicate wells of IFN-γ production by CD8+ T-cell responding to EBV LMP2A (426 – 434) peptide in human PBMC. The cells were tested in serial dilutions covering a wide range of average spot counts per condition, from just a few to hundreds of spots per well. Statistical analysis of the data using diagnostic Q-Q plots and the Shapiro-Wilk normality test showed that in the entire dynamic range of ELISPOT spot counts within replicate wells followed a normal distribution. This result implies that the Student t-Test and ANOVA are suited to identify positive responses. We also show experimentally that borderline responses can be reliably detected by involving more replicate wells, plating higher numbers of PBMC, addition of IL-7, or a combination of these. Furthermore, we have experimentally verified that the number of replicates needed for detection of weak responses can be calculated using parametric statistics.
PMCID: PMC4381212  PMID: 25738924
ELISPOT; statistics; t-Test; ANOVA; normal distribution; T-cells
18.  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.
PMCID: PMC3267993  PMID: 22189469
Evidential paradigm; Likelihood; Parametric linkage; Complex disease
19.  Paravertebral block is a proper alternative anesthesia for outpatient lithotripsy 
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.
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.
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.
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.
PMCID: PMC4173548  PMID: 25885985
Extracorporeal shock wave lithotripsy; local anesthetic; paravertebral block
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.
PMCID: PMC3381868  PMID: 22745516
Comorbidity; Environmental factor; Family-based association test; Maximum test statistic; Multiple traits; Ordinal traits
21.  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
22.  A Bayesian approach to efficient differential allocation for resampling-based significance testing 
BMC Bioinformatics  2009;10:198.
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.
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.
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 .
PMCID: PMC2718927  PMID: 19558706
23.  Nonparametric tests for differential gene expression and interaction effects in multi-factorial microarray experiments 
BMC Bioinformatics  2005;6:186.
Numerous nonparametric approaches have been proposed in literature to detect differential gene expression in the setting of two user-defined groups. However, there is a lack of nonparametric procedures to analyze microarray data with multiple factors attributing to the gene expression. Furthermore, incorporating interaction effects in the analysis of microarray data has long been of great interest to biological scientists, little of which has been investigated in the nonparametric framework.
In this paper, we propose a set of nonparametric tests to detect treatment effects, clinical covariate effects, and interaction effects for multifactorial microarray data. When the distribution of expression data is skewed or heavy-tailed, the rank tests are substantially more powerful than the competing parametric F tests. On the other hand, in the case of light or medium-tailed distributions, the rank tests appear to be marginally less powerful than the parametric competitors.
The proposed rank tests enable us to detect differential gene expression and establish interaction effects for microarray data with various non-normally distributed expression measurements across genome. In the presence of outliers, they are advantageous alternative approaches to the existing parametric F tests due to the robustness feature.
PMCID: PMC1199581  PMID: 16042764
24.  A simple powerful bivariate test for two sample location problems in experimental and observational studies 
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.
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.
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.
PMCID: PMC2880022  PMID: 20459659
25.  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.
PMCID: PMC4304842  PMID: 25615624

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