Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution.

Abstract:

:The Box-Cox power exponential (BCPE) distribution, developed in this paper, provides a model for a dependent variable Y exhibiting both skewness and kurtosis (leptokurtosis or platykurtosis). The distribution is defined by a power transformation Y(nu) having a shifted and scaled (truncated) standard power exponential distribution with parameter tau. The distribution has four parameters and is denoted BCPE (mu,sigma,nu,tau). The parameters, mu, sigma, nu and tau, may be interpreted as relating to location (median), scale (approximate coefficient of variation), skewness (transformation to symmetry) and kurtosis (power exponential parameter), respectively. Smooth centile curves are obtained by modelling each of the four parameters of the distribution as a smooth non-parametric function of an explanatory variable. A Fisher scoring algorithm is used to fit the non-parametric model by maximizing a penalized likelihood. The first and expected second and cross derivatives of the likelihood, with respect to mu, sigma, nu and tau, required for the algorithm, are provided. The centiles of the BCPE distribution are easy to calculate, so it is highly suited to centile estimation. This application of the BCPE distribution to smooth centile estimation provides a generalization of the LMS method of the centile estimation to data exhibiting kurtosis (as well as skewness) different from that of a normal distribution and is named here the LMSP method of centile estimation. The LMSP method of centile estimation is applied to modelling the body mass index of Dutch males against age.

journal_name

Stat Med

journal_title

Statistics in medicine

authors

Rigby RA,Stasinopoulos DM

doi

10.1002/sim.1861

subject

Has Abstract

pub_date

2004-10-15 00:00:00

pages

3053-76

issue

19

eissn

0277-6715

issn

1097-0258

journal_volume

23

pub_type

杂志文章
  • Location-scale cumulative odds models for ordinal data: a generalized non-linear model approach.

    abstract::Proportional odds regression models for multinomial probabilities based on ordered categories have been generalized in two somewhat different directions. Models having scale as well as location parameters for adjustment of boundaries (on an unobservable, underlying continuum) between categories have been employed in t...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.4780141105

    authors: Cox C

    更新日期:1995-06-15 00:00:00

  • A simulation-free approach to assessing the performance of the continual reassessment method.

    abstract::The continual reassessment method (CRM) is an adaptive design for Phase I trials whose operating characteristics, including appropriate sample size, probability of correctly identifying the maximum tolerated dose, and the expected proportion of participants assigned to each dose, can only be determined via simulation....

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.8746

    authors: Braun TM

    更新日期:2020-09-16 00:00:00

  • Power and sample size calculation for log-rank test with a time lag in treatment effect.

    abstract::The log-rank test is the most powerful non-parametric test for detecting a proportional hazards alternative and thus is the most commonly used testing procedure for comparing time-to-event distributions between different treatments in clinical trials. When the log-rank test is used for the primary data analysis, the s...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.3501

    authors: Zhang D,Quan H

    更新日期:2009-02-28 00:00:00

  • Adjusting for confounding by neighborhood using generalized linear mixed models and complex survey data.

    abstract::When investigating health disparities, it can be of interest to explore whether adjustment for socioeconomic factors at the neighborhood level can account for, or even reverse, an unadjusted difference. Recently, we proposed new methods to adjust the effect of an individual-level covariate for confounding by unmeasure...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.5624

    authors: Brumback BA,Zheng HW,Dailey AB

    更新日期:2013-04-15 00:00:00

  • Causal inference in survival analysis using pseudo-observations.

    abstract::Causal inference for non-censored response variables, such as binary or quantitative outcomes, is often based on either (1) direct standardization ('G-formula') or (2) inverse probability of treatment assignment weights ('propensity score'). To do causal inference in survival analysis, one needs to address right-censo...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.7297

    authors: Andersen PK,Syriopoulou E,Parner ET

    更新日期:2017-07-30 00:00:00

  • Group sequential testing of the predictive accuracy of a continuous biomarker with unknown prevalence.

    abstract::Group sequential testing procedures have been proposed as an approach to conserving resources in biomarker validation studies. Previously, we derived the asymptotic properties of the sequential empirical positive predictive value (PPV) and negative predictive value (NPV) curves, which summarize the predictive accuracy...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.6790

    authors: Koopmeiners JS,Feng Z

    更新日期:2016-04-15 00:00:00

  • Regression models for mixed Poisson and continuous longitudinal data.

    abstract::In this article we develop flexible regression models in two respects to evaluate the influence of the covariate variables on the mixed Poisson and continuous responses and to evaluate how the correlation between Poisson response and continuous response changes over time. A scenario for dealing with regression models ...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.2776

    authors: Yang Y,Kang J,Mao K,Zhang J

    更新日期:2007-09-10 00:00:00

  • Multivariate test power approximations for balanced linear mixed models in studies with missing data.

    abstract::Multilevel and longitudinal studies are frequently subject to missing data. For example, biomarker studies for oral cancer may involve multiple assays for each participant. Assays may fail, resulting in missing data values that can be assumed to be missing completely at random. Catellier and Muller proposed a data ana...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.6811

    authors: Ringham BM,Kreidler SM,Muller KE,Glueck DH

    更新日期:2016-07-30 00:00:00

  • A cluster model for space-time disease counts.

    abstract::Modelling disease clustering over space and time can be helpful in providing indications of possible exposures and planning corresponding public health practices. Though a considerable number of studies focus on modelling spatio-temporal patterns of disease, most of them do not directly model a spatio-temporal cluster...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.2424

    authors: Yan P,Clayton MK

    更新日期:2006-03-15 00:00:00

  • On estimation of the variance in Cochran-Armitage trend tests for genetic association using case-control studies.

    abstract::The Cochran-Armitage trend test has been used in case-control studies for testing genetic association. As the variance of the test statistic is a function of unknown parameters, e.g. disease prevalence and allele frequency, it must be estimated. The usual estimator combining data for cases and controls assumes they fo...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.2250

    authors: Zheng G,Gastwirth JL

    更新日期:2006-09-30 00:00:00

  • The power of focused tests to detect disease clustering.

    abstract::Statistical tests have been proposed for determining whether incident cases of adverse health effects are 'clustered' together. Several procedures, termed 'focused', specifically analyse disease surveillance data around pre-specified putative sources of environmental hazard. Little has been done to compare the perform...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.4780142103

    authors: Waller LA,Lawson AB

    更新日期:1995-11-15 00:00:00

  • Four-fold table cell frequencies imputation in meta analysis.

    abstract::Meta analysis is a collection of quantitative methods devoted to combine summary information from related but independent studies. Because research reports usually present only data reductions and summary statistics rather than detailed data, the reviewer must often resort to rather crude methods for constructing summ...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.2287

    authors: Di Pietrantonj C

    更新日期:2006-07-15 00:00:00

  • A sequential classification rule based on multiple quantitative tests in the absence of a gold standard.

    abstract::In many medical applications, combining information from multiple biomarkers could yield a better diagnosis than any single one on its own. When there is a lack of a gold standard, an algorithm of classifying subjects into the case and non-case status is necessary for combining multiple markers. The aim of this paper ...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.6780

    authors: Zhang J,Zhang Y,Chaloner K,Stapleton JT

    更新日期:2016-04-15 00:00:00

  • The k-in-a-row up-and-down design, revisited.

    abstract::The percentile-finding experimental design known variously as 'forced-choice fixed-staircase', 'geometric up-and-down' or 'k-in-a-row' (KR) was introduced by Wetherill four decades ago. To date, KR has been by far the most widely used up-and-down (U&D) design for estimating non-median percentiles; it is implemented mo...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.3590

    authors: Oron AP,Hoff PD

    更新日期:2009-06-15 00:00:00

  • Curtailed two-stage designs in Phase II clinical trials.

    abstract::When the accrual rate is low and the treatment period is long, a long observational period is required before information concerning the primary end point, such as binary response, becomes available in the study. Simon's two-stage designs are often employed in Phase II clinical trials to avoid giving patient an ineffe...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.3424

    authors: Chi Y,Chen CM

    更新日期:2008-12-20 00:00:00

  • The Wilcoxon-Mann-Whitney test under scrutiny.

    abstract::The Wilcoxon-Mann-Whitney (WMW) test is often used to compare the means or medians of two independent, possibly nonnormal distributions. For this problem, the true significance level of the large sample approximate version of the WMW test is known to be sensitive to differences in the shapes of the distributions. Base...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.3561

    authors: Fagerland MW,Sandvik L

    更新日期:2009-05-01 00:00:00

  • Some statistical issues in project prioritization in the pharmaceutical industry.

    abstract::Various aspects of portfolio management and project prioritization within the pharmaceutical industry are examined. It is shown that the cost and probability architecture of a project is a crucial aspect of its value. An appropriate simple tool for ranking projects is the Pearson index. Various difficulties are consid...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/(SICI)1097-0258(19961230)15:24<2689::AID-S

    authors: Senn S

    更新日期:1996-12-30 00:00:00

  • Combining biomarker trajectories to improve diagnostic accuracy in prospective cohort studies with verification bias.

    abstract::In this paper, we develop methods to combine multiple biomarker trajectories into a composite diagnostic marker using functional data analysis (FDA) to achieve better diagnostic accuracy in monitoring disease recurrence in the setting of a prospective cohort study. In such studies, the disease status is usually verifi...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.8079

    authors: Li H,Gatsonis C

    更新日期:2019-05-20 00:00:00

  • Statistical interim monitoring of the Cardiac Arrhythmia Suppression Trial.

    abstract::The Cardiac Arrythmia Suppression Trial was stopped much earlier than planned. Statistical considerations played a very important role in the decision. Flexible group sequential testing was developed for the trial by implementing a Lan and DeMets procedure with use of the permutation test. We compute P-values from the...

    journal_title:Statistics in medicine

    pub_type: 临床试验,杂志文章,多中心研究,随机对照试验

    doi:10.1002/sim.4780090915

    authors: Pawitan Y,Hallstrom A

    更新日期:1990-09-01 00:00:00

  • Bayesian methods for meta-analysis of causal relationships estimated using genetic instrumental variables.

    abstract::Genetic markers can be used as instrumental variables, in an analogous way to randomization in a clinical trial, to estimate the causal relationship between a phenotype and an outcome variable. Our purpose is to extend the existing methods for such Mendelian randomization studies to the context of multiple genetic mar...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.3843

    authors: Burgess S,Thompson SG,CRP CHD Genetics Collaboration.,Burgess S,Thompson SG,Andrews G,Samani NJ,Hall A,Whincup P,Morris R,Lawlor DA,Davey Smith G,Timpson N,Ebrahim S,Ben-Shlomo Y,Davey Smith G,Timpson N,Brown M,Ricket

    更新日期:2010-05-30 00:00:00

  • Exact logistic models for nested binary data.

    abstract::The use of logistic models for independent binary data has relied first on asymptotic theory and later on exact distributions for small samples. However, the use of logistic models for dependent analysis based on exact analysis is not as common. Moreover, attention is usually given to one-stage clustering. In this pap...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.4157

    authors: Troxler S,Lalonde T,Wilson JR

    更新日期:2011-04-15 00:00:00

  • Exact equivalence test for risk ratio and its sample size determination under inverse sampling.

    abstract::When data are dichotomous, this paper notes the utility of inverse sampling in establishing equivalence with respect to the risk ratio. This paper develops an exact equivalence test that accounts for the risk ratio under inverse sampling and further discusses the relationship between the exact equivalence test and the...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/(sici)1097-0258(19970815)16:15<1777::aid-s

    authors: Lui KJ

    更新日期:1997-08-15 00:00:00

  • Bayesian predictive approach for inference about proportions.

    abstract::This paper investigates the Bayesian procedures for comparing proportions. These procedures are especially suitable for accepting (or rejecting) the equivalence of two population proportions. Furthermore the Bayesian predictive probabilities provide a natural and flexible tool in monitoring trials, especially for choo...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.4780140924

    authors: Lecoutre B,Derzko G,Grouin JM

    更新日期:1995-05-15 00:00:00

  • Coping with time and space in modelling malaria incidence: a comparison of survival and count regression models.

    abstract::To study the effect of a mega hydropower dam in southwest Ethiopia on malaria incidence, we have set up a longitudinal study. To gain insight in temporal and spatial aspects, that is, in time (period  =  year-season combination) and location (village), we need models that account for these effects. The frailty model w...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.5752

    authors: Getachew Y,Janssen P,Yewhalaw D,Speybroeck N,Duchateau L

    更新日期:2013-08-15 00:00:00

  • Comparisons of the performance of different statistical tests for time-to-event analysis with confounding factors: practical illustrations in kidney transplantation.

    abstract::Confounding factors are commonly encountered in observational studies. Several confounder-adjusted tests to compare survival between differently exposed subjects were proposed. However, only few studies have compared their performances regarding type I error rates, and no study exists evaluating their type II error ra...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.6777

    authors: Le Borgne F,Giraudeau B,Querard AH,Giral M,Foucher Y

    更新日期:2016-03-30 00:00:00

  • A Bayesian multivariate joint frailty model for disease recurrences and survival.

    abstract::Motivated by a study for soft tissue sarcoma, this article considers the analysis of diseases recurrence and survival. A multivariate frailty hazard model is established for joint modeling of three correlated time-to-event outcomes: local disease recurrence, distant disease recurrence (metastasis), and death. The goal...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.7030

    authors: Wen S,Huang X,Frankowski RF,Cormier JN,Pisters P

    更新日期:2016-11-20 00:00:00

  • An index of disease activity in rheumatoid arthritis.

    abstract::This paper describes the Stoke Index which has been designed to give a global measure of disease activity in rheumatoid arthritis. The index is based on two objective laboratory measurements, one subjective and two semi-objective clinical measurements, chosen from 13 measurements using clinical judgement. Variable sel...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.4780121206

    authors: Jones PW,Ziade MF,Davis MJ,Dawes PT

    更新日期:1993-06-30 00:00:00

  • Multivariate meta-analysis: a robust approach based on the theory of U-statistic.

    abstract::Meta-analysis is the methodology for combining findings from similar research studies asking the same question. When the question of interest involves multiple outcomes, multivariate meta-analysis is used to synthesize the outcomes simultaneously taking into account the correlation between the outcomes. Likelihood-bas...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/sim.4327

    authors: Ma Y,Mazumdar M

    更新日期:2011-10-30 00:00:00

  • Modelling age-specific risk: application to dementia.

    abstract::We give up-to-date methods for estimating the age-specific incidence of a disease and for estimating the effect of risk factors. We recommend taking age as the basic time scale of the analysis; then, the hazard function can be interpreted as the age-specific incidence of the disease. This choice raises a delayed entry...

    journal_title:Statistics in medicine

    pub_type: 杂志文章

    doi:10.1002/(sici)1097-0258(19980915)17:17<1973::aid-s

    authors: Commenges D,Letenneur L,Joly P,Alioum A,Dartigues JF

    更新日期:1998-09-15 00:00:00

  • Accounting for competing risks in randomized controlled trials: a review and recommendations for improvement.

    abstract::In studies with survival or time-to-event outcomes, a competing risk is an event whose occurrence precludes the occurrence of the primary event of interest. Specialized statistical methods must be used to analyze survival data in the presence of competing risks. We conducted a review of randomized controlled trials wi...

    journal_title:Statistics in medicine

    pub_type: 杂志文章,评审

    doi:10.1002/sim.7215

    authors: Austin PC,Fine JP

    更新日期:2017-04-15 00:00:00