Abstract:
:One is often interested in the ratio of two variables, for example in genetics, assessing drug effectiveness, and in health economics. In this paper, we derive an explicit geometric solution to the general problem of identifying the two tangents from an arbitrary external point to an ellipse. This solution permits numerical integration of a bivariate normal distribution over a wedge-shaped region bounded by the tangents, which yields an evaluation of the tangent slopes as confidence limits on the ratio of the component variables. After suitable adjustment of the confidence coverage of the ellipse, these confidence limits are shown to be equivalent to those from Fieller's method. However, the geometric approach allows additional interpretation of the data through identification of the points of tangency, the ellipse itself, and expressions for the coverage probability of the confidence interval. Numerical evaluations using the theoretical expressions for the geometric confidence intervals (but ignoring sample variation in the underlying parameters) suggested that they perform well overall and are slightly conservative. Simulations that do take account of sample variation in the underlying parameters again suggested that the intervals perform well overall, although here they are slightly anti-conservative. Coverage probabilities for the confidence intervals were only weakly dependent on the distance and correlation of the ellipse, but there were asymmetries in the failure rates of the upper and lower confidence limits in some configurations. The probability of no real solution existing was also evaluated. These ideas are illustrated by a practical example.
journal_name
Stat Medjournal_title
Statistics in medicineauthors
Walter SD,Gafni A,Birch Sdoi
10.1002/sim.3398subject
Has Abstractpub_date
2008-12-10 00:00:00pages
5956-74issue
28eissn
0277-6715issn
1097-0258journal_volume
27pub_type
杂志文章abstract::For patients who were previously treated for prostate cancer, salvage hormone therapy is frequently given when the longitudinal marker prostate-specific antigen begins to rise during follow-up. Because the treatment is given by indication, estimating the effect of the hormone therapy is challenging. In a previous pape...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.5890
更新日期:2014-01-30 00:00:00
abstract::A good measure of field vaccine efficacy should evaluate the direct protective effect of vaccination on the person who receives the vaccine. The conventional estimator for vaccine efficacy depends on population level factors that are either unrelated or indirectly related to the direct biological action of the vaccine...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.4780120309
更新日期:1993-02-01 00:00:00
abstract::Genetic networks for gene expression data are often built by graphical models, which in turn are built from pair-wise correlations of gene expression levels. A key feature of building graphical models is the evaluation of conditional independence of two traits, given other traits. When conditional independence can be ...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.3274
更新日期:2008-08-30 00:00:00
abstract::The principles and historical development of clinical trials are outlined briefly. Some issues that extend the basic philosophy first put forward by Sir Austin Bradford Hill 40 years ago and that will need consideration in the future application of clinical trials are discussed. ...
journal_title:Statistics in medicine
pub_type: 传,历史文章,杂志文章
doi:10.1002/sim.4780010414
更新日期:1982-10-01 00:00:00
abstract::The analysis of multivariate time-to-event (TTE) data can become complicated due to the presence of clustering, leading to dependence between multiple event times. For a long time, (conditional) frailty models and (marginal) copula models have been used to analyze clustered TTE data. In this article, we propose a gene...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.8506
更新日期:2020-05-30 00:00:00
abstract::We consider the problem of comparing cumulative incidence functions of non-mortality events in the presence of informative coarsening and the competing risk of death. We extend frequentist-based hypothesis tests previously developed for non-informative coarsening and propose a novel Bayesian method based on comparing ...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.3397
更新日期:2008-12-10 00:00:00
abstract::This paper considers the effect of non-differential outcome misclassification on the population attributable fraction and the population prevented fraction. I examine the bias in the attributable and the prevented fraction derived from a risk ratio estimate as a function of the sensitivity and specificity of the outco...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.4780100308
更新日期:1991-03-01 00:00:00
abstract::The change in c-statistic is frequently used to summarize the change in predictive accuracy when a novel risk factor is added to an existing logistic regression model. We explored the relationship between the absolute change in the c-statistic, Brier score, generalized R(2) , and the discrimination slope when a risk f...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.5598
更新日期:2013-02-20 00:00:00
abstract::This paper introduces a new spatial scan statistic designed to adjust cluster detection for longitudinal confounding factors indexed in space. The functional-model-adjusted statistic was developed using generalized functional linear models in which longitudinal confounding factors were considered to be functional cova...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.8459
更新日期:2020-04-15 00:00:00
abstract::The publication of Fisher's correspondence on statistics has shed new light on his views on randomization. Quotations from this correspondence and from other works of Fisher are used to illustrate the role of randomization in clinical trials. It is concluded that Fisher's views not only are coherent but, despite havin...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.4780130305
更新日期:1994-02-15 00:00:00
abstract::The identification of new adverse drug reactions is often tricky. For a given case, the relationship between drug exposure and symptom occurrence is usually questionable. It could be investigated statistically from a series of drug-event association cases with an independence test between the two variables. Analysing ...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.4780100621
更新日期:1991-06-01 00:00:00
abstract::Our objective is to develop a model to estimate the relative risk of disease in each area, Ai, i=1, ... , n, of a region and to identify areas of unusually high or low risk. We use a product partition model (PPM) in which we assume that the true relative risks can be partitioned into a number of components or sets of ...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.3253
更新日期:2008-08-30 00:00:00
abstract::It is not uncommon for a continuous outcome variable Y to be dichotomized and analysed using logistic regression. Moser and Coombs (Statist. Med. 2004; 23:1843-1860) provide a method for converting the output from a standard linear regression analysis using the original continuous outcome Y to give much more efficient...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.3474
更新日期:2009-01-30 00:00:00
abstract::We consider the estimation of parameters in a particular segmented generalized linear model with additive measurement error in predictors, with a focus on linear and logistic regression. In epidemiologic studies segmented regression models often occur as threshold models, where it is assumed that the exposure has no i...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/(sici)1097-0258(19970130)16:2<169::aid-sim
更新日期:1997-01-15 00:00:00
abstract::In lifetime data, like cancer studies, there may be long term survivors, which lead to heavy censoring at the end of the follow-up period. Since a standard survival model is not appropriate to handle these data, a cure model is needed. In the literature, covariate hypothesis tests for cure models are limited to parame...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.8530
更新日期:2020-07-30 00:00:00
abstract::In survival analyses, inverse-probability-of-treatment (IPT) and inverse-probability-of-censoring (IPC) weighted estimators of parameters in marginal structural Cox models are often used to estimate treatment effects in the presence of time-dependent confounding and censoring. In most applications, a robust variance e...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.7823
更新日期:2018-10-30 00:00:00
abstract::We compared eight nominal 95 per cent confidence intervals for the ratio of two Poisson parameters, both assumed small, on their true coverage (the probability that the interval includes the ratio of Poisson parameters) and median width. The commonly used log-linear interval, justified by asymptotic considerations, pr...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.3234
更新日期:2008-09-10 00:00:00
abstract::In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log-SDF can be represented using a common set of basis functions. The basis shared by the colle...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.7972
更新日期:2018-12-30 00:00:00
abstract::Longitudinal studies are often concerned with estimating the recurrence rate of a non-fatal event. In many cases, only the total number of events occurring during successive time intervals is known. We compared a mixed Poisson-gamma regression method proposed by Thall and a quasi-likelihood method proposed by Zeger an...
journal_title:Statistics in medicine
pub_type: 临床试验,杂志文章,随机对照试验
doi:10.1002/sim.4780121406
更新日期:1993-07-30 00:00:00
abstract::Paired count data usually arise in medicine when before and after treatment measurements are considered. In the present paper we assume that the correlated paired count data follow a bivariate Poisson distribution in order to derive the distribution of their difference. The derived distribution is shown to be the same...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.2382
更新日期:2006-06-15 00:00:00
abstract::Relative survival is used to estimate patient survival excluding causes of death not related to the disease of interest. Rather than using cause of death information from death certificates, which is often poorly recorded, relative survival compares the observed survival to that expected in a matched group from the ge...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.2399
更新日期:2005-12-30 00:00:00
abstract::We have formulated the problem of determining whether there has been an upturn in HIV-1 seroconversion incidence over the first five years of follow-up in the Multicenter AIDS Cohort Study (MACS) as that of locating the minimum of a quadratic regression or examination of two-knot piecewise spline models. Under a quadr...
journal_title:Statistics in medicine
pub_type: 杂志文章,多中心研究
doi:10.1002/sim.4780120207
更新日期:1993-01-30 00:00:00
abstract::The original article to which this Correction refers was published in Statistics in Medicine 2000 19(14): 1901-1914. ...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/1097-0258(20001115)19:21<3017::aid-sim785>
更新日期:2000-11-15 00:00:00
abstract::When estimating the probability of natural conception from observational data on couples with an unfulfilled child wish, the start of assisted reproductive therapy (ART) is a competing event that cannot be assumed to be independent of natural conception. In clinical practice, interest lies in the probability of natura...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.6280
更新日期:2014-11-20 00:00:00
abstract::We review two recent trends: the emergence of evidence-based medicine and the growing use of Bayesian statistics in medical applications. Evidence-based medicine requires an integrated assessment of the available evidence, and associated uncertainty, but there is also an emphasis on decision-making, for individual pat...
journal_title:Statistics in medicine
pub_type: 杂志文章,评审
doi:10.1002/1097-0258(20001215)19:23<3291::aid-sim627>
更新日期:2000-12-15 00:00:00
abstract::There is an increasing interest in the use of propensity score methods to estimate causal effects in observational studies. However, recent systematic reviews have demonstrated that propensity score methods are inconsistently used and frequently poorly applied in the medical literature. In this study, we compared the ...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.2328
更新日期:2006-06-30 00:00:00
abstract::Subjective judgements of complex variables are commonly recorded as ordered categorical data. The rank-invariant properties of such data are well known, and there are various statistical approaches to the analysis and modelling of ordinal data. This paper focuses on the non-additive property of ordered categorical dat...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/(sici)1097-0258(19981230)17:24<2923::aid-s
更新日期:1998-12-30 00:00:00
abstract::This paper reviews methods for mapping geographical variation in disease incidence and mortality. Recent results in Bayesian hierarchical modelling of relative risk are discussed. Two approaches to relative risk estimation, along with the related computational procedures, are described and compared. The first is an em...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.4780110802
更新日期:1992-06-15 00:00:00
abstract::Assessing the calibration of methods for estimating the probability of the occurrence of a binary outcome is an important aspect of validating the performance of risk-prediction algorithms. Calibration commonly refers to the agreement between predicted and observed probabilities of the outcome. Graphical methods are a...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.8281
更新日期:2019-09-20 00:00:00
abstract::Longitudinal studies with repeated measures are often subject to non-response. Methods currently employed to alleviate the difficulties caused by missing data are typically unsatisfactory, especially when the cause of the missingness is related to the outcomes. We present an approach for incomplete categorical data in...
journal_title:Statistics in medicine
pub_type: 杂志文章
doi:10.1002/sim.982
更新日期:2002-01-30 00:00:00