Statistics in Medicine

The extent of heterogeneity in a meta‐analysis partly determines the difficulty in drawing overall conclusions. This extent may be measured by estimating a between‐study variance, but interpretation is then specific to a particular treatment effect metric. A test for the existence of heterogeneity exists, but depends on the number of studies in the meta‐analysis. We develop measures of the impact of heterogeneity on a meta‐analysis, from mathematical criteria, that are independent of the number of studies and the treatment effect metric. We derive and propose three suitable statistics: H is the square root of the χ² heterogeneity statistic divided by its degrees of freedom; R is the ratio of the standard error of the underlying mean from a random effects meta‐analysis to the standard error of a fixed effect meta‐analytic estimate, and I² is a transformation of ^H that describes the proportion of total variation in study estimates that is due to heterogeneity. We discuss interpretation, interval estimates and other properties of these measures and examine them in five example data sets showing different amounts of heterogeneity. We conclude that H and I², which can usually be calculated for published meta‐analyses, are particularly useful summaries of the impact of heterogeneity. One or both should be presented in published meta‐analyses in preference to the test for heterogeneity. Copyright © 2002 John Wiley & Sons, Ltd.

Nhiều lần ước lượng dữ liệu khuyết bằng phương trình xích là một cách tiếp cận linh hoạt và thiết thực để xử lý dữ liệu bị mất. Chúng tôi mô tả các nguyên tắc của phương pháp này và trình bày cách ước lượng dữ liệu cho các biến số phân loại và định lượng, bao gồm cả các biến số phân phối lệch. Chúng tôi đưa ra hướng dẫn về cách chỉ định mô hình ước lượng và số lần ước lượng cần thiết. Chúng tôi mô tả việc phân tích thực tế các dữ liệu đã được ước lượng nhiều lần, bao gồm cả quá trình xây dựng mô hình và kiểm tra mô hình. Chúng tôi nhấn mạnh những hạn chế của phương pháp và thảo luận các khả năng gặp phải sai lầm. Chúng tôi minh họa các ý tưởng bằng một bộ dữ liệu trong lĩnh vực sức khỏe tâm thần, kèm theo các đoạn mã Stata. Bản quyền © 2010 John Wiley & Sons, Ltd.

Identification of key factors associated with the risk of developing cardiovascular disease and quantification of this risk using multivariable prediction algorithms are among the major advances made in preventive cardiology and cardiovascular epidemiology in the 20th century. The ongoing discovery of new risk markers by scientists presents opportunities and challenges for statisticians and clinicians to evaluate these biomarkers and to develop new risk formulations that incorporate them. One of the key questions is how best to assess and quantify the improvement in risk prediction offered by these new models. Demonstration of a statistically significant association of a new biomarker with cardiovascular risk is not enough. Some researchers have advanced that the improvement in the area under the receiver‐operating‐characteristic curve (AUC) should be the main criterion, whereas others argue that better measures of performance of prediction models are needed. In this paper, we address this question by introducing two new measures, one based on integrated sensitivity and specificity and the other on reclassification tables. These new measures offer incremental information over the AUC. We discuss the properties of these new measures and contrast them with the AUC. We also develop simple asymptotic tests of significance. We illustrate the use of these measures with an example from the Framingham Heart Study. We propose that scientists consider these types of measures in addition to the AUC when assessing the performance of newer biomarkers. Copyright © 2007 John Wiley & Sons, Ltd.

The propensity score is a subject's probability of treatment, conditional on observed baseline covariates. Conditional on the true propensity score, treated and untreated subjects have similar distributions of observed baseline covariates. Propensity‐score matching is a popular method of using the propensity score in the medical literature. Using this approach, matched sets of treated and untreated subjects with similar values of the propensity score are formed. Inferences about treatment effect made using propensity‐score matching are valid only if, in the matched sample, treated and untreated subjects have similar distributions of measured baseline covariates. In this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified: comparing means and prevalences of baseline characteristics using standardized differences; ratios comparing the variance of continuous covariates between treated and untreated subjects; comparison of higher order moments and interactions; five‐number summaries; and graphical methods such as quantile–quantile plots, side‐by‐side boxplots, and non‐parametric density plots for comparing the distribution of baseline covariates between treatment groups. We describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero, thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified. We highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity‐score model. In particular, methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative. Copyright © 2009 John Wiley & Sons, Ltd.

Các nghiên cứu dịch tễ học quan sát thường gặp nhiều xung đột tiềm ẩn, từ nhiễu đồng biến và do mối nhân quả ngược, điều này hạn chế khả năng xác định mạnh mẽ mối quan hệ nhân quả của chúng. Đã có nhiều tình huống nổi bật trong đó các thử nghiệm kiểm soát ngẫu nhiên của chính xác các can thiệp đã được khảo sát trong các nghiên cứu quan sát đã cho ra kết quả khác biệt rõ rệt. Trong các lĩnh vực khoa học quan sát khác, việc sử dụng các phương pháp biến công cụ (IV - Instrumental Variable) là một phương án tiếp cận để củng cố các suy luận nhân quả trong các tình huống không thực nghiệm. Sử dụng các biến đổi gen mầm uỷ để làm các công cụ cho các tiếp xúc có thể điều chỉnh môi trường là một dạng phân tích IV có thể thực hiện trong các nghiên cứu dịch tễ học quan sát. Phương pháp này được gọi là 'hoán vị Mendel', và có thể được coi như tương tự với các thử nghiệm kiểm soát ngẫu nhiên. Bài viết này giới thiệu phương pháp hoán vị Mendel, làm nổi bật sự tương đồng với các phương pháp IV, cung cấp ví dụ về việc thực hiện phương pháp này và thảo luận các hạn chế của phương pháp cũng như một số phương pháp để giải quyết những vấn đề này. Bản quyền © 2007 John Wiley & Sons, Ltd.

Reference centile curves show the distribution of a measurement as it changes according to some covariate, often age. The LMS method summarizes the changing distribution by three curves representing the median, coefficient of variation and skewness, the latter expressed as a Box‐Cox power. Using penalized likelihood the three curves can be fitted as cubic splines by non‐linear regression, and the extent of smoothing required can be expressed in terms of smoothing parameters or equivalent degrees of freedom. The method is illustrated with data on triceps skinfold in Gambian girls and women, and body weight in U.S.A. girls.

Interpretation of regression coefficients is sensitive to the scale of the inputs. One method often used to place input variables on a common scale is to divide each numeric variable by its standard deviation. Here we propose dividing each numeric variable by two times its standard deviation, so that the generic comparison is with inputs equal to the mean ±1 standard deviation. The resulting coefficients are then directly comparable for untransformed binary predictors. We have implemented the procedure as a function in R. We illustrate the method with two simple analyses that are typical of applied modeling: a linear regression of data from the National Election Study and a multilevel logistic regression of data on the prevalence of rodents in New York City apartments. We recommend our rescaling as a default option—an improvement upon the usual approach of including variables in whatever way they are coded in the data file—so that the magnitudes of coefficients can be directly compared as a matter of routine statistical practice. Copyright © 2007 John Wiley & Sons, Ltd.

Appropriate quantification of added usefulness offered by new markers included in risk prediction algorithms is a problem of active research and debate. Standard methods, including statistical significance and c statistic are useful but not sufficient. Net reclassification improvement (NRI) offers a simple intuitive way of quantifying improvement offered by new markers and has been gaining popularity among researchers. However, several aspects of the NRI have not been studied in sufficient detail.

In this paper we propose a prospective formulation for the NRI which offers immediate application to survival and competing risk data as well as allows for easy weighting with observed or perceived costs. We address the issue of the number and choice of categories and their impact on NRI. We contrast category‐based NRI with one which is category‐free and conclude that NRIs cannot be compared across studies unless they are defined in the same manner. We discuss the impact of differing event rates when models are applied to different samples or definitions of events and durations of follow‐up vary between studies. We also show how NRI can be applied to case–control data. The concepts presented in the paper are illustrated in a Framingham Heart Study example.

In conclusion, NRI can be readily calculated for survival, competing risk, and case–control data, is more objective and comparable across studies using the category‐free version, and can include relative costs for classifications. We recommend that researchers clearly define and justify the choices they make when choosing NRI for their application. Copyright © 2010 John Wiley & Sons, Ltd.

Publication bias and related bias in meta‐analysis is often examined by visually checking for asymmetry in funnel plots of treatment effect against its standard error. Formal statistical tests of funnel plot asymmetry have been proposed, but when applied to binary outcome data these can give false‐positive rates that are higher than the nominal level in some situations (large treatment effects, or few events per trial, or all trials of similar sizes). We develop a modified linear regression test for funnel plot asymmetry based on the efficient score and its variance, Fisher's information. The performance of this test is compared to the other proposed tests in simulation analyses based on the characteristics of published controlled trials. When there is little or no between‐trial heterogeneity, this modified test has a false‐positive rate close to the nominal level while maintaining similar power to the original linear regression test (‘Egger’ test). When the degree of between‐trial heterogeneity is large, none of the tests that have been proposed has uniformly good properties. Copyright © 2005 John Wiley & Sons, Ltd.