Using logistic regression in perinatal epidemiology: an introduction for clinical researchers. Part 2: the logistic regression equation

Summary. In Part 1 basic concepts were introduced as a preparation for an introductory explanation of logistic regression. Logistic regression is a statistical modelling technique, designed for the estimation of the simultaneous effects of predictors on the risk of a certain dichotomous outcome variable where each effect is estimated while adjusting for the effect of the other factors considered. The basic concepts - odds, odds ratio, confounding and interaction - were introduced in such a way that they naturally lead to the concept of logistic regression. In Part 2 the concepts are translated into simple equations. By studying these equations the equivalence between such mathematical expressions and the underlying clinical assessment of risk will become clear.     

Using logistic regression in perinatal epidemiology: an introduction for clinical researchers. Part 1: basic concepts

Logistic regression is a statistical modelling technique which may be applied to estimate the simultaneous effect of a set of predictors (e.g. gestational age, birthweight) on the risk of a certain outcome variable (e.g. neonatal death) which can take either one of two possible values (yes/no, alive/dead) or in the situation where one wants to estimate the effect of a particular risk factor (e.g. sex) while adjusting (correcting) for the effect of other risk factors (e.g. gestational age). Since this situation often occurs both in medical or epidemiological research and in daily practice it is important to have a flexible and readily interpretable technique to predict risk of mortality and morbidity. Since the logistic regression technique is a powerful and widely applicable tool which is appearing more and more often in the epidemiological literature, a basic understanding of this technique becomes necessary for the clinical researcher. In this paper we explain logistic regression to medical researchers who do not have any particular statistical background. Part 1 covers the basic concepts. Part 2 will describe the actual representation of the basic concepts in a logistic framework.     

Terms in reproductive and perinatal epidemiology: 2. Perinatal terms

This is the second of a two part glossary of terms used in reproductive and perinatal epidemiology. The purpose is to provide a reference for terms that are widely (if not always consistently) used in this field. While a glossary cannot resolve all these problems, it provides a point of reference for understanding them. Part 1 covered terms relevant mostly to events and conditions before birth. Part 2 emphasises terms used during the time around and after birth.     

Validation data-based adjustments for outcome misclassification in logistic regression: an illustration

Misclassification of binary outcome variables is a known source of potentially serious bias when estimating adjusted odds ratios. Although researchers have described frequentist and Bayesian methods for dealing with the problem, these methods have seldom fully bridged the gap between statistical research and epidemiologic practice. In particular, there have been few real-world applications of readily grasped and computationally accessible methods that make direct use of internal validation data to adjust for differential outcome misclassification in logistic regression. In this paper, we illustrate likelihood-based methods for this purpose that can be implemented using standard statistical software. Using main study and internal validation data from the HIV Epidemiology Research Study, we demonstrate how misclassification rates can depend on the values of subject-specific covariates, and we illustrate the importance of accounting for this dependence. Simulation studies confirm the effectiveness of the maximum likelihood approach. We emphasize clear exposition of the likelihood function itself, to permit the reader to easily assimilate appended computer code that facilitates sensitivity analyses as well as the efficient handling of main/external and main/internal validation-study data. These methods are readily applicable under random cross-sectional sampling, and we discuss the extent to which the main/internal analysis remains appropriate under outcome-dependent (case-control) sampling.     

广义估计方程与多水平logistic回归模型在临床纵向数据分析中的应用及比较

目的探讨广义估计方程和多水平模型的应用与临床纵向研究以解决个体重复观测数据内部的相关性问题。方法根据临床纵向实例数据的特点,拟合因变量为二分类的广义估计方程和多水平模型,并与一般logistic模型比较。结果广义估计方程和多水平模型的分析结果与一般logistic模型不同。由于未能考虑个体内重复观测数据的相关性,一般logistic模型错误显示临床分期与近期疗效相关,而广义估计方程和多水平模型分析结果则显示相关无统计学意义。经分层分析也未发现临床分期与近期疗效的关联。结论广义估计方程和多水平模型都能有效地考虑重复观测数据内部相关性并能处理有缺失值的资料。与多水平模型相比,广义估计方程的参数估计较为稳定,可有效的估计各解释变量的效应。     

The use of classification and regression trees in clinical epidemiology

A critique is presented of the use of tree-based partitioning algorithms to formulate classification rules and identify subgroups from clinical and epidemiological data. It is argued that the methods have a number of limitations, despite their popularity and apparent closeness to clinical reasoning processes. The issue of redundancy in tree-derived decision rules is discussed. Simple rules may be unlikely to be "discovered" by tree growing. Subgroups identified by trees are often hard to interpret or believe and net effects are not assessed. These problems arise fundamentally because trees are hierarchical. Newer refinements of tree technology seem unlikely to be useful, wedded as they are to hierarchical structures.     

The epidemiology of perinatal mortality in multiple births.

The epidemiology of perinatal mortality in multiple pregnancies was investigated from data on 16,831 multiple births from New York City''s computerized vital records for 1978-1984. Twins had a sixfold higher rate of neonatal death and a threefold higher rate of fetal death during labor than had singleton infants. Much of this excess mortality can be explained by the lower birthweight distribution in twins: between 1,001 and 2,500 grams twins had birthweight-specific death rates equivalent to or substantially less than singletons. However, in infants of normal birthweights, twins had more than three times the mortality risk of singletons. For twins in vertex presentation between 1,001 and 3,000 grams, cesarean section did not appreciably reduce neonatal mortality risk. For twins in vertex presentation who weighted more than 3,000 grams the neonatal mortality rate was more than four times higher in vaginal deliveries than in cesarean sections (exact p = 0.034). Efforts to prevent intrapartum and neonatal mortality in multiple births should aim at reducing the incidence of low birthweight twins. More research is needed on the etiology of perinatal problems in normal birthweight twins (greater than or equal to 2,501 grams), especially on the effects of different modes of delivery.     

Using logistic regression to estimate the adjusted attributable risk of low birthweight in an unmatched case-control study.

Other authors have shown how to estimate attributable risk based on stratification. In this paper, we show how to estimate adjusted attributable risks, standard errors, and confidence intervals from an unmatched case-control study that has population-based controls and uses the logistic regression model to estimate relative risk. We apply the method to data from a case-control study of low birthweight. The method is conceptually simple, has no assumptions beyond those of the logistic model, makes use of computer-intensive statistical techniques (the bootstrap), and extends to interactions. A Fortran computer program to carry out the computations is available from the authors upon request.     

Terms in reproductive and perinatal epidemiology: I. Reproductive terms

This is the first of a two part glossary of terms used in reproductive and perinatal epidemiology.     

How to get started with a systematic review in epidemiology: an introductory guide for early career researchers

Background

Systematic review is a powerful research tool which aims to identify and synthesize all evidence relevant to a research question. The approach taken is much like that used in a scientific experiment, with high priority given to the transparency and reproducibility of the methods used and to handling all evidence in a consistent manner.Early career researchers may find themselves in a position where they decide to undertake a systematic review, for example it may form part or all of a PhD thesis. Those with no prior experience of systematic review may need considerable support and direction getting started with such a project. Here we set out in simple terms how to get started with a systematic review.

Discussion

Advice is given on matters such as developing a review protocol, searching using databases and other methods, data extraction, risk of bias assessment and data synthesis including meta-analysis. Signposts to further information and useful resources are also given.

Conclusion

A well-conducted systematic review benefits the scientific field by providing a summary of existing evidence and highlighting unanswered questions. For the individual, undertaking a systematic review is also a great opportunity to improve skills in critical appraisal and in synthesising evidence.     

Marginal structural models for analyzing causal effects of time-dependent treatments: an application in perinatal epidemiology

Marginal structural models (MSMs) are causal models designed to adjust for time-dependent confounding in observational studies of time-varying treatments. MSMs are powerful tools for assessing causality with complicated, longitudinal data sets but have not been widely used by practitioners. The objective of this paper is to illustrate the fitting of an MSM for the causal effect of iron supplement use during pregnancy (time-varying treatment) on odds of anemia at delivery in the presence of time-dependent confounding. Data from pregnant women enrolled in the Iron Supplementation Study (Raleigh, North Carolina, 1997-1999) were used. The authors highlight complexities of MSMs and key issues epidemiologists should recognize before and while undertaking an analysis with these methods and show how such methods can be readily interpreted in existing software packages, including SAS and Stata. The authors emphasize that if a data set with rich information on confounders is available, MSMs can be used straightforwardly to make robust inferences about causal effects of time-dependent treatments/exposures in epidemiologic research.     

Efficient regression calibration for logistic regression in main study/internal validation study designs with an imperfect reference instrument

An extension to the version of the regression calibration estimator proposed by Rosner et al. for logistic and other generalized linear regression models is given for main study/internal validation study designs. This estimator combines the information about the parameter of interest contained in the internal validation study with Rosner et al.'s regression calibration estimate, using a generalized inverse-variance weighted average. It is shown that the validation study selection model can be ignored as long as this model is jointly independent of the outcome and the incompletely observed covariates, conditional, at most, upon the surrogates and other completely observed covariates. In an extensive simulation study designed to follow a complex, multivariate setting in nutritional epidemiology, it is shown that with validation study sizes of 340 or more, this estimator appears to be asymptotically optimal in the sense that it is nearly unbiased and nearly as efficient as a properly specified maximum likelihood estimator. A modification to the regression calibration variance estimator which replaces the standard uncorrected logistic regression coefficient variance with the sandwich estimator to account for the possible misspecification of the logistic regression fit to the surrogate covariates in the main study, was also studied in this same simulation experiment. In this study, the alternative variance formula yielded results virtually identical to the original formula. A version of the proposed estimator is also derived for the case where the reference instrument, available only in the validation study, is imperfect but unbiased at the individual level and contains error that is uncorrelated with other covariates and with error in the surrogate instrument. Replicate measures are obtained in a subset of study participants. In this case it is shown that the validation study selection model can be ignored when sampling into the validation study depends, at most, only upon perfectly measured covariates. Two data sets, a study of fever in relation to occupational exposure to antineoplastics among hospital pharmacists and a study of breast cancer incidence in relation to dietary intakes of alcohol and vitamin A, adjusted for total energy intake, from the Nurses' Health Study, were analysed using these new methods. In these data, because the validation studies contained less than 200 observations and the events of interest were relatively rare, as is typical, the potential improvements offered by this new estimator were not apparent.     

大连地区2型糖尿病危险因素的非条件Logistic回归分析

目的：探讨2型糖尿病危险因素，为制定适宜的干预措施提供依据。方法：在大连地区2型糖尿病抽样调查的基础上，采用单因素及多因素非条件Logistic回归分析方法进行分析。结果： 糖尿病家族史（OR＝2．339）、肥胖（体重指数，BMI，其OR＝1．462）、收缩压升高（OR＝1．016）、高血脂（OR＝1．615）、年龄（OR＝1．043）是2型糖尿病的主要危险因素。结论：对高危人群及全人群采取措施适当 控制体重、血压等是预防该病发生的重要手段。     

The importance of assessing the fit of logistic regression models: a case study.

BACKGROUND. The logistic regression model is being used with increasing frequency in all areas of public health research. In the calendar year 1989, over 30% of the articles published in the American Journal of Public Health employed some form of logistic regression modeling. In spite of this increase, there has been no commensurate increase in the use of commonly available methods for assessing model adequacy. METHODS. We review the current status of the use of logistic regression modeling in the American Journal of Public Health. We present a brief overview of currently available and easily used methods for assessing the adequacy of a fitted logistic regression model. RESULTS. An example is used to demonstrate the methods as well as a few of the adverse consequences of failing to assess the fit of the model. One important adverse consequence illustrated in the example is the inclusion of variables in the model as a result of the influence of one subject. CONCLUSIONS. Failure to address model adequacy may lead to misleading or incorrect inferences. Recommendations are made for the use of methods for assessing model adequacy and for future editorial policy in regard to the review of articles using logistic regression.     

Bivariate logistic regression: modelling the association of small for gestational age births in twin gestations.

Clustered binary responses, such as disease status in twins, frequently arise in perinatal health and other epidemiologic applications. The scientific objective involves modelling both the marginal mean responses, such as the probability of disease, and the within-cluster association of the multivariate responses. In this regard, bivariate logistic regression is a useful procedure with advantages that include (i) a single maximization of the joint probability distribution of the bivariate binary responses, and (ii) modelling the odds ratio describing the pairwise association between the two binary responses in relation to several covariates. In addition, since the form of the joint distribution of the bivariate binary responses is assumed known, parameters for the regression model can be estimated by the method of maximum likelihood. Hence, statistical inferences may be based on likelihood ratio tests and profile likelihood confidence intervals. We apply bivariate logistic regression to a perinatal database comprising 924 twin foetuses resulting from 462 pregnancies to model obstetric and clinical risk factors for the association of small for gestational age births in twin gestations.     

The use of cusums and other techniques in modelling continuous covariates in logistic regression.

The assessment of continuous covariates singly as possible predictors in a multivariable logistic regression model is an important first step in the analysis. An approach to plotting which uses a cusum (cumulative sum) of the binary response variable is described. Extreme-deviation statistics associated with the cusum may be used to detect monotonic and non-monotonic trends. Probability plots of the covariate in the two groups defined by the response variable may help to determine the appropriate scale (transformation) of the covariate and to anticipate possible problems with the logistic fit. The ratio of the variances in the response/non-response groups is informative about the need for a quadratic term in the logistic model. Smoothed scatterplots of the response are valuable in displaying the observed and fitted values. The techniques are illustrated with two data sets.