The method of generalized estimating equations (GEE) is often used to analyze longitudinal and other correlated response data, particularly if responses are binary. However, few descriptions of the method are accessible to epidemiologists. In this paper, the authors use small worked examples and one real data set, involving both binary and quantitative response data, to help end-users appreciate the essence of the method. The examples are simple enough to see the behind-the-scenes calculations and the essential role of weighted observations, and they allow nonstatisticians to imagine the calculations involved when the GEE method is applied to more complex multivariate data.

BACKGROUND As the definitional formula for population attributable fraction is not usually directly usable in applications, separate estimation formulas are required. However, most epidemiology textbooks limit their coverage to Levin's formula, based on the (dichotomous) distribution of the exposure of interest in the population. Few present or explain Miettinen's formula, based on the distribution of the exposure in the cases; and even fewer present the corresponding formulas for situations with more than two levels of exposure. Thus, many health researchers and public health practitioners are unaware of, or are not confident in their use of, these formulas, particularly when they involve several exposure levels, or confounding factors. METHODS/RESULTS A heuristic approach, coupled with pictorial representations, is offered to help understand and interconnect the structures behind the Levin and Miettinen formulas. The pictorial representation shows how to deal correctly with several exposure levels, and why a commonly used approach is incorrect. Correct and incorrect approaches are also presented for situations where estimates must be aggregated over strata of a confounding factor.

In an article published in Annals of Internal Medicine in 2001, Redelmeier and Singh reported that Academy Award–winning actors and actresses lived almost 4 years longer than their less successful peers. However, the statistical method used to derive this statistically significant difference gave winners an unfair advantage because it credited an Oscar winner's years of life before winning toward survival subsequent to winning. When the authors of the current article reanalyzed the data using methods that avoided this “immortal time” bias, the survival advantage was closer to 1 year and was not statistically significant. The type of bias in Redelmeier and Singh's study is not limited to longevity comparisons of persons who reach different ranks within their profession; it can, and often does, occur in nonexperimental studies of life- or time-extending benefits of medical interventions. The current authors suggest ways in which researchers and readers may avoid and recognize this bias.

Whereas Farr adopted a tongue-in -cheek style, Bradford Hill3 spelled out the reason for the longevity difference: ‘Few men become bishops before they have pass

Analyzing the relationship between the baseline value and subsequent change of a continuous variable is a frequent matter of inquiry in cohort studies. These analyses are surprisingly complex, particularly if only two waves of data are available. It is unclear for non-biostatisticians where the complexity of this analysis lies and which statistical method is adequate. With the help of simulated longitudinal data of body mass index in children, we review statistical methods for the analysis of the association between the baseline value and subsequent change, assuming linear growth with time. Key issues in such analyses are mathematical coupling, measurement error, variability of change between individuals, and regression to the mean. Ideally, it is better to rely on multiple repeated measurements at different times and a linear random effects model is a standard approach if more than two waves of data are available. If only two waves of data are available, our simulations show that Blomqvist’s method – which consists in adjusting for measurement error variance the estimated regression coefficient of observed change on baseline value – provides accurate estimates. The adequacy of the methods to assess the relationship between the baseline value and subsequent change depends on the number of data waves, the availability of information on measurement error, and the variability of change between individuals.