Logistic regression in case‐control studies: The effect of using independent as dependent variables

Nagelkerke, Nico; Moses, Stephen; Plummer, Francis A.; Brunham, Robert C.; Fish, David G.

doi:10.1002/sim.4780140806

Cited by 29 publications

(30 citation statements)

References 8 publications

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“…Where neither of the above conditions are satisÿed, Nagelkerke et al [1] advocate ÿtting a standard prospective regression model to Y 2 in terms of x using the Y 1 -control data only. We would expect this to be approximately valid when the proportion of cases in the population is small.…”

Section: Use Only the Controls (Cont)mentioning

confidence: 99%

“…Fitting a standard prospective regression model to Y 2 in terms of x is justiÿed theoretically if Y 1 and Y 2 are conditionally independent given x. If Y 1 and x are conditionally independent given Y 2 , we can still ÿt a logistic regression with only the constant term being a ected by the sampling scheme; see Nagelkerke et al [1]. These two sets of conditions are vaguely interesting but, except where x is discrete with su ciently few categories for the use of saturated models to be feasible, they are of little use for data analysis.…”

Section: Introductionmentioning

confidence: 99%

“…We discuss the methods of analysis that have been proposed or used, both formal and ad hoc, add some new methods, and explore the relative e ciency and robustness properties of the methods as a means of forming practical recommendations. Previous work on this topic includes References [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

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Secondary analysis of case-control data

2006

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We extend the discussion of Lee et al. and others on methods for performing secondary analyses of case-control sampled data and carry out an extensive investigation of efficiency and robustness. We find that, with the exception of the 'analyse-the-controls-only' strategy for populations in which cases are rare, ad hoc methods in common usage often lead to extremely misleading conclusions and that it is not possible to tell in advance when this will happen. Weighted likelihood and semi-parametric maximum likelihood methods are justified theoretically. We find that semi-parametric maximum likelihood can be as much as twice as efficient as the weighted method, but is subject to bias in estimating parameters of interest when the nuisance models this method requires have been mis-specified. The weighted method needs no nuisance models and thus is robust in this regard, but we cannot tell when it is going to be very inefficient without sophisticated modelling as through the SPML method. Practitioners should routinely use both methods and will often have to weigh up the practical consequences of severe inefficiency and lack of robustness in the context of their enquiries.

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Section: Use Only the Controls (Cont)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Secondary analysis of case-control data

2006

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“…In particular, one cannot use an explanatory variable as a dependent variable in an auxiliary analysis without special precautions (see Nagelkerke et al 1995).…”

Section: Problems To Avoidmentioning

confidence: 99%

Logistic Regression in Rare Events Data

King

Zeng²

2001

Polit. anal.

3,138

799

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We study rare events data, binary dependent variables with dozens to thousands of times fewer ones (events, such as wars, vetoes, cases of political activism, or epidemiological infections) than zeros ("nonevents"). In many literatures, these variables have proven difficult to explain and predict, a problem that seems to have at least two sources. First, popular statistical procedures, such as logistic regression, can sharply underestimate the probability of rare events. We recommend corrections that outperform existing methods and change the estimates of absolute and relative risks by as much as some estimated effects reported in the literature. Second, commonly used data collection strategies are grossly inefficient for rare events data. The fear of collecting data with too few events has led to data collections with huge numbers of observations but relatively few, and poorly measured, explanatory variables, such as in international conflict data with more than a quarter-million dyads, only a few of which are at war. As it turns out, more efficient sampling designs exist for making valid inferences, such as sampling all available events (e.g., wars) and a tiny fraction of nonevents (peace). This enables scholars to save as much as 99% of their (nonfixed) data collection costs or to collect much more meaningful explanatory variables. We provide methods that link these two results, enabling both types of corrections to work simultaneously, and software that implements the methods developed.

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“…Standard analysis of the data available, disregarding the original case-control design, can clearly be biased by the over-representation of cases and the association between the new outcome variable and the case-control indicator. Nagelkerke et al [6] show that valid estimates are only obtained under very strict conditions. If the controls in the case-control study are representative of the non-diseased population, then a cross-sectional analysis of the controls can address questions of prevalence of the new outcome and its association with other exposures measured in the original study.…”

Section: Introductionmentioning

confidence: 98%

Re‐use of case–control data for analysis of new outcome variables

Reilly

Torrång

Klint

2005

Statistics in Medicine

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Case-control studies are usually defined to investigate risk factors for a single disease of interest. However, subsequent to data collection, investigators may wish to examine as an 'outcome' a variable that was an exposure in the original study. A naive analysis that disregards the sampling strategy that gave rise to the data is clearly prone to bias. We present here a simple approach to the analysis of such data using an appropriately weighted regression model. Viewing the problem as a two-stage design provides a unified framework for recognizing and defining the necessary weights when confronted with a variety of real data problems that at first seem unrelated. We provide illustrations that highlight the generality of the approach and demonstrate that the method gives essentially the same results as more specialized methods that require non-standard tools for analysis.

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Logistic regression in case‐control studies: The effect of using independent as dependent variables

Cited by 29 publications

References 8 publications

Secondary analysis of case-control data

Secondary analysis of case-control data

Logistic Regression in Rare Events Data

Re‐use of case–control data for analysis of new outcome variables

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