Relaxation Penalties and Priors for Plausible Modeling of Nonidentified Bias Sources

By Sander Greenland. 2009

57 citations recorded by the source corpus.

In designed experiments and surveys, known laws or design feat ures provide checks on the most relevant aspects of a model and identify the target parameters. In contrast, in most observational studies in the health and social sciences, the primary study data do not identify and may not even bound target parameters. Discrepancies between target and analogous identified parameters (biases) are then of paramount concern, which forces a major shift in modeling strategies. Conventional approaches are based on conditional testing of equality constraints, which correspond to implausible point-mass priors. When these constraints are not identified by available data, however, no such testing is possible. In response, implausible constraints can be relaxed into penalty functions derived from plausible prior distributions. The resulting models can be fit within familiar full or partial likelihood frameworks. The absence of identification renders all analyses part of a sensitivity analysis. In this view, results from single models are merely examples of what might be plausibly inferred. Nonetheless, just one plausible inference may suffice to demonstrate inherent limitations of the data. Points are illustrated with misclassified data from a study of sudden infant death syndrome. Extensions to confounding, selection bias and more complex data structures are outlined.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8d4c17face10c1e1400f177eb86267f47213b6f6

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Citations in the corpus

For and Against Methodologies: Some Perspectives on Recent Causal and Statistical Inference Debates (2017, methodology): “…by replacing point-by-point parameter variations with random coefficients, penalty functions, or prior distributions based on genuine contextual information (Gustafson and Greenland 2006; Greenland and Lash 2008; Greenland 2009b; Lash et al. 2009; Gustafson 2010; Gustafson and McCandless 2014).”
Good practices for quantitative bias analysis. (2014, methodology): “One may avoid impossible adjustments by using the priors in proper Bayesian procedures, or by using a bias model whose parameters are independent of the data.(30,70) Nonetheless, encountering impossible adjusted data is often of substantive importance, as it may represent a fundamental disconnect be”
All your data are always missing: incorporating bias due to measurement error into the potential outcomes framework. (2015, background): “In a way, this title is incomplete: if it were not so cumbersome, it could read, ‘even with no explicit missing data, all of the information needed to identify the average treatment effect is always missing’.(6) We begin with the premise that all of the potential outcomes are hidden.”
Philosophy and the practice of Bayesian statistics (2010, unknown): “Modern Bayesian models in particular are full of unobserved, latent, and unobservable variables, and nonidentifiability is an inevitable concern in assessing such models; see, for example, Gustafson (2005); Vansteelandt et al. (2006); Greenland (2009).”