Discussion of "Perils and potentials of self-selected entry to epidemiological studies and surveys" by N. Keiding and T.A. Louis

Perils and potentials of self‐selected entry to epidemiological studies and surveys

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processesThe models started to be formulated about 40 years ago and vigorous development is ongoing Longitudinal observational studies as well as intervention studies are best modeled via a subclass called regression graph models and, especially traceable regressions Regression graphs include two types of undirected graph and directed acyclic graphs in ordered sequences of joint responses Response components may correspond to discrete or continuous random variables and may depend exclusively on variables which have been generated earlier These aspects are essential when causal hypothesis are the motivation for the planning of empirical studies 
To turn the graphs into useful tools for tracing developmental pathways and for predicting structure in alternative models, the generated distributions have to mimic some properties of joint Gaussian distributions Here, relevant results concerning these aspects are spelled out and illustrated by examples With regression graph models, it becomes feasible, for the first time, to derive structural effects of (1) ignoring some of the variables, of (2) selecting subpopulations via fixed levels of some other variables or of (3) changing the order in which the variables might get generated Thus, the most important future applications of these models will aim at the best possible integration of knowledge from related studies

Graphical Markov models, unifying results and their interpretation

We describe how graphical Markov models emerged in the past 40 years, based on three essential concepts that had been developed independently more than a century ago. Sequences of joint or single regressions and their regression graphs are singled out as being the subclass that is best suited for analyzing longitudinal data and for tracing developmental pathways, both in observational and in intervention studies. Interpretations are illustrated using two sets of data. Furthermore, some of the more recent, important results for sequences of regressions are summarized.

/pdf/graphical-markov-models-overview-3y92oers67.pdf

Graphical Markov models: overview

We describe how graphical Markov models started to emerge in the last 40 years, based on three essential concepts that had been developed independently more than a century ago. Sequences of joint or single regressions and their regression graphs are singled out as being best suited for analyzing longitudinal data and for tracing developmental pathways. Interpretations are illustrated using two sets of data and some of the more recent, important results for sequences of regressions are summarized.

Graphical Markov models combine conditional independence constraints with graph- ical representations of stepwise data generating processes. The models started to be formulated about 40 years ago and vigorous development is ongoing. Longitudinal observational studies as well as intervention studies are best modelled via a subclass called regression graph models and, especially traceable regressions. Regression graphs include two types of undirected graph and directed acyclic graphs in ordered sequences of joint responses. Response components may correspond to discrete or continuous random variables or to both types and may depend exclu- sively on variables which have been generated earlier. These aspects are essential when causal hypothesis are the motivation for the planning of empirical studies. To turn the graphs into useful tools for tracing pathways of dependence, for understanding development over time and for predicting structure in alternative models, the generated distri- butions have to mimic some properties of joint Gaussian distributions. Here, relevant results concerning these aspects are spelled out and illustrated by examples. With regression graph models, it becomes feasible, for the

/pdf/graphical-markov-models-unifying-results-and-their-4zmjdvbrn5.pdf

We say that the signs of association measures among three variables fX;Y;Zg are transitive if a positive association measure between the variable X and the intermediate variable Y and further a positive association measure between Y and the endpoint variable Z imply a positive association measure between X and Z. We introduce four association measures with dierent stringencies, and discuss conditions for the transitivity of the signs of these association measures. When the variables follow exponential family distributions, the conditions become simpler and more interpretable. Applying our results to two data sets from an observational study and a randomized experiment, we demonstrate that the results can help us to draw conclusions about the signs of the association measures between X and Z based only on two separate studies about fX;Y g and fY;Zg.

/pdf/qualitative-evaluation-of-associations-by-the-transitivity-1r5k3s2cmq.pdf

Qualitative Evaluation of Associations by the Transitivity of the Association Signs

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Qualitative Evaluation of Associations by the Transitivity of the Association Signs