arXiv subjects

Georgia D. Tomova

Publications and source records attributed to Georgia D. Tomova.

2 recordsLinked to original sources

arXiv2026

Lord's 'paradox' explained: the 50-year warning on the use of 'change scores' in observational data

In 1967, Frederick Lord posed a conundrum that has confused scientists for over half a century. Subsequently named Lord's 'paradox', the puzzle centres on the observation that two different approaches to estimating the effect of an exposure on the 'change' in an outcome can produce radically different results. Approach 1 involves comparing the mean 'change score' between exposure groups and Approach 2 involves comparing the follow-up outcome between exposure groups conditional on the baseline outcome. Resolving this puzzle starts with recognising the three reasons that a variable may change value: (A) 'endogenous change', which represents autocorrelation from baseline, (B) 'random change', which represents change from transient random processes, and (C) 'exogenous change', which represents all non-endogenous, non-random change and contains all change that is potentially modifiable by other baseline variables. In observational data, neither Approach 1 nor Approach 2 can reliably estimate the causal effect of an exposure on 'exogenous change' in an outcome. Approach 1 is susceptible to diluted or opposite-sign estimates whenever the exposure causes, or is caused by, the baseline outcome. Approach 2 is susceptible to inflated estimates due to measurement error in the baseline outcome and time-varying confounding bias when the baseline outcome is a mediator. The measurement error can be reduced with multiple measures of the baseline outcome, and the time-varying confounding can be reduced using g- methods. Lord's 'paradox' offers several enduring lessons for observational data science including the importance of a well-defined research question and the problems with analysing change scores in observational data.

stat.ME↗

arXiv2023

Depicting deterministic variables within directed acyclic graphs (DAGs): An aid for identifying and interpreting causal effects involving tautological associations, compositional data, and composite variables

Deterministic variables are variables that are fully explained by one or more parent variables. They commonly arise when a variable has been algebraically constructed from one or more parent variables, as with composite variables, and in compositional data, where the 'whole' variable is determined from its 'parts'. This article introduces how deterministic variables may be depicted within directed acyclic graphs (DAGs) to help with identifying and interpreting causal effects involving tautological associations, compositional data, and composite variables. We propose a two-step approach in which all variables are initially considered, and an explicit choice is then made whether to focus on the deterministic variable(s) or the determining parents. Depicting deterministic variables within DAGs bring several benefits. It is easier to identify and avoid misinterpreting tautological associations, i.e., self-fulfilling associations between variables with shared algebraic parent variables. In compositional data, it is easier to understand the consequences of conditioning on the 'whole' variable, and correctly identify total and relative causal effects. For composite variables, it encourages greater consideration of the target estimand and greater scrutiny of the consistency and exchangeability assumptions. DAGs with deterministic variables are a useful aid for planning and interpreting analyses involving tautological associations, compositional data, and/or composite variables.

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