Ubiquitous bias and false discovery due to model misspecification in analysis of statistical interactions: The role of the outcome’s distribution and metric properties.

Abstract

Studies of interaction effects are of great interest because they identify crucial interplay between predictors in explaining outcomes. Previous work has considered several potential sources of statistical bias and substantive misinterpretation in the study of interactions, but less attention has been devoted to the role of the outcome variable in such research. Here, we consider bias and false discovery associated with estimates of interaction parameters as a function of the distributional and metric properties of the outcome variable. We begin by illustrating that, for a variety of noncontinuously distributed outcomes (i.e., binary and count outcomes), attempts to use the linear model for recovery leads to catastrophic levels of bias and false discovery. Next, focusing on transformations of normally distributed variables (i.e., censoring and noninterval scaling), we show that linear models again produce spurious interaction effects. We provide explanations offering geometric and algebraic intuition as to why interactions are a challenge for these incorrectly specified models. In light of these findings, we make two specific recommendations. First, a careful consideration of the outcome's distributional properties should be a standard component of interaction studies. Second, researchers should approach research focusing on interactions with heightened levels of scrutiny.

Factorizing polygenic epistasis improves prediction and uncovers biological pathways in complex traits

“…In the future, sparse models (Bayesian or frequentist) could test which SNPs affect which EFs. Third, statistical interaction tests are susceptible to false positives from phenotype scaling [33,51,64,65] and/or LD with unmeasured causal variants [18,[47][48][49][50]. Indeed, the EFA signals in UKB depend on phenotype scale, and the biological EF enrichment in urate is driven by a single large-effect gene.…”

Compensating or Boosting Genetic Propensities? Gene-Family Socioeconomic Status Interactions by Educational Outcome Selectivity

“…Moreover, identifying GxE interactions is notoriously challenging, especially in the presence of dichotomous outcomes (e.g., Domingue et al, 2020). Recent studies show that the results obtained employing a linear probability model to study interactions can introduce ubiquitous bias and false discovery (Domingue et al 2022(Domingue et al , 2020Rohrer and Arslan 2021;Schuetze and Von Hippel 2023). The issue in studying the GxSES interaction for the probability Y of a dichotomous outcome with a linear probability model is that the effect of G on Y, conditional on SES, is constrained by the truncated nature of Y, thus also depending on the expected value of Y conditional on SES.…”

“…Methodologially, we follow the standard suggestions in the specialized literature and replicate the analyses using logistic and non-parametric locally weighted scatterplot smoothing (LOWESS) models on our dichotomous outcome (Domingue et al 2020(Domingue et al , 2022. We have also employed a novel solution, estimating unconditional quantile regressions (Firpo, Sergio, Fortin, Nicole M., and Lemieux, Thomas 2009; Rios-Avila 2020) using years of education as a continuous outcome.…”

“…We also estimate unconditional quantile regression models with years of education as the dependent variable. In this way, we address the concern that the application of a linear probability model to analyze interaction with dichotomous dependent variables can lead to false discovery attributable to the scaling of the outcome variable (Domingue et al 2022(Domingue et al , 2020Rohrer and Arslan 2021;Schuetze and Von Hippel 2023). Second, we also estimate sibling fixed-effect models to address the concern that the effect of PGI constructed in population GWAS studies is biased due to omitted environmental influences, such as genetic nurture effects (Kong et al, 2018;Young et al, 2018).…”

How Many Participants Do I Need to Test an Interaction? Conducting an Appropriate Power Analysis and Achieving Sufficient Power to Detect an Interaction

“…Finally, we focused on articles using a between-participants design (Criterion 3) and a regular regression framework (including analysis of variance [ANOVA]; Criterion 4) with a one-degree-of-freedom test (Criterion 5). The reason for these foci was that within-participants designs, nonlinear functions, multilevel modeling, polytomous variables, and so on all involve different formulas for statistical power calculations (see Brysbaert, 2019; Demidenko, 2008; Domingue et al, 2022; Mathieu et al, 2012). However, we will later show how mixed designs and planned-contrast analysis can be used to increase power.…”