Understanding interactions between risk factors, and assessing the utility of the additive and multiplicative models through simulations

PLoS One. 2021 Apr 26;16(4):e0250282. doi: 10.1371/journal.pone.0250282. eCollection 2021.

Abstract

Understanding the genetic background of complex diseases requires the expansion of studies beyond univariate associations. Therefore, it is important to use interaction assessments of risk factors in order to discover whether, and how genetic risk variants act together on disease development. The principle of interaction analysis is to explore the magnitude of the combined effect of risk factors on disease causation. In this study, we use simulations to investigate different scenarios of causation to show how the magnitude of the effect of two risk factors interact. We mainly focus on the two most commonly used interaction models, the additive and multiplicative risk scales, since there is often confusion regarding their use and interpretation. Our results show that the combined effect is multiplicative when two risk factors are involved in the same chain of events, an interaction called synergism. Synergism is often described as a deviation from additivity, which is a broader term. Our results also confirm that it is often relevant to estimate additive effect relationships, because they correspond to independent risk factors at low disease prevalence. Importantly, we evaluate the threshold of more than two required risk factors for disease causation, called the multifactorial threshold model. We found a simple mathematical relationship (square root) between the threshold and an additive-to-multiplicative linear effect scale (AMLES), where 0 corresponds to an additive effect and 1 to a multiplicative. We propose AMLES as a metric that could be used to test different effects relationships at the same time, given that it can simultaneously reveal additive, multiplicative and intermediate risk effects relationships. Finally, the utility of our simulation study was demonstrated using real data by analyzing and interpreting gene-gene interaction odds ratios from a rheumatoid arthritis case-control cohort.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Alleles
  • Anti-Citrullinated Protein Antibodies / metabolism
  • Arthritis, Rheumatoid / epidemiology*
  • Arthritis, Rheumatoid / genetics*
  • Arthritis, Rheumatoid / immunology
  • Databases, Genetic
  • Europe / epidemiology
  • Gene Frequency
  • Genetic Loci
  • Genetic Predisposition to Disease / genetics*
  • Genome-Wide Association Study
  • HLA-DRB1 Chains / genetics
  • Humans
  • Models, Statistical*
  • Polymorphism, Single Nucleotide*
  • Protein Tyrosine Phosphatase, Non-Receptor Type 22 / genetics
  • Risk Factors

Substances

  • Anti-Citrullinated Protein Antibodies
  • HLA-DRB1 Chains
  • PTPN22 protein, human
  • Protein Tyrosine Phosphatase, Non-Receptor Type 22

Grants and funding

L.M.D.G.: Ulla och Gustaf af Uggla Foundation 2018-02670 https://staff.ki.se/ulla-and-gustaf-af-uggla-foundation L.M.D.G.: Reumatikerförbundet R-861801, R-932138 https://reumatiker.se L.M.D.G.: Konung Gustaf V:s 80-årsfond FAI-2018-0518, FAI-2019-0597 https://www.kungahuset.se/monarkinhovstaterna/kungligastiftelser/forskning/konunggustafvs80arsfond/ L.M.D.G.: Stiftelsen Professor Nanna Svartz Fond 2019-00318 https://www.stiftelsemedel.se/stiftelsen-professor-nanna-svartz-fond/ The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.