Interaction

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Interaction Effect Modification Association
Modification
and Other Confusing Concepts
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Types of Third Variables
Exposure of Interest
Confounders Effect Modifiers Mechanisms
These categories are not mutually exclusive
Health Outcome
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Third Variable Associations in Epidemiology

• Confounding by a 3rd variable masks the causal
  effect of interest by mixing the effects of the
  3rd variable and the exposure of interest
  
• CONTROL CONFOUNDING - stratification or modeling
• Effect modification by a 3rd variable provides
  information about the nature of the underlying
  causal effect of the exposure on the outcome
  
• DESCRIBE EFFECT MODIFICATION - effects at levels
  of 3rd variable
  
• A 3rd variable that is an intermediary between
  exposure and outcome, provides information about
  the mechanisms/pathways of the causal effect
  
• DESCRIBE MECHANISMS - direct and indirect effects

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Definitions and Background
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Terminology

• Synergy - Antagonism
• Interaction
• Association Modification
• Effect Modification
• Effect-measure Modification

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on the topic of synergy (or its negative
counterpart antagonism), which is a major
conceptual area in epidemiology, there exists
fundamental controversy as to definitions.
Rothman (1980)
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Four Contexts for Defining Interaction

• Statistical - in reference to a specific
  statistical model
  
• Biological - in reference to the combined
  biological effects of two component causes on
  disease risk
  
• Public Health - in reference to the public
  health importance of the attributable risk for
  the combined exposures
  
• Individual Decision Making - in reference to the
  effect of combined risks in an individual
  (clinical setting)

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Statistical Interaction

• Statistical interaction is intended to denote
  the interdependence between the effects of 2 or
  more risk factors within the context of a
  specific statistical model relating Es to D
• The general model is R (A,B) f (K0, KaA,
  KbB, KabAB)
  
• Interaction in the statistical context is
  completely dependent on the form of the
  statistical model that is chosen - the f or
  link function

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Statistical Interaction

• Linear Link Function R (A,B) K0 KaA
  KbB KabAB
  
• Logistic Link Function e (K0 KaA
  KbB KabAB)
  
• R (A,B) ----------------------
  ------------------------------
  
• 
  1 e (K0 KaA KbB
  KabAB)
  
• The value of KabAB depends on which model is
  chosen to represent the association between E and
  D and R (A,B)

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Statistical Interaction

• This situation exists when the purpose of the
  statistical model is to predict or describe the
  pattern of disease as well as possible - but not
  to necessarily elucidate the underlying
  biological or other causal relationships
• Thus, the focus is on the overall efficient
  statistical functioning of the model to describe
  and predict the outcome
  
• e.g., the use of a regression model to predict
  those who use mammography screening from
  individual demographic data, or to predict body
  fat from skinfold thickness at various
  anthropometric sites - these skinfolds do not
  cause the body fat

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Statistical Interaction

• Statistical interaction is inherently ambiguous
  and depends entirely on how the model is defined
  
• Also dependent on how the variables have been
  represented in the model (e.g., continuous vs
  categorical raw vs log-transformed)

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Biological Interaction

• Can be defined as the interdependent operation
  of 2 or more causes to produce disease
  
• Agent A increases the number of cells
  susceptible to carcinogen B - asbestos and
  smoking. A and B are both causes but they can
  act together biologically to increase disease
  risk
• This can be unambiguously defined using
  Rothmans Sufficient Component Cause Model (SCC)
  of disease causation

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Sufficient Component Causes Model - Rothman

• Any set of conditions which inevitably produce
  disease is a sufficient cause
  
• Any disease may have multiple sufficient causes
• Any element in the set of conditions comprising
  a sufficient cause is a component cause
  
• A necessary cause is a component cause of all
  the sufficient causes of a disease

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• Three sufficient causes of disease within an
  individual
  
• these combinations of U-A-B-E are all minimally
  sufficient to cause disease
  
• in this case U is a necessary component of all
  the sufficient causes

component causes of sufficient cause 1
causal complement of U
Think about sufficient causes as different,
complete pathways to disease
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Implications of the sufficient component causes
model

• Interaction - by definition, component causes
  acting within the same sufficient cause are
  interacting to produce disease.
  
• They work interdependently to produce disease.
  Thus, biological interaction is the participation
  of two or more component causes in the same
  sufficient cause
• Because of the SCC model, biological interaction
  can be unambiguously defined as a departure from
  the additivity of risks.
  

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Public Health Interaction

• The primary concern when evaluating interaction
  in the public health context is the number of
  cases occurring in the population and the
  proportional contribution of each risk factor to
  this burden
• For public health purposes, the effects of 2
  factors, A and B, may be considered independent
  if the number of cases of D that would occur in
  the population does not depend on the extent to
  which A and B occur in the same individuals

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Public Health Interaction

• This, interaction in the Public Health context
  is also represented by a departure from additivity

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Interaction in Individual Decision Making

• Similar to public health situation
• A physician advising a women about oral
  contraceptive use might reasonably want to know
  about her blood pressure, despite the fact that
  the risk ratio for cerebrovascular complications
  related to oral contraceptive use are the same in
  hypertensives and non-hypertensives
• BUT, there is an increase in the absolute risk
  among hypertensive women, making hypertension and
  contraceptive use interact in terms of that
  particular patients risk of a poor health outcome

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Interaction in Individual Decision Making

• Thus, interaction in the context of individual
  decision making is also represented by a
  departure from additivity

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Describing Effect Modification We Can Use 3
Reference Points
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1. No Additional Effect Reference Point for
Joint Effects
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2. Additive Reference Point for Describing Joint
Effects
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2. Additive Reference Point for Describing Joint
Effects
R(A,B) - R(A-,B-) R(A,B-) - R(A-,B-)
R(A-,B) - R(A-,B-)
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3. Multiplicative Reference Point for Describing
Joint Effects
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3. Multiplicative Reference Point for Describing
Joint Effects
R(A,B) R(A,B-) R(A-,B) ------------
------------ ------------R(A-,B-)
R(A-,B-) R(A-,B-)
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Reference Points for Describing Joint Effects -
Summary
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Describing Joint Effects
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Three Different Modification Terminologies
One reference point Interaction or Effect
Modification Usually, they mean a model
based departure from multiplicativity (not
really effect but association)
Two reference points Association modification (R
R) and effect modification (ER)
Multiple reference Joint Effects
points
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One Reference Point Effect Modification

• Most common but inadequate
• RR or OR is the outcome used to assess
  modification
  
• Modification is deviation from multiplicativity
• Positive modification is when the presence of the
  high risk category of a third variable increases
  the Risk or Odds Ratio.
  
• Negative modification is when the presence of the
  high risk category of a third variable decreases
  the risk or odds ratio. This is very common
  because most joint effects are less than
  multiplicative.

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Two Reference Points Association Effect
Modification

• Less common and better
• Effect measured by RD, Association measured
  by RR
  
• Association modification deviation from
  multiplicativity
  
• Effect modification deviation from additivity

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Multiple Reference Points Joint Effects

• Even less common but best
• Joint effects are described in relation to
  multiplicativity, additivity, and no additional
  effects.
  
• Better because it is more descriptive and it uses
  more points of reference
  
• Better because it recognizes that two predictors
  of disease will always have some joint effects
  and the job is to describe those joint effects.
  The other approaches require a decision as to
  when deviation from one particular point is
  significant.

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Describing Effect Modification Vs Describing
Joint Effects

• Effect modification describes deviation from
  only one point on the joint effects scale
  
• Most researchers make that the point of
  multiplicativity
  
• Some find the point of additivity more
  meaningful
  
• Joint effects can be described as
• Greater than multiplicative
• Multiplicative
• Greater than additive but less than
  multiplicative
  
• Additive
• Less than additive
• Crossover