This document discusses interaction, which occurs when the effect of one variable depends on the level of another variable. It defines quantitative versus qualitative interaction and notes that qualitative interaction indicates interaction is present on both additive and multiplicative scales. An example of qualitative interaction between caffeine consumption and smoking on time to conception is provided. The document also discusses the reciprocity of interaction, how interaction can be distinguished from confounding, and challenges in interpreting observed heterogeneity, including the possibilities of random variability, confounding, bias, and differences in exposure levels across groups.

1. Defining and Assessing Heterogeneity of
Effects: Interaction
School of Pharmacy, SKKU
Sunhong Kwon

2. 6.7 The nature and Reciprocity of Interaction
6.7.1 Quantitative Versus Qualitative Interaction
Quantitative interaction Qualitative interaction
 when the association between
factor A and outcome Y exists
and is of the Same direction in
each stratum formed by Z, but
the strength of the association
varies across strata
 when the effects of A on the
outcome Y are in opposite
directions (crossover) according to
the presence of the third variable
Z
 when there is an association in
one of the strata formed by Z but
not in the other

3. • Example of qualitative interaction
– To examine the effects of caffeine consumption on waiting time to
conception
Main exposure of
interest
- The point estimates of the effects of high caffeine consumption appear
to cross over as a function of smoking.
(i.e., there is a positive association of high caffeine intake with delayed
conception in nonsmokers and a negative association in smokers)

4. • When qualitative interaction is present,
– it is always present in both the additive and the multiplicative models
and is thus independent of the measurement scale.
– the scale does not need to be specified.
• The occurrence of qualitative interaction indicates that interaction is
present in both scales.

5. • Figure imply the presence of an additive interaction between
hypertension status and anger proneness in relation to risk of CHD
• a difference was shown in normotensives but not among hypertensive ->
qualitative interaction.
• it must also be present in a multiplicative scale.
the age-adjusted relative hazard comparing individuals with high and lower scores; 2.97 vs 1.05

6. 6.7.2 Reciprocity of Interaction
• If Z modifies the effect of A, then A modifies the effect of Z,
Interaction is completely reciprocal.
• the choice of A as the suspected risk factor of interest and Z as the
potential effect modifier is arbitrary and a function of the hypothesis
being evaluated.
• When deciding which variable should be treated as the effect modifier and
which as the factor of primary interest, there is no intrinsic hierarchical
value.
Risk factor of
interest
Effect modifier
Positively associated negatively associated
Table 6-22

7. 6.8 INTERACTION, CONFOUNDING EFFECT AND ADJUSTMENT
• Although on occasion the same variable may be both a confounder and an
effect modifier, confounding and interaction are generally distinct
phenomena.
• Confounding effects are undesirable, as they make it difficult to evaluate
whether a statistical association is also causal.
• Interaction is part of the web of causation and may have important
implications for prevention.
• When a variable is found to be both a confounding variable and an effect
modifier, adjustment for this variable is contraindicated.
– This is because when there is interaction the notion of an overaII
adjusted (weighted) mean value (main effect) makes little sense.
– example
• OR: 2.0 for men & 25.0 for women -> average is meaningless
• OR: 0.3 for men & 3.5 for women
-> "average, gender-adjusted” OR may denote no association

8. • Regardless of whether a "Z-adjusted" effect is reported, it is often informative
to report the stratum-specific values as well.
• One solution : to carry out statistical testing and not to adjust if the homogeneity
null hypothesis is rejected

9. 6.8.1 Joint Presence of Two Factors that Interact as a Confounding Variable.
• When there is interaction, the joint presence of variable that interact may
produce confounding effect, even if each individual variable is not
identified as a confounder.
• Because the prevalence of the joint presence of B and C is higher in those
exposed to A and because, in addition, there is strong interaction between
B and C, the crude incidence is greater in the individuals exposed to A
than in the unexposed.

10. 6.9 STATISTICAL MODELING AND STATISTICAL TESTS
FOR INTERACTION
• To examine interaction
– Use complex statistical approaches to evaluate interaction.
Ex) the regression equation including "interaction terms”
– Assess whether an observed heterogeneity is statistically significant.
• Statistical tests of homogeneity are not sufficient to evaluate interaction
fully.

11. 6.10 INTERPRETING INTERACTION
6.10.1 Heterogeneity Due to Random Variability
• random variability
– produced by the stratification by a suspected effect modifier.
– may occur in spite of an a priori specification of interaction in the
context of the hypothesis to be evaluated.
– A more common situation is when interaction is not specified a priori
but the investigator decides to carry out subgroup analysis.
• Sample size inevitably decreases as more strata are created in subgroup
analysis, making it likely that heterogeneity would occur by chance alone.
• The detection of heterogeneity should be assessed vis-a-vis its plausibility.
• After observed by means of subgroup analysis, interaction has to be
confirmed in a study especially designed to evaluate it.

12. 6.10.2 Heterogeneity Due to Confounding
• When associations between A and Y in strata formed by Z are being
explored, differential confounding effects across strata may be responsible
for the heterogeneity of effects.

13. • The possibility that interaction may be explained partially or entirely by a
confounding effect makes it essential to adjust for potential confounders
when assessing interaction.
• In most real-life instances, confounding may either exaggerate or decrease
heterogeneity.

14. 6.10.3 Heterogeneity Due to Bias
• The observed heterogeneity may also result from differential bias across
strata.
• EX) when stratification according to educational status was undertaken,
the apparent decreased risk of miscarriage in blacks was seen only in the
lower educational strata. This pattern of an apparent modification of the
race effect by educational level is probably due to the underascertainment
bias operating only in less educated blacks.

15. • Example of possible misclassification resulting in apparent interaction
: an earlier, aggressive treatment of preeclampsia in those with "high"
prenatal care may be the explanation for the lesser increase in gestational
diabetes-related odds of severe eclampsia; on the other hand, the authors
also suggested that, in those with a low level of care, preexisting diabetes
may have been misclassified as gestational, which may have artificially
increased the strength of the association in these individuals.

16. • Example of heterogeneity due to information bias
– validity levels differ between smokers and nonsmokers

17. 6.10.4 Heterogeneity Due to Differential Intensity of Exposure
• heterogeneity in the levels of exposure to the risk factor of interest
according to the alleged effect modifier
• Ex) the potential effect modification by gender of the relationship of
smoking to respiratory diseases -> may be created or exaggerated by the
fact that the level of exposure to smoking is higher in men than in women.

18. 6.10.5 Interaction and Host Factors
• Facilitation and level of exposure are also the result of anatomical or
pathophysiological characteristics of the host.
Ex) short nose dog; lung cancer vs. long nose dog; nasal cancer
– the importance of considering the intensity and/ or facilitation of
exposure when attempting to explain heterogeneity of effects.
– Effective exposure dose is obviously a function of the net result of the
amount of "exposure" in the individual's environment
• Effect modifiers can act on different portals of entry.
Ex) exposure to the same intensity of a skin pathogen(e.g., streptococcus)
skin rash vs. normal skin
• The biological mechanism of effect modification can also vary at the
metabolic or cellular level. (e.g., genetic disorders such as phenylketonuria)

19. 6.11 INTERACTION AND SEARCH FOR NEW RISK FACTORS
IN LOW-RISK GROUPS
• The strength of an association measured by a relative difference (e.g., a
relative risk) is a function of the relative prevalence of other risk factors.
• The idea of studying "emergent" risk factors in individuals with no known
risk factors is on occasion considered in the design of a study.
– It may limit the generalizability of the study findings to the general
population, which includes both low- and high-risk individuals.
– Associations that rely on synergism between risk factors may be
missed altogether.
• the "low-risk“ approach may underestimate the potential impact

20. 6.12 INTERACTION AND "REPRESENTATIVENESS"
OF ASSOCIATIONS
• An important assumption when generalizing results from a study is
that the study population should have an "average" susceptibility to the
exposure under study with regard to a given outcome.
• When susceptibility is unusual, results cannot be easily generalized.
Ex) Swiss children vs. African children
• Although it is difficult to establish to which extent the susceptibility of a
given study population differs from an "average" susceptibility, the
assessment of its epidemiological profile (based on well-known risk factors)
may indicate how "usual" or "unusual" that population is.
• This strategy is limited because level of susceptibility to a known risk
factor may not be representative of the level of susceptibility regarding
the exposure under study.