11 Chapter 11: Effect Modification

Chapter 11: Effect Modification

Objectives

After completing this module, you should be able to:

Define effect modification (also known as interaction).

Explain the similarities and differences between confounding and effect modification.

Describe methods to assess effect modification.

11.1 Introduction

In epidemiology, effect modification is a natural phenomenon in which the effect measure for one factor varies at different levels of another factor (Porta, 2008). Effect modification is also known as interaction, and the two terms can be used interchangeably. Effect modifiers are the factors on which the association between an exposure and an outcome varies. A common scenario in epidemiology is the measure of association (odds ratio, risk ratio, hazard ratio, etc.) being weaker among certain population subgroups and stronger among other population subgroups. The variables that define such subgroups are the effect modifiers.

One important caveat is that although we can stratify the association between an exposure and an outcome by any attribute (variable), not all variables are potential effect modifiers. If we are to propose a given variable as an effect modifier, there ideally should be a biological or psycho-social justification and hypothesis for the effect modification.

Thus, the questions that we need to ask are:

1. Is there a subgroup in our study population where the association between exposure and outcome is particularly strong (or particularly weak)?

2. What is the biological or psycho-social justification or rationale for this variation in the strength of association between the exposure and the outcome?

If we can answer the second question, we have a strong rationale and justification for effect modification assessment. Without such justification, any variations in the strength of association between an exposure and an outcome may be simply coincidental, and the findings will not be as helpful in advancing our understanding of the outcome of interest. Examples of such justifications and the presentation of study findings can be found later in this chapter.

11.2 Effect Modification vs. Confounding

Effect modification is similar to confounding (the mixing of effects between the exposure of interest and an extraneous variable) as both involve an extraneous variable, in addition to the exposure and outcome of interest, that is not in the causal pathway. The difference is that confounders are disruptions that we need to control, whereas effect modifiers are natural phenomena that we need to present (most commonly in stratified analyses). When we find confounders, we want to control (adjust) for their effects when we report the study findings. However, when we find effect modifiers, we need to stop and stratify the analyses by their levels. In other words, we need to report the association between the exposure and the outcome by subgroups since the association may be weaker in certain subgroups and stronger in other subgroups.

11.3 Effect Modification Assessment by Stratified Analyses

The most common method for assessing effect modification is stratification, in the same way that a variable is assessed for confounding. We need to compare the overall measure of association against the stratified measures of association. If we calculated the overall odds ratio vs. the group-specific odds ratio and we found that the overall odds ratio is above or below all stratified odds ratios, then the stratifying variable is a confounder, not an effect modifier. If the overall odds ratio is between the stratified odds ratios, then the stratifying variable is indeed an effect modifier.

When we have performed stratified analyses and found a potential effect modifier, we need to make similar considerations regarding chance as the best explanation for the observed findings and assess the p-value of the variations in the measure of association. A technique to make this assessment is the Breslow-Day test of heterogeneity.

For the time being, let us consider once again the association between coffee drinking and heart attacks (Table 11.3.1).

Table 11.3.1 Overall association between coffee consumption (at baseline) and heart attacks (at one-year follow-up) in a cohort study: possible interaction with (and effect modification by) physical activity

		Heart attack (Outcome)
		Yes	No	Total	Incidence (Risk) of heart attack
Coffee Drinking (Exposure)	Coffee drinkers (Exposed) (+) (n = 1160)	820 (a)	340 (b)	1160 (a+b)	820/1160 = 0.7068 = 70.68%
	Non-drinkers (Non-exposed) (-) (n = 840)	180 (c)	660 (d)	840 (c+d)	180/840 = 0.2142 = 21.42%
	Total	1000	1000	2000

Unadjusted Risk Ratio (Crude RR): 3.29

Coffee drinkers had a 3.29 times higher incidence (risk) of heart attack than participants who did not drink coffee.

However, physical activity (exercise) may be an effect modifier in the association between coffee drinking and heart attacks. The rationale/justification is that high physical activity can potentially reduce or nullify the effect of a poor diet (including too much coffee drinking) on cardiovascular disease (including heart attack). A lack of physical activity combined with a poor diet can potentially increase your risk of cardiovascular disease.

If we have data on which participants were or were not physically active at baseline, we can stratify our analyses by physical activity level. In other words, we can present the association between coffee consumption only among those who were physically active (as one subgroup), and separately, the association only among those who were physically inactive (as the other subgroup). Then, we can consider the subgroup unadjusted RR compared to the overall unadjusted RR. Please note that these stratified analyses have not yet accounted for confounding of the association by smoking.

In the study, there were 900 physically active participants and 1100 participants who were physically inactive. The findings of stratified analyses are as follows:

Association between coffee drinking and heart attacks only among physically active participants (n = 900 participants):

		Heart attack (Outcome)
		Yes (+)	No (-)	Total	Incidence (Risk) of heart attack
Coffee Drinking (Exposure)	Coffee drinkers (Exposed) (+) (n = 480)	216 (a)	264 (b)	480 (a+b)	= b / (a+b) = 216/480 = 0.450 = 45.0%
	Non-drinkers (Non-exposed) (-) (n = 420)	105 (c)	315 (d)	420 (c+d)	= d / (c+d) = 105/420 = 0.250 = 25.0%
	Total			900

Risk ratio (RR) for coffee drinking and heart attacks among physically active participants:

RR among physically active participants = Incidence (among exposed) / Incidence (among non-exposed)

RR among physically active participants = 0.450 / 0.250 = 1.80 (95% CI = 1.63, 1.99)

Interpretation: Among physically active participants, coffee drinkers had a 1.8 times higher risk (incidence) of having a heart attack than non-coffee drinkers (RR = 1.80).

Association between coffee drinking and heart attacks only among physically inactive participants:

		Heart attack (Outcome)
		Yes (+)	No (-)	Total	Incidence (Risk) of heart attack
Coffee Drinking (Exposure)	Coffee drinkers (Exposed) (+) (n = 680)	604 (a)	76 (b)	680 (a+b)	604/680 = 0.888 = 88.8%
	Non-drinkers (Non-exposed) (-) (n = 420)	75 (c)	345 (d)	420 (c+d)	75/420 = 0.179 = 17.9%
	Total			1100

Risk ratio (RR) among physically inactive participants:

RR among physically inactive participants = Incidence (among exposed) / Incidence (among non-exposed)

RR among physically inactive participants = 0.888/0.179 = 4.96 (95% CI = 3.99,6.16)

Interpretation: Among physically inactive participants, coffee drinkers had a nearly 5 times higher risk (incidence) of having a heart attack than non-coffee drinkers (RR = 4.96)!

Adjusting for Confounders in Effect Modification Assessment

From the material on confounders in Chapter 10, we realize that smoking is an independent risk factor for heart attacks; thus, it is a confounder in the association between coffee drinking and heart attacks. Therefore, the strength of the association between coffee drinking and heart attacks may be partly attributed to smoking, and the influence of smoking on the association between coffee drinking and heart attacks needs to be controlled (even when stratified into subgroups based on physical activity levels).

Although there are many ways to control for confounding (restriction, matching, randomization, and statistical analyses), the most feasible one, given the study design, is to adjust for the effect of smoking in multivariable regression analyses (along with sex, age, family history of coronary heart disease, personal medication intake, and history of angina, for example). We will report the confounders-adjusted measure of association (adj. OR, adj. RR, adj. HR, etc.) in the overall and stratified analyses accordingly. An example of stratified analyses can be found in Table 11.3.2. Please note that the rows have been switched in order to conform to the conventional format.

Table 11.3.2 Stratified associations between coffee consumption and heart attacks (myocardial infarction) by levels of physical activity (row percentage, n = 2000 participants)

		Heart attack (Outcome)
		No (n = 1000)	Yes (n = 1000)	Unadjusted RR (95% CI)	Adjusted RR* (95% CI)
Among physically active participants
Coffee Drinking (Exposure)	Non-drinkers (Non-exposed) (-) (n = 420)	315 (75.0%)	105 (25.0%)	1.0 (Ref.)	1.0 (Ref.)
	Coffee drinkers (Exposed) (+) (n = 480)	264 (55.0%)	216 (45.0%)	1.80 (1.63, 1.99)	0.95 (0.85, 1.15)
	Total = 900
Among physically inactive participants
Coffee Drinking (Exposure)	Non-drinkers (Non-exposed) (-) (n = 420)	345 (82.1%)	75 (17.9%)	1.0 (Ref.)	1.0 (Ref.)
	Coffee drinkers (Exposed) (+) (n = 680)	76 (11.2%)	604 (88.8%)	4.96 (3.99, 6.16)	1.10 (0.95, 1.20)
	Total = 1100

*Adjusted for smoking status (current smokers vs. non-smokers), sex, age, family history of coronary heart disease, personal medication intake, and history of angina.

Interpretation: Among physically active participants, coffee drinkers had a 1.8 times higher risk of having a heart attack than non-drinkers. Among physically inactive participants, coffee drinkers had a 4.96 times higher risk of having a heart attack than non-drinkers. However, after adjusting for potential confounders, coffee drinking did not have a statistically significant association with the risk of heart attack in both groups.

11.4 Additive vs. Multiplicative Interaction

There are two models of interaction (effect modification) (Porta, 2008):

Additive interaction refers to a model in which the combined effect of the exposure and the effect modifier (interacting variable) is the sum of the effects. If the joint effect is different from the sum of the effects, then it is said that the interaction is additive interaction.

Multiplicative interaction refers to a model in which the combined effect of the exposure and the effect modifier (interacting variable) is the multiplicative product of their individual effects.

We cannot identify additive or multiplicative interaction using stratification. We need to calculate what is called the “joint effect table” by treating each of the exposure and effect modifier groups as a separate category of exposure. The numbers in the tables remain the same, but the comparison groups in the table will change slightly. The joint effect table can be calculated based on the given example on effect modification by physical activity (in the cohort study on coffee drinking vs. heart attack) as follows:

		Heart attack (Outcome)
Exposure groups		Yes (+)	No (-)	Incidence (Risk) of heart attack	RR (95% CI)
(no coffee, active)	Active non-drinkers (Non-exposed) (-) (n = 420)	105 (c)	315 (d)	= 105/420 = 0.250 = 25.0%	1.00 (Reference group)
(coffee, active)	Active Coffee drinkers (Exposed) (+) (n = 480)	216 (a)	264 (b)	= 216/480 = 0.450 = 45.0%	1.80 (95% CI = 1.48, 2.18)
(no coffee, inactive)	Inactive non-drinkers (Exposed) (+) (n = 420)	75 (a)	345 (b)	= 75/420 = 0.179 = 17.9%	0.72 (95% CI = 0.55, 0.93)
(coffee, inactive)	Inactive Coffee drinkers (Exposed) (+) (n = 680)	604 (a)	76 (b)	= 604/680 = 0.888 = 88.8%	3.55 (95% CI = 3.00, 4.20)

Based on the risk ratio, we can make the observed joint effect table as follows:

 

Table 2.1 Risk ratio of heart attack by coffee consumption and physical activity

	Coffee consumption
Physical activity	Non-coffee drinkers	Coffee drinkers
Physically active	RR = 1.0 (Ref.) (a)	RR = 1.80 (b)
Physically inactive	RR = 0.72 (c)	Observed joint RR = 3.55* (d)

*(the observed joint effect)

(For some reason, being physically inactive was slightly protective against heart attack among non-drinkers of coffee. Let’s put that aside for now.)

The expected joint effect model for additive interaction is as follows:

	Coffee consumption
Physical activity	Non-coffee drinkers	Coffee drinkers
Physically active	RR = 1.0 (Ref.)	RR = 1.80
Physically inactive	RR = 0.72	Expected joint RR (additive) = RR(b) + [RR(c)-1] = 1.80 + (0.72-1) = 1.80 + (-0.23) = 1.57

Based on the observation:

Observed joint effect RR ≠ Expected joint effect RR (additive model)

Our observed joint RR is different from our expected joint RR (additive model); thus, we can say that there was an additive interaction between the exposure (coffee consumption) and the effect modifier (physical activity).

The expected joint effect model for multiplicative interaction is as follows:

	Coffee consumption
Physical activity	Non-coffee drinkers	Coffee drinkers
Physically active	RR = 1.0 (Ref.)	RR = 1.80
Physically inactive	RR = 0.72	Expected joint RR (multiplicative) = RR(b) * RR(c) = 1.80 * 0.72 = 1.29

Based on the observation:

Observed joint effect RR ≠ Expected joint effect RR (multiplicative model)

Our observed joint RR is different from our expected joint RR (multiplicative model); thus, we can say that there was a multiplicative interaction between the exposure (coffee consumption) and the effect modifier (physical activity).

11.5 Examples of Effect Modification Justification and Presentation in Behavioral Health

Example 1: Variations in the association between alcohol consumption and history of depressed mood by sex and year level among secondary students in Thailand

The findings presented here are modified from a published article using data from the National School Survey on Alcohol Consumption, Substance Use and Other Health-Risk Behaviors 2016 (Wichaidit et al., 2019). The investigators provided the rationale for the assessment of effect modification as follows:

“A systematic review of the literatures showed that alcohol use was associated with depression in adult population across multiple settings[19]. The association between alcohol use and depression may be particularly strong among younger adolescents[20], yet studies have not systematically assessed this variation. The association may also vary by gender: some studies found that the association between alcohol use and depression is higher among boys[16], although possibly confounded by higher prevalence of substance use comorbidity[20]…. Description of variations in the association between alcohol use and depression between sex and age groups can identify the group where the association is strongest, and help to inform stakeholders with regard to allocation of resources and services accordingly.”

Quoted from the Introduction section (Wichaidit et al., 2019)

Thus:

Exposure = Alcohol consumption

Outcome = History of depressed mood

Effect modifiers = Sex and year level (as a proxy for age group)

Although the investigators did mention knowledge gaps regarding variations in the association between drinking and depressed mood among adolescents by sex and age, the investigators did not offer a strong theoretical framework underlying the variations.

In the same paragraph, the investigators identified potential confounders a priori based on reviewing the scientific literature:

“Other independent predictors of depression that could confound the association between alcohol and depression include family history of depression[3,4], exposure to psychosocial adversity and stressful life events[3,4,21], nature of living arrangements[21], parental behaviors[22], and psychiatric co-morbidities[21].”

Quoted from the Introduction section (Wichaidit et al., 2019)

The findings of the study are shown in Table 11.5.1

 

Table 11.5.1 Association between alcohol consumption over the past year and history of depressed mood among Thai adolescents, overall and stratified

Drinking behavior	Unadjusted OR (95% CI)	Adjusted OR* (95% CI)
All study participants
Past-year drinking (Ref.: No drinking in the past year)	2.12 (1.98, 2.28)	1.78 (1.60, 1.98)
Among girls in Years 7 & 9
Past-year drinking (Ref.: No drinking in the past year)	2.88 (2.51, 3.31)	2.38 (2.03, 2.79)
Among boys in Years 7 & 9
Past-year drinking (Ref.: No drinking in the past year)	2.21 (1.79, 2.74)	1.74 (1.43, 2.11)
Among girls in Year 11 & Vocational Certificate Year 2
Past-year drinking (Ref.: No drinking in the past year)	1.97 (1.69, 2.30)	1.65 (1.34, 2.03)
Among boys in Year 11 & Vocational Certificate Year 2
Past-year drinking (Ref.: No drinking in the past year)	1.43 (1.17, 1.75)	1.19 (0.99, 1.42)

Adapted from a manuscript published in an open access journal (Wichaidit et al., 2019).

Bold text denotes statistical significance.

*Adjusted for region, religion, school type, living situation, grade point average (GPA), smoking, past-year adverse experience, and having at least one parent who had issues with addiction or violence.

The overall measure of association between alcohol consumption and depressed mood is between the strata. The associations were strongest among girls in Years 7 and 9 and weakest among boys in Year 11 or equivalent. The investigators did not perform the Breslow-Day test to assess the extent to which chance was the best explanation for the observed heterogeneity in the association between alcohol consumption and depressed mood.

Example 2: Variations in the association between experience of economic distress and selected behavioral health outcomes by availability of emergency cash reserves

In this nationally representative phone-based cross-sectional study, the investigators assessed “…the extent that the availability of emergency cash reserves modified the association between experience of economic distress during the COVID-19 pandemic and behavioral health outcomes in the general adult population of Thailand” (Wichaidit et al., 2022). The investigators provided the rationale for the assessment of effect modification as follows:

“Studies have found associations between financial distress and depression (Ford et al., 2019), perceived stress, and worsened self-reported general health (Sweet et al., 2013). Based on the family stress model proposed by Pauline Boss (Boss, 2002), a given event or situation (including economic distress) can induce stress at varying degrees, depending on moderation by available resources and perception of the event or situation. A study based on the family stress model showed that economic pressure was associated with money-related stress (Prawitz, Kalkowski & Cohart, 2013), and the association was moderated by financial adjustments (i.e., use of available resources) and perception of the event as being within the internal locus within one’s ability to control, as opposed to an external locus outside of one’s control (i.e., perception).

Emergency cash reserves, also known as “precautionary savings” or “financial emergency fund”, refers to an amount of available cash to help meet “modest unexpected expenses—such as a car repair or a [leaking] roof”(Chen, 2019). Having emergency cash reserves is a type of resource for financial adjustment that has been shown to be associated with subjective well-being (Bell et al., 2014). Availability of emergency cash reserves may also enable individuals experiencing economic distress to perceive an unexpected expense as an issue within their internal locus of control (Prawitz & Cohart, 2016; Dwiastanti, 2017), which would lessen the level of stress and behavioral health issues that the distress can induce. Based on the reviewed literature, we hypothesize that availability of emergency cash reserves may help to moderate the association between economic distress and behavioral health outcomes.”

Quoted from the Introduction section (Wichaidit et al., 2022)

Thus:

Exposure = History of economic distress

Outcome = Behavioral health outcomes (will include only anxiety in this sub-section)

Effect modifier = Availability of emergency cash reserves

One notable difference between the introduction in this example and the previous example is the review of theoretical frameworks (i.e., Pauline Boss’ Family Stress Model and the internal locus of control) and the application of the frameworks to the research question. The investigators also stated a hypothesis that could be tested using the study data, which helped to emphasize deductive reasoning.

The findings of the study are shown in Table 11.5.2.

Table 11.5.2 Association between experience of economic distress and anxiety, overall and stratified by availability of emergency cash reserves

Drinking behavior	No anxiety disorder	Anxiety disorder	Unadjusted OR (95% CI)	Adjusted OR* (95% CI)
All study participants (Overall association) (n = 1498)
Did not experience distress (n = 596)	96.8% ± 0.7%	3.2% ± 0.7%	Reference	Reference
Experienced distress (n = 902)	92.4% ± 0.9%	7.6% ± 0.9%	2.54 (1.53, 4.22)	2.47 (1.45, 4.19)
Among participants with emergency cash reserves (n = 295)
Did not experience distress (n = 187)	98.4% ± 0.9%	1.6% ± 0.9%	Reference	Reference
Experienced distress (n = 108)	96.3% ± 0.9%	3.7% ± 1.8%	2.39 (0.53, 10.87)	3.20 (0.55, 18.79)
Among participants without emergency cash reserves (n = 1203)
Did not experience distress (n = 409)	95.8% ± 1.0%	4.2% ± 1.0%	Reference	Reference
Experienced distress (n = 794)	91.9% ± 1.0%	8.1% ± 1.0%	2.03 (1.17, 3.52)	1.93 (1.09, 3.41)

Adapted from a manuscript published in an open access journal (Wichaidit et al., 2022).

Bold text denotes statistical significance.

Breslow-Day test p-value = 0.851

*Adjusted for sex, age, marital status, education level, and personal monthly income.

The overall measure of association between experience of economic distress and anxiety disorder is between the two stratified measures of association. The association was stronger among participants with emergency cash reserves and weaker among participants without emergency cash reserves, although the difference was not statistically significant (Breslow-Day test p-value = 0.851). The findings of the study did not fully support our hypothesis, as chance could not be ruled out as the best explanation for the observed differences in odds ratios by strata. The investigators thus made the following remarks in the manuscript:

“We did not find evidence of moderation (i.e., effect modification) in the association between experience of economic distress and behavioral health outcomes by availability of emergency cash reserves to support our hypothesis based on the family stress model (Boss, 2002). However, comparison of the overall adjusted OR to the stratified adjusted OR for anxiety disorder and depressive symptoms showed that the overall adjusted OR was between the two strata, which was what we would expect from effect modifiers. Thus the absence of statistical evidence for the moderation should not be considered as evidence that the family stress model was not relevant for the study population.”

Quoted from the Discussion section (Wichaidit et al., 2022)

The R codes needed to replicate the study findings, as well as records of correspondence between peer reviewers and the investigators, are available in the published article online (see References section). Please also note that the details of the study and the constructs presented in this sub-section can be found in greater detail in Chapter 16: Financial Epidemiology.

11.6 Conclusion

Effect modification (also known as interaction) is a natural phenomenon in which the effect measure for one factor varies at different levels of another factor. Effect modifiers are extraneous variables in the association between the exposure and the outcome that are not in the causal pathway. However, confounders alter the association between the exposure and the outcome so it deviates from the truth; therefore, confounders must be controlled. On the other hand, effect modifiers are natural phenomena that must be described, most commonly by performing stratified analyses after describing the overall association. However, not all extraneous variables should be considered effect modifiers. Assessment of effect modification should be based on strong notions regarding the biological or psychosocial mechanisms in which the effect modifier can make the association between an exposure and an outcome particularly strong or weak in certain population subgroups.

References

Porta, M. (Ed.). (2008). A Dictionary of Epidemiology (5th ed.). Oxford University Press.

Wichaidit, W., Prommanee, C., Choocham, S., Chotipanvithayakul, R., & Assanangkornchai, S. (2022). Modification of the association between experience of economic distress during the COVID-19 pandemic and behavioral health outcomes by availability of emergency cash reserves: Findings from a nationally-representative survey in Thailand. PeerJ, 10, e13307. https://doi.org/10.7717/peerj.13307

Wichaidit, W., Pruphetkaew, N., & Assanangkornchai, S. (2019). Variations by sex and age in the association between alcohol use and depressed mood among Thai adolescents. PLOS ONE, 14(12), https://doi.org/10.1371/journal.pone.0225609