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Interactions

Do these two variables have a relationship with each other as well as with the outcome, or there is strong evidence in the literature showing that these variables have an interactive effect?

If interaction exists, there will be significantly different slopes in the two variable lines. So, plot the results as graphs; if necessary set the other variables to their mean for calculation.

When the effects of breastfeeding or bottle feeding on infant mortality were studied from a Malaysian Family Life Survey, it was found that the effects of breastfeeding were strongly positive for decreasing infant mortality when sanitation was poor; bottle feeding was very dangerous under these conditions. But when sanitation was better there was much less effect (Habicht J-P, Da Vazano J, Butz BA:  Mother's Milk and Sewage: Their Interactive Effects on Infant Mortality.  Pediatrics 1988;81:456-461.). The effects of breast- or bottle-feeding on infant mortality are said to be synergistic; and the relationship analytically is interactive. Specifically, the effects on the outcome -- mortality -- of each independent factor when operating together are more than additive.

For malaria to occur in a certain area two factors need to exist at the same time: the parasite must be in the environment, and mosquitoes must be around to transmit the parasite. Much of Africa is in this situation, and malaria is a grave problem. However, at high altitude or in developed urban areas, there are no mosquitoes and malaria is not transmitted, even though the parasite is certainly infecting a part of the population that travels in and out of the area. Similarly, in many parts of the world mosquitoes are plentiful -- even in Alaska -- but malaria is not transmitted as there are few if any carriers. This is another biological synergism, which would be seen as an interaction in analysis, something like this:

Prevalence of malaria

Parasite in environment? Mosquito in environment?
Yes No
Yes High None
No None None

 

For program design, it is important to determine whether significant interactions are occurring, as this can determine whether you need two interventions to get an effect, or whether one or another may be expected to have an impact. In the malaria example, either no mosquitoes or no parasites will lead to no malaria problem. In the breastfeeding example, the table in general terms looks like this:

Actual Perinatal Infant Mortality Rates by Sanitation and Breastfeeding

Sanitation and Water

Feeding

Bottle Breast
Poor 196 per 1000 52 per 1000
Good 27 per 1000 17 per 1000

 

Here again a synergism of inappropriate feeding and poor sanitation causes the poor outcome; but fix one or the other and the problem is solved (or reduced).

This illustrates a general principle: when two factors acting together cause a problem -- when you need factor 1 AND factor 2, an intervention that reduces factor 1 OR factor 2 will be effective. Specifically, in contrast to what is sometimes heard, a multi-factoral problem does NOT necessarily call for a multiple response; indeed if there are synergisms or interactions there may be opportunities for very economical single interventions.

The effects can be in the other direction too. For example, EITHER poor water supply OR poor sanitation may cause diarrhea, in which case BOTH need to be fixed to improve child health. This can go either way depending on circumstances, which is one reason that these two factors usually should be examined together as a routine part of analysis of nutritional data (and have been used for illustration in several parts of the PANDA). When the two factors do not affect each other -- in other words do not interact -- their effects will be additive and no significant interaction will be found. If they are less than additive, this will also be picked up as an interaction.

One easy way to see and interpret interactions is through standard graphs. Here, the outcome is (as usual) on the vertical y-axis, and two categories of a factor are on the x-axis; two lines are drawn for the two possibilities of the other factor. For example in the malaria example, malaria prevalence might be on the y-axis, parasite in the environment -- no/yes -- as the two points on the x-axis, and two lines drawn for mosquitoes in the environment -- no/yes again. The result will look like this:

Mean Prevalence of Malaria by Presence of Parasite and Vector (Mosquito) in the Environment

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Similar results can be seen for the feeding and sanitation example. What we look for is significant differences in slope. If the slopes are the same, the effects are additive, and there is no interaction. You should get in the habit of sketching out these graphs -- that’s all that’s needed -- as a usual way of clarifying what’s being found, and talking about the results. One possible finding from Water and Sanitation Interaction is shown for Bangladesh if you CLICK HERE .

Results from analyzing water and sanitation effects on underweight vary a lot depending on conditions, and can go either way in terms of their combined effect. This is not surprising, since both can contribute to transmission of diarrheal disease, but depending on different circumstances one may or may not act synergistically with the other. For instance, bad toilet facilities may not affect diarrhea transmission if there is plentiful water and good hygienic habits; and so on. At the extremes, three combinations are possible -- additive, no interaction; more than additive, when you need both conditions bad; and less than additive, when either condition bad will cause the problem. The two latter will analytically give significant interactions, and are readily displayed using ‘two-by-two graphs’, like this:

Graph 1:

NO INTERACTION: The chart below shows an example of water and sanitation without interaction. Both water and sanitation have an effect, independent of one another and improving either will lead to some improvement in the outcome (prevalence of underweight) and the improvement of both will be even more effective (but not necessarily cost-effective).

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Graph 2:

MORE THAN ADDITIVE: "normal" synergism, where improving only one factor will lead to the improvement in malnutrition and improving both factors will not lead to any additional effect.

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Graph 3:

LESS THAN ADDITIVE: When the results are less than additive, neither factor shows an effect when improved alone because both are needed to see an improvement.

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Interaction is the independent operation of two or more causes to produce or prevent an effect. It can also define different effects of one or more factors depending on the levels of the other factor, in which case it is referred to as an effect modifier.

 

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Interaction can be very important in program design. The results determine when it is likely to need two interventions together to get an effect; or, as in the previous case with water and latrine with low arm circumference, it tells when only one or the other intervention is necessary for the same effect. Some of the terms for detecting interaction include: 

Logical reasons must arise that make looking for an interaction worthwhile, for example, 1) Will there be a bigger effect of improving breast feeding practices in the poor? 2) Will a behavioral change intervention only work with literate mothers? Beyond these logical explorations, looking for interactions for the fun of it will only lead to confusion and most likely lost time. 
The next section on regression will cover interaction in more detail. In regression, multiplying two variables of interest together creates interaction variables. Often at least one of these will be a dummy variable.
Plotting interaction results as graphs will result in lines with noticeably different slopes. This is the meaning of interaction.

Find more on interaction in the REGRESSION section that follows.

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