If you want to have a good belly laugh, I recommend searching the web for "comical causation vs correlation relationships." Among the spurious correlations that I found funniest were "each day in the US, over 6000 people exposed to tap water will die," or "as sunscreen use increases, the number of shark attacks goes up," or "as the use of indoor air-conditioning has increased worldwide, global temperatures have risen." So, the old adage "relationships are tricky" applies to situations far beyond the interpersonal. And it's because relationships are so tricky that statistical tests never "prove" that a relationship exists; instead by rejecting the null hypothesis, statistics merely quantify the probability that no relationship exists.

There is definitive evidence from both basic and clinical research demonstrating that practice and training are central to favorable functional outcomes. Accordingly, there is value in exploring the different ways that these key elements of neurologic physical therapy have their influence. This exploration also provides an opportunity to consider the many different ways that relationships between the 2 variables in which we are most interested, our intervention (ie, independent variable [or predictor]) and the outcome (dependent variable), can be influenced by a third variable that we may or may not have considered. One way to group these third variables is by whether they lie on the causal pathway (ie, mediators and moderators) or they do not lie on the causal pathway (confounders and covariates),1,2 as illustrated in the Figure. In essence, variables that lie on the causal pathway can be said to contribute to the "active ingredient" that result in a change in the outcome of interest.

Figure. When exploring the "active ingredient" in neurorehabilitation, the primary focus is generally on the causal pathway (black arrow) that directly links the intervention to the outcome. However, it is important to consider the influence of mediators and moderators (which lie on the causal pathway [gray arrows]), as well as confounders and covariates (which do not lie on the causal pathway [open arrows]).

Mediators are intervening variables that lie along the causal pathway between the intervention and the outcome of interest. For instance, published studies have shown that high-intensity aerobic exercise augments the effects of repetitive task-practice training on upper extremity function in persons with stroke.3 There is also evidence that aerobic activity increases the concentration of the brain-derived neurotropic factor (BDNF), which is associated with use-dependent plasticity in persons with stroke.4 This may suggest that increased BDNF concentrations mediate the effects of the aerobic training + repetitive task practice training, and if so, then some of the effects of the intervention are mediated by the BDNF.

Moderators are variables that change the size (or direction) of the relationship between the intervention and the outcome. A moderator may either have a direct effect on the outcome, or it may interact with the intervention in a way that influences the relationship between the intervention and the outcome. As an example, there is evidence that, in older adults, the relationship between self-rated memory function and depressive symptoms is different among those with high versus low ratings of self-efficacy.5 If so, self-efficacy may moderate the relationship between self-rated memory function and depressive symptoms. Moderators can account for some of the variability in outcomes, and answer certain questions about who will be most responsive to a treatment. As part of study design, known or potential modifiers may be valuable for stratification in randomized studies.

Confounders are variables that are related to both the intervention and the outcome, but are not on the causal pathway. For example, individuals who have lower functional status may be less able to perform high levels of repetitions in a study of repetitive task practice training (independent variable), and may also have lower scores on functional outcomes (dependent variable). Because functional status is related both to the intervention and the outcome, this confounding variable may represent an alternate reason for the results observed in a study.

Covariates are variables that explain a part of the variability in the outcome. Covariates are not influenced by the intervention, and do not change the relationship between the intervention and the outcome. On their own, covariates predict at least part of the outcome in both the intervention group and the comparison/control group. Age and sex are classic covariates, and in the stroke literature lesion size/type and corticospinal tract integrity are also common covariates. There is also growing recognition that it maybe important to consider genetic factors as covariates.6

Consideration of the way mediators and moderators influence the outcomes of an intervention can form the basis of a mechanistic rationale for the combination of interventions. It is valuable to keep in mind that whether a variable is acting as a mediator, moderator, confounder, or covariate is not an inherent property of the variable. The role played by a variable depends how it is related to the intervention and outcome measure in a particular study. For this reason, a variable that is a moderator in one study may be a covariate in another study. Understanding the potential influence of parameters that are not the focus of a study is important for identifying what interventions work, for whom they work, when they work best, and in what settings they are most useful.

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