Interpreting interactions of ordinal or continuous variables in moderated regression using the zero slope comparison: tutorial, new extensions, and cancer symptom applications

Using an innovative multiple regression procedure in a cancer population (Part 1): detecting and probing relationships of common interacting symptoms (pain, fatigue/weakness, sleep problems) as a strategy to discover influential symptom pairs and clusters

Background

The majority of patients with advanced cancer experience symptom pairs or clusters among pain, fatigue, and insomnia. Improved methods are needed to detect and interpret interactions among symptoms or diesease markers to reveal influential pairs or clusters. In prior work, I developed and validated sequential residual centering (SRC), a method that improves the sensitivity of multiple regression to detect interactions among predictors, by conditioning for multicollinearity (shared variation) among interactions and component predictors.

Materials and methods

Using a hypothetical three-way interaction among pain, fatigue, and sleep to predict depressive affect, I derive and explain SRC multiple regression. Subsequently, I estimate raw and SRC multiple regressions using real data for these symptoms from 268 palliative radiation outpatients.

Results

Unlike raw regression, SRC reveals that the three-way interaction (pain × fatigue/weakness × sleep problems) is statistically significant. In follow-up analyses, the relationship between pain and depressive affect is aggravated (magnified) within two partial ranges: 1) complete-to-some control over fatigue/weakness when there is complete control over sleep problems (ie, a subset of the pain–fatigue/weakness symptom pair), and 2) no control over fatigue/weakness when there is some-to-no control over sleep problems (ie, a subset of the pain–fatigue/weakness–sleep problems symptom cluster). Otherwise, the relationship weakens (buffering) as control over fatigue/weakness or sleep problems diminishes.

Conclusion

By reducing the standard error, SRC unmasks a three-way interaction comprising a symptom pair and cluster. Low-to-moderate levels of the moderator variable for fatigue/weakness magnify the relationship between pain and depressive affect. However, when the comoderator variable for sleep problems accompanies fatigue/weakness, only frequent or unrelenting levels of both symptoms magnify the relationship. These findings suggest that a countervailing mechanism involving depressive affect could account for the effectiveness of a cognitive behavioral intervention to reduce the severity of a pain, fatigue, and sleep disturbance cluster in a previous randomized trial.