We consider the effect on estimation of simultaneous variable centering and interaction effects in linear regression. We technically define, review, and amplify many of the statistical issues for interaction models with centering in order to create a useful and compact reference for teachers, students, and applied researchers. In addition, we investigate a sequence of models that have an interaction effect and/or variable centering and derive expressions for the change in the regression coefficients between models from both an intuitive and mathematical perspective. We demonstrate how these topics may be employed to motivate discussion of other important areas, e.g., misspecification bias, multicollinearity, design of experiments, and regression surfaces. This paper presents a number of results also given elsewhere but in a form that gives a unified view of the topic. The examples cited are from the area of medical statistics.1

A gastrointestinal-renal kaliuretic signaling axis has been proposed to regulate potassium excretion in response to acute potassium ingestion independent of the extracellular potassium concentration and aldosterone. Here we studied this presumed axis in 32 individuals in our clinical pharmacology unit while on a 20 mmol sodium and 60 mmol potassium diet. The serum potassium concentration, potassium excretion, aldosterone, and insulin were measured following either a 35 mmol oral potassium load, a potassium- and sodium-deficient complex meal, or a potassium-deficient complex meal plus 35 mmol potassium. This design allowed determination of the component effects on potassium handling of the meal and potassium load separately. The meal plus potassium test was repeated following aldosterone blockade with eplerenone to specifically evaluate the role of aldosterone. In response to the potassium-deficient meal plus 35 mmol potassium, the serum potassium did not increase but the hourly mean potassium excretion increased sharply. This kaliuresis persisted following aldosterone blockade with eplerenone, further suggesting independence from aldosterone. Thus, a gastrointestinal-renal kaliuretic signaling axis exists in humans mediating potassium excretion independent of changes in the serum potassium concentration and aldosterone. The implication of this mechanism is yet to be determined but may account for a significant component of potassium excretion following a complex potassium-rich meal.

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The combination of an aldosterone receptor antagonist added to an angiotensin-converting enzyme inhibitor has been demonstrated to reduce cardiovascular and renal end points in hypertensive humans but can produce hyperkalemia in the common clinical setting of impaired renal function. We investigated the effects of dual therapy on acute and chronic potassium handling in hypertensive humans with renal impairment by conducting a randomized crossover clinical trial of 4 weeks of 40 mg lisinopril/25 mg spironolactone versus placebo in 18 participants with a glomerular filtration rate of 25 to 65 mL/min. Study end points, following an established protocol, were hourly determinations of dynamic renal potassium excretion (mmol/h) and serum potassium (mmol/L) after 35 mmol oral potassium challenge in addition to ambulatory potassium concentration. After 4 weeks, ambulatory potassium concentration was 4.87 mmol/L with lisinopril/spironolactone versus 4.37 with placebo (P<0.001). Lisinopril/spironolactone produced only a modest 0.44 mmol/h reduction in stimulated potassium excretion (P=0.03) but a substantial 0.67 mmol/L increase in serum potassium (P<0.001) in response to 35 mmol potassium; these findings are consistent with impaired extrarenal/transcellular potassium disposition. We found the increase in serum potassium after an oral potassium challenge to be a strong predictor of the increase in ambulatory potassium with lisinopril/spironolactone. Our study suggests that dual renin-angiotensin-aldosterone blockade may impair extrarenal/transcellular potassium disposition in addition to reducing potassium excretion in humans with renal impairment, and that acute changes in dynamic potassium handling are predictive of chronic changes in ambulatory potassium concentration with dual renin-angiotensin-aldosterone blockade.

Multilevel modeling is an increasingly