Estimating Sample Size Required to Establish an Association Between Walnut Intake and Cognitive Change in Older Adults: An Application of Monte Carlo Power Analysis

Objectives
Observational studies support a cross-sectional association between walnut intake and cognitive function among older adults, but few of these studies identify walnut intake as a predictor of cognitive change. This project estimates the sample size required to establish a statistically significant association between walnut intake and cognitive change in an observational study using Monte Carlo power analysis.

Methods
Initial observations were drawn from the 2012, 2014, and 2016 Health and Retirement Study (HRS) and the 2013 Health Care and Nutrition Study (HCNS; age ≥ 65, n = 3632). Global cognitive function was measured using the Telephone Interview for Cognitive Status and two operationalizations of walnut intake were investigated (none, low intake (.01 – .08 servings/day), and moderate intake (> .08 servings/day); no intake vs. any intake). Latent growth models adjusting for covariates and complex sample design were used to estimate age-based developmental trajectories of TICS scores as a function of walnut intake. Parameter estimates from these models were used as starting values in Monte Carlo simulation models replicated for sample sizes from 1000–50,000.

Results
Model estimation required around 1200 hours of processing time. When measured as a trichotomous variable, the observed association between walnut intake and cognitive change was weak (for moderate intake, b = −0.030, SE = .03) and would require at least 42,000 observations to reduce the standard error to a level where 80% or more of random samples would identify the effect as statistically significant (P < .05). When measured as a dichotomous variable, the observed effect was small (b = −0.013, SE = 0.025) and required a sample size of at least 39,000 observations to identify power above .80.

Conclusions
Given that the HRS and HCNS are nationally-representative studies, the population size from which an adequate sample would need to be drawn to identify walnut intake as a significant predictor of cognitive decline would exceed the number of adults age 65 and older currently living in the US. Rather than increase sample size of observational studies, researchers should apply quasi-experimental methods and detailed measurement of walnut intake to establish an association between walnut intake and cognitive change.