Using Planned Missing Data to Leverage Resources in a Single Mediator Model

Prevention researchers often use mediation analyses to understand the causal chain of relations between variables. Because resources typically limit the choice of measures and number of participants in a study, researchers often choose between collecting a large sample of data with an inexpensive measure or collecting a smaller sample of data with a more expensive measure. To address issues of limited resources in study design, a design with purposeful missing data may maximize power and reduce cost by collecting data from a large sample of participants with the inexpensive mediator(s) and a small subsample with the expensive measure.

Method: A Monte Carlo simulation study evaluated the utility of a planned missing data design in a mediation analysis that incorporates multiple measures of the same mediation construct. Data are generated from a latent variable mediation model with manifest X and Y variables and a latent mediator variable with 3 observed indicator variables, M₁ - M₃. The following factors were manipulated: missingness (20, 50, & 80%) under the missing completely at random mechanism on variable M₁;  loadings of the 3 mediation measures to reflect small, medium, and large loadings; mediated effect size (all combinations of zero, small, medium, & large paths); and sample size (N = 100, 200, 500, & 1000). I evaluated 5 approaches of incorporating available measures into an analysis: a latent variable model where all 3 mediators are indicators of a latent mediation construct (Method 1), an auxiliary variable model where M₁ is the mediator, and the other mediation variables are auxiliary variables (Method 2), an auxiliary variable model where M₁ is the mediator, and M₂ serves as a single auxiliary variable (Method 3), an analysis using maximum likelihood estimation including  all available data but incorporating only one mediator, M₁  (Method 4), and  an analysis using listwise deletion and incorporating only one mediator, M₁ (Method 5).

Results: The main outcome of interest was power to detect the mediated effect. The main effects of mediation effect size, sample size, and missing rate performed as expected with power increasing for increasing effect sizes, increasing N, and decreasing missing rates. Power was the greatest for analysis methods that included all 3 mediators, and power decreased with analysis methods that included fewer variables.  Across all design cells relative to the complete data condition, the latent variable model (Method 1) with 20% missingness on M₁ produced only 2.06% loss in power for the mediated effect; with 50% missingness, 6.02% loss; and 80% missingess, only 11.86% loss. Method 2 exhibited 20.72% power loss at 80% missingness, even though the total amount of data utilized was the same as Method 1. Methods 3 –  5, based on fewer variables, exhibited greater power loss. Compared to an average power loss of 11.55% across all levels of missingness for Method 1, average power losses for Methods 3, 4, and 5, were 23.87%, 29.35%, and 32.40%, respectively.

Conclusion. A planned missing design in mediation analysis may benefit researchers in terms of quality of the mediator, financial cost, and statistical power to detect the mediated effect.