To use or not to use Sobel's test for hypothesis testing of indirect effects and confidence interval estimation

Traditionally in epidemiology and social sciences computation of the mediated effect involves performing 2 regressions. First to fit a linear regression using outcome, exposure, and confounders, and second to fit a linear regression using outcome, exposure, mediator, and confounder. The coefficient of the exposure (say q1) from first regression is treated as the total effect of the exposure onto the outcome and the coefficient of the exposure (say f1) from the second regression is treated as the direct effect of the exposure onto the outcome. The difference in these 2 coefficients (q1 f1Þ is attributed as the indirect effect. Following the seminal work of Baron and Kenny (hereafter referred to as BK) [1] an alternate way for computing the indirect effect was developed which also comprises of carrying out 2 regressions; (a) to fit linear regression of the mediator, exposure, and confounder and (b) to fit the linear regression of the outcome with exposure, mediator, and confounders. The indirect effect under BK approach is computed using the product of the regression coefficient of the exposure (say g) from regression (a) and the regression coefficient (say a) of the mediator from regression (b), this is commonly referred to as the product approach (g a). When the outcome and mediator are continuously measured, and the regression model is a linear model fit using ordinary least squares, both the above approaches yield same indirect effect. However, estimates from traditional and BK methods do not coincide when different sample sizes are used [2] and when the outcome/mediator are measured as binary or count variable