What are the heteroskedasticity and autocorrelation of residuals? 

To be reliable, a multivariate analysis model has to verify some conditions. Two of them are homoskedasticity and non autocorrelation of residuals. 

Heteroskedasticity (=non homoskedasticity) of residuals is defined as the presence of a relationship between the residuals of the model and the value of one or a set of explanatory variables. This means that the coefficients of the model should not be the same for all the sample, but should have different values for subset of the sample. In this case, the coefficients computed by the regression will be unreliable. 

Autocorrelation of residuals is defined as the presence of a relationship between the residuals. In this case, the value of the variable to explain for a subgroup of patients depends on the value of the variable to explain for another subgroup of patients. 

How are assessed heteroskedasticity and autocorrelation in EMS?

In EMS, residuals heteroskedasticity is assessed by the Levene's test or the White's test, depending of the number of patients included in the multivariate analysis (threshold at 200 subjects).
Residuals autocorrelation is not yet assessed.

What is the Newey-West correction?

Newey and West (1987) proposed a new way to compute the coefficients of regression analysis to ensure their reliability in presence of residuals heteroskedasticity and/or autocorrelation. On EMS, the Newey-West correction is  automatically applied if a heteroskedasticity is detected.

For more details, see this article:

Newey, Whitney K., and Kenneth D. West. "A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix." Econometrica 55, no. 3 (1987): 703-08. Accessed November 16, 2020. doi:10.2307/1913610.