Reflections on modern methods: demystifying robust standard errors for epidemiologists

All statistical estimates from data have uncertainty due to sampling variability. A standard error is one measure of uncertainty of a sample estimate (such as the mean of a set of observations or a regression coefficient). Standard errors are usually calculated based on assumptions underpinning the statistical model used in the estimation. However, there are situations in which some assumptions of the statistical model including the variance or covariance of the outcome across observations are violated, which leads to biased standard errors. One simple remedy is to userobust standard errors, which are robust to violations of certain assumptions of the statistical model. Robust standard errors are frequently used in clinical papers (e.g. to account for clustering of observations), although the underlying concepts behind robust standard errors and when to use them are often not well understood. In this paper, we demystify robust standard errors using several worked examples in simple situations in which model assumptions involving the variance or covariance of the outcome are misspecified. These are: (i) when the observed variances are different, (ii) when the variance specified in the model is wrong and (iii) when the assumption of independence is wrong.