This fourth article in a seven part series presents the Core GRADE (Grading of Recommendations Assessment, Development and Evaluation) approach to addressing risk of bias, publication bias, and rating up certainty. In Core GRADE, randomised controlled trials begin as high certainty evidence and non-randomised studies of interventions (NRSI) as low certainty. To assess certainty of evidence for risk of bias, Core GRADE users first classify individual studies as low or high risk of bias. Decisions regarding rating down for risk of bias will depend on the weights of high and low risk of bias studies and similarities or differences between the results of high and low risk of bias studies. For publication bias, a body of evidence comprising small studies funded by industry should raise suspicion. Core GRADE users appraising results from well conducted NSRI can consider rating up certainty of evidence when risk ratios from pooled estimates suggest large or very large effects.