Centring in regression analyses: a strategy to prevent errors in statistical inference.

Regression analyses are perhaps the most widely used statistical tools in medical research. Centring in regression analyses seldom appears to be covered in training and is not commonly reported in research papers. Centring is the process of selecting a reference value for each predictor and coding the data based on that reference value so that each regression coefficient that is estimated and tested is relevant to the research question. Using non-centred data in regression analysis, which refers to the common practice of entering predictors in their original score format, often leads to inconsistent and misleading results. There is very little cost to unnecessary centring, but the costs of not centring when it is necessary can be major. Thus, it would be better always to centre in regression analyses. We propose a simple default centring strategy: (1) code all binary independent variables +1/2; (2) code all ordinal independent variables as deviations from their median; (3) code all 'dummy variables' for categorical independent variables having m possible responses as 1 - 1/m and -1/m instead of 1 and 0; (4) compute interaction terms from centred predictors. Using this default strategy when there is no compelling evidence to centre protects against most errors in statistical inference and its routine use sensitizes users to centring issues.