7. Multidimensional Bias Analysis

The preceding three chapters have described the techniques for conducting simple bias analysis to assess errors caused by selection bias, residual confounding, or misclassification. However, simple bias analysis implies that the researcher has one and only one estimate to assign to each of the values for the error model’s bias parameters. In many situations, that is not the case. There are many bias parameters for which validation data do not exist, so the values assigned to the bias parameter are educated guesses. In this situation, the analyst is better served by making more than one educated guess for each value and then combining values in different sets. In other situations, multiple different measures of the bias parameter may exist, and there may be no basis for the analyst to select just one as the best estimate of the truth from among those available. For example, when both internal and external validation studies have been conducted, or there were multiple external estimates each in populations slightly different to the one under study, the analyst has no basis to select one value for the bias parameter over another. Frequently, internal estimates are more useful than external estimates because they derive from the same source population as yielded the study’s estimate of association. If there is the possibility of selection bias into the internal validation study, however, then it is possible that the subjects included in the validation study do not provide a good estimate of the bias parameter in the remainder of the study population. In this situation, the analyst may want to use values informed by all of the available validation studies as independent estimates.

Multidimensional bias analysis is a direct extension of simple bias analysis whereby the methods for simple bias analysis are repeated with a range of values for the bias parameter(s). This method provides the researcher with some information regarding the range of estimates of association that are possible, given different assumptions regarding the value of the bias parameters. For example, if there are no data regarding the bias parameters, then multidimensional bias analysis could be used to determine the minimum amount of bias that would convert a positive association to a null association. The analyst could then assess the plausibility of the values that must be assigned to the bias parameters to accomplish the conversion.