Analysing indicators of performance, satisfaction, or safety using empirical logit transformation

Performance, satisfaction, and safety indicators are commonly measured on a percentage scale. Such indicators are often subject to ceiling or floor effects and performance may be inherently non-linear. For example, improving from 85% to 95% might be more difficult and need more effort than improving from 55% to 65%. As such, analysis of these indicators is not always straightforward and standard linear analysis could be problematic. We present the most common approach to dealing with this problem: a logit transformation of the score, following which standard linear analysis can be conducted on the transformed score. We also demonstrate how estimates can be back-transformed to percentages for easier communication of findings. In this paper, we discuss the benefits of this method, use algebra to describe the relevant steps in the transformation process, provide guidance on interpretation, and provide a tool for analysis.Summary boxPerformance, satisfaction, or safety indicators in healthcare are commonly measured on a percentage scaleStandard linear analysis could be problematic owing to ceiling or floor effects or non-linearityA logit transformation of the score is the most common solutionEstimates can be back-transformed to percentages for a more intuitive interpretationIn recent years, efforts to improve the quality and safety of healthcare have resulted in the introduction of systems for monitoring the performance of healthcare providers and the satisfaction and safety of patients. New quality and performance indicators have been created, to which financial and reputational rewards for providers are often attached. Although performance indicators are measured for each patient, they are often only reported in aggregate form (eg, at the practice or hospital level). Therefore, an indicator that begins as a binary outcome (that is, the target is either met or not met for each patient),1 becomes a proportion (that is, the percentage of patients for whom …