[Analysis of left-censored quantitative outcome: example of procalcitonin level]

When the sensitivity of an assay used to quantify a marker is poor, some of the values are below the detection limit resulting in left-censoring. Analysis of such data requires appropriate statistical techniques. In this study, we aimed at comparing various methods used to deal with left-censored outcome in regression analysis.

The application was a real study evaluating the performance of procalcitonin for the diagnosis of bacterial infections among elderly patients. Among 85 patients, eleven had a procalcitonin value below the detection limit. A simulation study was then performed with data sampled according to a Gaussian distribution with parameters estimated on observed data. Various levels of left-censoring were simulated (13, 25 and 50%). A linear regression model was used to explain procalcitonin variations according to another marker, C reactive protein. To handle left-censoring, several methods were used: complete case analysis, simple imputation and multiple imputation methods, and parametric modelling. In the simulation study, estimations according to different methods were compared in terms of bias and mean square error according to each left-censoring level. Estimations obtained with real data were also compared according to the methods used. All analyses were implemented using SAS software.

In the simulation study, parametric modelling using maximum likelihood showed best performances whatever the level of censoring. On the other hand, methods using complete cases and simple imputation by the detection limit were highly skewed. On observed data, estimations of the slope varied slightly according to the methods. However the p-values (Wald test) of beta=0 varied from 0.0001 to 0.13 leading to different decisions according to the method used.

Left-censoring handling in data analysis requires special attention, as different methods may yield results leading to different conclusions.