Different ceiling approaches to deal with exposure outliers in Cox model settings

Outliers may distort the results of statistical analyses as they often represent extreme values that can arise either legitimately or as a result of measurement error. The purpose of this study is to assess how outlier-handling methods affect survival analysis with continuous exposure variables, using simulation studies based on both synthetic and real-world data. In our simulation study, exposure variables are generated from four distributions: standard normal, chi-squared, the distribution of body mass index, and the distribution of physical activity, with the latter two based on data collected in the 2010 Health Professional Follow-Up Study. Three scenarios are considered: 1) no outliers or measurement error, 2) only true outliers (without measurement error), and 3) outliers induced by measurement error. A commonly-used outlier-handling method is the ceiling/winsorization approach, which replaces outliers with a specified cutoff. In this paper, we propose a less aggressive ceiling method—the tail-median ceiling approach—which replaces the values of potential outliers with their median. In addition to these ceiling approaches, we also evaluate the following outlier-handling methods: (i) trimming extreme observations, (ii) median score transformation. To determine the cutoffs used in the ceiling methods, three boxplot-related rules are considered. Cox proportional hazards models are fitted to estimate the regression coefficient of the exposure, and the estimates are evaluated based on percent bias, empirical standard deviation, 95% confidence interval coverage, Type 1 error rate and statistical power. In the presence of outliers without measurement error, the tail-median ceiling method performs better than both the traditional ceiling and median score methods in terms of bias and efficiency. The tail-median ceiling method typically has an acceptable percent bias when the percentile cutoff for outliers is less than 3rd percentile from both ends. When outliers arise from measurement error, nearly all outlier-handling methods produce less biased estimates than leaving the data unchanged, although no single method consistently delivers satisfactory results. It is important to differentiate between true outliers without measurement error and outliers induced by measurement error. In scenarios involving true outliers, the tail-median ceiling method outperforms both the median score and traditional ceiling methods.