Estimating median hospital charges and confidence intervals for multiple imputed data using quantile regression

Background

Hospital charges are an important outcome in injury control research; however, these typically skewed distributions present analytic challenges. When analyzing charges, the median may be preferred to the mean due to its robustness to extreme values. The Crash Outcome Data Evaluation System (CODES) uses multiple imputed probabilistically linked motor vehicle crash and hospital outcomes (including charges) data. A maximum likelihood estimate (MLE) of the median assumes that transformed charges follow a normal distribution, and is estimable via the sample mean for imputed data. We present an alternative solution, the quantile regression estimate (QRE), which does not rely on distributional assumptions of normality.  

Methods

Simulations were performed to compare the QRE and MLE of the median using CODES data and charges drawn from a transformed-normal (lognormal) distribution in terms of bias and coverage probability of 95% confidence intervals for the population median.

Results

Considerable differences were noted between the QRE and MLE for six CODES datasets of varying size (4,827 to 1,366,321 records). When charges were simulated based on observed CODES charges, the MLE estimate was biased upwards ($2,604) and had poor coverage (6%) while the QRE estimate had negligible bias ($58) and good coverage (96%).  When charges were drawn from a lognormal distribution, QRE and MLE estimates had negligible bias and close to expected coverage (94% and 92%, respectively).

Conclusions

The QRE is robust to distributional assumptions, whereas the MLEs dependence on the existence of an appropriate transformation limits its usefulness.

 

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