Modeling Hospital Length of Stay Data: Pitfalls and Opportunities

Abstract

Hospital length of stay (LOS) represents an important resource utilization aspect in adult cardiac surgery. Ad and colleagues' [1] recent paper identifies significant modifiable clinical variables that are predictive of LOS. A multivariate linear regression predictive model is used to produce expected LOS values and observed-to-expected summary ratios are created for short (<6 days) and extended LOS (>14 days). This ratio is equal to 1.4 in the first group and 0.84 in the second group.Predictive models should avoid overfitting and be well calibrated [2,3]. Overfitting occurs when the model captures important data features and some of the sample's random noise. To objectively evaluate the predictive performance of a model, first model building should occur on a training dataset and its validation on an external dataset [2]. Judging the performance of a model on the training dataset (called the model's apparent performance) is known to produce overly optimistic model performance.There are ways to reduce or avoid overfitting, such as splitting the data into training and testing subsets. Other methods involve resampling, in which this process is repeated dozens or hundreds of times and the results are aggregated. Specific resampling techniques are k-fold cross-validation, generalized cross-validation, or bootstrapping. Upon model selection, calibration is the process of adjusting the model coefficients to ensure that observed and model-based expected values are in good agreement.A question remains whether the observed-to-expected LOS ratios in [1] being different from one reflect a true, underlying clinical reality (that one could also replicate on an external dataset), or the multivariable model's apparent performance. Perhaps resampling could shed some light on this matter.Furthermore, LOS data are generally right-skewed and ordinary least squares regression does not adequately accommodate large LOS values. When used for prediction, least squares regression will produce expected LOS values that follow a bellshaped distribution, in contradiction with the right-skewed observed LOS in Figure 1 of Ad and colleagues [1]. Figure 2 in Ad and colleagues [1] shows that expected LOS values (y-axis) are shorter than the observed LOS (x-axis), fact confirmed by the Pearson correlation of 0.632 (1). Alternative approaches to modeling LOS data involve normality-improving data transformations or Poisson regression.We appreciate Dr Andrei's comments [1] on our study [2] in which we sought to assess the reliability of the Society of Thoracic Surgeons (STS) risk prediction for extended and shorter LOS and examine whether modifiable clinical variables are associated with length of stay (LOS) in first-time cardiac surgery patients. We examined the data from more than 3,000 cardiac surgery patients at our center and found that the STS risk model was reliably predictive of short and extended LOS. In addition, our analyses found that potentially modifiable clinical variables, such as low preoperative hematocrit and blood transfusion, wer...

Analyzing the Correlation Between Surgeon Experience and Patient Length of Hospital Stay

“…Analysis of the patient's LOS against a surgeon's experience was conducted via a GLM instead of a linear regression as the response variable is a count variable and would violate the conditions of a linear regression analysis with normality assumption [15]. We used the GLM model for the Poisson distribution with a logit link function.…”

Hospital Length of Stay: A cross-Specialty Analysis and Beta-Geometric Model

“…Ad et al [10] is typical of such a modeling approach, which the authors remark in [11] is not of their own design but a more than 30 years old standard risk model of the Society of Thoracic Surgeons [12]. High LOS admissions are known to have a prominent financial impact.…”

“…The problem with mixture probabilities may be overfitting, especially with the small sample sizes that are typically considered. As noted in [11], this is an important pitfall in modeling LOS.…”

“…A recent debate [11] concerning the statistical representation of LOS is a thoracic surgery department [10] highlighted the prevalence of thin-tailed statistical modeled in this context.…”

Length of hospital stay, diuretic dosing, and regression strategies

“…First, it is well known that the “length of stay” has a right skewed distribution (2, 3). Accordingly, the mean length of stay was 7.9±6.4 days, which was found to be not distributed normally [large standard deviation (SD)].…”