Length of stay is one of the most frequently used metrics for quality measurement in intensive care units (ICUs). Its definition is deceptively simple: discharge date-time minus admission date-time. There are varying opinions about when admission to the ICU begins and when a patient is considered discharged from the unit. For this article let’s assume that only one true definition exists for each of these time points, as I want to explore what goes into comprising length of stay, and how that can play a part in misleading researchers and healthcare executives.

Figure 1 below gives the LOS distribution for patients admitted to an ICU. (Data courtesy of MDN’s ICUTracker software).

**Figure 1. Distribution of Unadjusted ICU Length of Stay (days)**

The distribution is highly skewed to the right. This makes analyzing ICULOS problematic. There are two possible remedies: truncate the values at a set maximum, for example 30 days; or take a log transformation. If we do the latter we get what’s shown in Figure 2 below. The frequency of LOS looks fairly symmetric and close to a normal distribution.

**Figure 2. Distribution of Log-Transformed ICU length of Stay (days)**

So let’s go with the log transformation. To compare ICUs, we take the mean value for each unit. Right? Not so fast. There are numerous factors that affect how long a patient stays in the ICU, which must be accounted for, or the results can be misleading.

What sort of components might influence LOS for a particular ICU? Performance of the ICU clinical staff; case-mix of the patients; ICU-specific factors (e.g. open or closed management, type of ICU, availability of step-down units in the hospital, etc…); and so-called random factors. (The latter are really comprised of both unmeasured variables and truly random variation). Each of those components has a unique distribution, which we’ll assume are independent and additive. That’s probably not realistic but it’s a decent starting point.

Given that there are four components affecting LOS, and only one corresponds to clinician performance, it’s imperative to adjust for patient case-mix and ICU-specific factors. There are various ways to do that, which are beyond the scope of this article. However I’ve gone ahead and applied one of these methods to arrive at the individual components that were influencing the values in Figure 2. The results (converted back into the original units of days) are shown in Figure 3 below. Doctors and hospitals are both centered on zero, meaning that their influence might subtract from or add to a patient’s LOS.

**Figure 3. Distribution of LOS and its individual components**

Random factors are thought to be unexpected or unmeasured events that might prolong LOS, e.g. lack of bed space on the general wards. Finally, there is the expected LOS due to the patients (diagnosis, physiology, medications, comorbidities, etc..). Since patient-related factors are the most important feature, their distribution is the most similar to the measured LOS; but not identical. In this example it is the patient-related factors that induce skewness in overall LOS.

From Figure 3 it is easy to see why evaluating ICUs based on raw LOS would be fraught with errors. The best way to evaluate LOS is to adjust for patient-related factors and then look at the residuals. While residuals are a mix of hospital doctor, and random factors, they give a clearer picture of how much LOS variation is due to institutional factors.

So let’s assume you’ve taken the log of ICULOS and adjusted for patient factors, then converted the results back to fractional days (e.g. 2.65, 10.02, 5.63, etc…). Now you want to present your results comparing ICUs. There is one more pitfall to consider. Results for a binary variable like mortality are usually presented as a ratio of observed deaths: expected deaths. But is a ratio the right metric for LOS? The answer can be found in Table 1 below.

**Table 1. Ratio of observed/expected LOS vs. difference in observed and expected LOS: some examples**

Observed ICULOS | Expected ICULOS | Ratio Observed:Expected | OMELOS* |

0.5 days | 0.4 days | 1.25 | 0.1 days |

0.5 days | 0.9 days | 0.55 | -0.4 days |

2.0 days | 2.2 days | 0.91 | -0.2 days |

2.0 days | 2.5 days | 0.80 | -0.5 days |

12.0 days | 10.0 days | 1.20 | 2.0 days |

* OMELOS = observed – expected LOS

When the observed LOS is small, the ratio makes small departures from expected seem rather large. This difference between the ratio and OMELOS diminishes as observed LOS increases. So taking the OMELOS rather than the ratio is a smart choice, particularly when observed LOS is low to moderate.

In review, there are three major reasons for why LOS is misconstrued: neglecting to take into account the skewed nature of ICU LOS distribution, not accounting for patient case-mix, and taking the ratio of observed:expected LOS rather than the difference. Unless these items are addressed, comparisons of ICUs’ LOS is an exercise of dubious value.

*Prescient Healthcare Consulting has been actively involved on ICU LOS research, and is continually refining methods to achieve a fair inter-hospital comparison of that metric. For more details please contact info@prescient-healthcare.com.*

## Recent Comments