Exclusions to Analysis
The risk-adjusted length of stay analysis includes all inpatient records categorized into one of the 15 selected DRGs with the following exceptions:
- patients who died in the hospital
- patients who left against medical advice or discontinued care
- patients who were transferred to another short-term acute care hospital
- patients with an invalid (or missing) length of stay
- patients with an invalid (or missing) ASG score
- patients with an invalid (or missing) age
Construction of Reference Database
The reference database for length of stay is indexed by DRG, ASG score, cancer status, and age category. The methods used to construct this comparative database were similar to those employed in constructing the comparative database used for in-hospital mortality.
Trimming methodology was used to remove outlier length of stay values from the study population. Identification of outliers is imperative for the elimination of extreme scores that have a significant and unrepresentative impact on the mean (average). For the 1998 Hospital Performance Report the risk-adjusted mean is the primary descriptive measure for length of stay.
The trimming (that is, deleting) of individual records from the database was performed after all other exclusions were satisfied. If the length of stay on a particular record was less than the lower trim point or in excess of the upper trim point, that record was removed from the database, and thus, from subsequent analyses.
For the Pennsylvania comparative database, upper and lower trim points were calculated using the "+/- 3.0 interquartile range" method. This non-parametric methodology is used because historically the distribution for length of stay data does not follow a "normal, bell-shaped" pattern. The distribution is generally right-skewed, with values gathered closely together at the lower end of the distribution, becoming more widely dispersed at the upper end of the distribution.
Upper and lower trim points for length of stay were calculated for each DRG by each ASG/cancer/age category statewide, providing 45 potential combinations for each DRG.
Trim points were determined as follows:
Q1 = the first quartile (25th percentile length of stay value) of all patient records from the comparative database in a particular category
Q3 = the third quartile (75th percentile length of stay value) of all patient records from the comparative database in a particular category
IQR = Q3 Q1
Lower Trim Point = Q1 (3.0 x IQR)
Upper Trim Point = Q3 + (3.0 x IQR)
Risk Adjustment Computations
Trimmed and risk-adjusted length of stay averages are reported for each DRG by each hospital. Length of stay values may vary within a DRG category due to variance in ASG, cancer status, and age data. Therefore, in order to report a comparable risk-adjusted average length of stay for each of the fifteen DRGs within each hospital, a risk-adjustment technique was employed. The following steps were implemented:
First, statewide relative weights for each ASG/cancer/age category combination within each DRG were determined using the reference database for length of stay. After all exclusions were satisfied and outlier trimming was performed, the relative weight for each ASG/cancer/age category within each DRG was calculated using the formula:
Relative Weight =
|Average Length of Stay for an ASG/cancer/age combination|
|Average Length of Stay for the DRG|
Next, each hospital's risk index for each DRG was calculated. Each hospital had fifteen risk indices associated with length of stay for each of the fifteen DRGs featured in the 1998 HPR.
A Hospital's Risk Index for a particular DRG=
(ni x RWi)
where, for each of the ASG/cancer/age combinations within the DRG
RWi = the statewide relative weight for the ith combination
ni = the number of cases for the hospital of the ith combination
and ni = the total number of cases for the hospital for the DRG
Finally, for each hospital the trimmed and risk-adjusted average length of stay is then calculated for each of the fifteen DRGs.
Trimmed and Risk-Adjusted Avg Length of Stay =
Avg Length of Stay for a DRG
Risk Index for a DRG