Comparative Analysis of HCUP and NHDS Inpatient Discharge Data: Appendix

Appendix

Estimates of Standard Error for NHDS Statistics

A variety of statistics were estimated based on these data: 1) total number of discharges, 2) in-hospital mortality, and 3) average length of stay (calculated as the difference between discharge and admission dates). The standard errors were calculated as follows.

Total Numbers of Discharges

From the NHDS documentation, constants a and b were obtained for 1995. The standard error for the estimate of total discharges is:

SE _TD = (a W _TD2 + bW _TD) ^1/2

where W_TD is the weighted sum of total discharges (i.e., the estimate of total discharges).

This estimate of standard error is valid only if:

(1) estimated total discharges exceeds 366,657 or
(2) estimated total discharges exceeds 60,769 and estimated total days exceeds 283,338.

Percent Mortality

Let P be the estimated proportion of in-hospital deaths. The standard error of this proportion expressed as a percent is:

Where the constant c is given by NHDS documentation. This estimate of the standard error is valid only if:

(1) estimated total discharges exceeds 366,657 and the estimated number of deaths exceeds zero, or
(2) both estimated total discharges and estimated total deaths exceed 60,769.

Average Length of Stay

Let ALOS be the estimated average length of stay based on a weighted number of discharges equal to TD. If the weighted sum of patient length of stay is TLOS, and

ALOS = TLOS  
        TD      

then the estimated standard error is:

Constants a₁, a₂, b₁, and b₂ were obtained from the NHDS documentation concerning standard error calculations for average length of stay.

Tests of Statistical Significance

To test for a statistically significant difference between an NIS estimate, X, and an NHDS estimate, Y, the following procedure was used. The difference is significant if

where SE_X is the estimated standard error for the NIS estimate and SE_Y is the estimated standard error of the NHDS estimate. S is equal to 1.96 for significance at the .05 level and S is equal to 2.576 for significance at the .01 level.

If a valid estimate of either standard error, SE_X or SE_Y, could not be obtained, then a significance test was not performed.

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