The in-hospital mortality analysis includes all inpatient records categorized into one of the 15 selected DRGs with the following exceptions:
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) ASG score
patients with an invalid (or missing) age
For the actual number and percent of statewide cases excluded from analysis, refer to Table 2. For the actual number and percent of regional cases excluded from analysis, refer to the Table of Contents for the appropriate table.
Construction of Reference Database
A Pennsylvania statewide comparative database was computed for the 1998 Pennsylvania acute care hospital inpatient data. The reference database for the measure of in-hospital mortality is indexed by DRG, ASG score, cancer status, and age category. ASG score, cancer status and age category were used as risk adjustment factors in the statistical analysis for in-hospital mortality. Indirect standardized was adopted as the risk-adjustment technique. In order to best support the statistical methods that were utilized, it was decided that the patient count in each of the final ASG/cancer/age
categories should be twenty or more. When the number of patients in an ASG/cancer/age category did not meet this minimum threshold, combination of categories was warranted. (There is a maximum of 45 different combinations of ASG/cancer/age
categories. Because of the high volume DRGs that were selected for this HPR, it was not typically necessary to combine categories in order to achieve a minimum number of 20 patients per combination of ASG/cancer/age category.)
The algorithm used to combine categories was determined under the premise that ASG is regarded as the best indicator of patient risk, followed by cancer status, then age category. (Note that age in years, as an independent predictor of mortality, was already evaluated and retained where statistically significant in the Atlas severity score developed
by CIC-MediQual).
When an age category had a small patient count, it was combined with an adjacent age category. Age categories are defined as:
age 64 and under
age 65 through age 79
age 80 and over
Patients were next risk-adjusted with respect to cancer status. When small patient counts were encountered, the adjustment algorithm combined patients with a history of cancer with those patients who do not have cancer diagnosis codes present. Cancer categories were combined only when age category collapsing would not improve small patient counts. The three applicable categories are:
no cancer (that is, no cancer diagnosis codes present)
malignant neoplasm or cancer in situ (ICD.9.CM diagnosis codes 140.0 – 208.9 inclusive or 230.0 – 234.9 inclusive)
history of cancer (ICD.9.CM diagnosis codes V10.00 – V10.90 inclusive)
When the patient count for an ASG level was small, and all acceptable collapsing of cancer status categories were performed, collapsing of ASG levels was necessary. When combining ASG levels, counts for scores 0 and 1 may have been combined; and counts for scores 3 and 4 may have been combined. An ASG score of 2 was considered an independent category. The following table displays the conversion of probabilities to admission severity categories:
Admission Severity Group Probability of Death
0 (no risk of clinical instability) 0.000 – 0.001
1 (minimum risk of clinical instability) 0.002 – 0.011
2 (moderate risk of clinical instability) 0.012 – 0.057
3 (severe risk of clinical instability) 0.058 – 0.499
4 (maximum risk of clinical instability) 0.500 – 1.000
Calculation of the Expected Mortality Rate
Using the Pennsylvania comparative database, the statewide mortality rate was calculated for the final ASG/cancer/age
category combinations within each of the fifteen DRGs. These mortality rates were computed for each ASG/cancer/age category by dividing the total number of deaths in that category by the total number of patients in that ASG/cancer/age
category. This mortality rate, computed across all hospitals, provides a standard comparison for individual hospitals.
Actual In-hospital Mortality Compared With Expected In-hospital Mortality
The number of deaths for each hospital within each DRG during 1998 is the actual or observed in-hospital mortality. The number of deaths "expected" for each hospital within each DRG is calculated using the statewide expected mortality rates for each of ASG/cancer/age category combinations for a particular DRG.
Note, that since there are 5 ASG categories, 3 cancer categories, and 3 age categories, there are potentially 45 different combinations of these categories for every DRG. In the notation presented for the calculation of the Expected Number of Deaths, the variable, i, can range from 1 to 45. (For a particular DRG, the maximum of the variable, i, is given by the number of final combinations of ASG/cancer/age categories.) The ith combination is a generic term used to signify each of the final combinations of ASG/cancer/age categories.
The expected number of mortalities for each DRG within each hospital is calculated as follows:
Expected Number of Deaths = (pi
x ni)
where, for each of the final combinations of ASG/cancer/age within the DR
pi = the statewide mortality rate for the ith combination
ni = the number of cases for the hospital of the ith combination
The estimated probability of death, p, for each DRG within each hospital is calculated as follows:
p = (Expected Number of Deaths)/N
where, N= the total number of cases for a particular DRG within a particular hospital
(ni = N)
The following example illustrates the calculation of the expected mortality for DRG 127 (Heart Failure and Shock) at
Hospital "A".
DRG 127 (Heart Failure and Shock)
Hospital "A"
Statewide Comparative Database
Expected Mortality at Hospital "A"
Admission Severity Group
Cancer Status
Age Category
Number of Patients Treated
Mortality Rate
Product: Number x
Mortality Rate
0
No Cancer
Under Age 65
2
0.019608
0.0392
1
No Cancer
Under Age 65
10
0.004388
0.0439
Age 65-79
5
0.004261
0.0213
Age 80 & Over
1
0.017094
0.0171
2
No Cancer
Under Age 65
20
0.009498
0.1900
Age 65-79
80
0.013526
1.0821
Age 80 & Over
70
0.020612
1.4429
Malignant Neoplasm or Cancer In Situ
Under Age 65
1
0.055901
0.0559
Age 65-79
5
0.039179
0.1959
Age 80 & Above
3
0.030471
0.0914
History of Cancer
Age 80 & Above
5
0.009050
0.0452
3
No Cancer
Under Age 65
10
0.069703
0.6970
Age 65-79
50
0.075641
3.7821
Age 80 & Over
150
0.086699
13.0049
Malignant Neoplasm or Cancer In Situ
Under Age 65
1
0.135135
0.1351
Age 65-79
7
0.110887
0.7762
Age 80 & Above
12
0.090056
1.0807
History of Cancer
Under Age 65
2
0.000000
0.0000
Age 65-79
4
0.032338
0.1294
Age 80 & Above
6
0.064350
0.3861
4
No Cancer
Under Age 65
2
0.266667
0.5333
Age 65-79
5
0.343096
1.7155
Age 80 & Over
7
0.406417
2.8449
History of Cancer
All Age Categories Combined
5
0.250000
1.2500
Total
463
29.5601
Summary
Hospital "A" had a total of 463 patients treated for
DRG 127 (Heart Failure and Shock). Of those 463 patients, the expected number of
deaths is 29.5601. (Note: For display purposes the calculations for the expected
mortality within each combination of ASG/cancer/age category have been rounded
to four decimal places.)
Binomial Test
Though a hospital's observed mortality may
be comparable to the state norm, random variation plays a factor in these
comparisons. Statistical evaluation can determine when the difference between
the observed and the expected value is too large to be attributed solely to
chance. Statistical evaluation of in-hospital mortality was performed for each
DRG using the binomial test. The binomial test is appropriate for situations
where the possible outcome is dichotomous; in this case, death or survival for
each patient. The binomial test is based upon the following assumptions:
the probability of death for each patient within a DRG is
the expected mortality rate provided by the reference database. This
probability of death is assumed to be a constant number from one patient to
the next.
the death or survival of one patient has no impact on the
death or survival of any other patient. In other words, patients are
independent entities.
Inferential Error
A type of inferential error that can be made
in statistics is called Type I error or false positive. The probability of
committing a Type I error is equal to the level of significance established by
the researcher. For this analysis, the level of significance has been set to
0.05. In the context of the Hospital Performance Report, a Type I error occurs
when the difference between the observed in-hospital mortality and the expected
in-hospital mortality is declared statistically significant, when in fact, the
difference is due to chance. That is, for a particular DRG, the hospital is
declared to be statistically higher or lower than expected, when in reality the
hospital's level of performance is comparable to the state norm. Since the
level of significance has been set to 0.05, there is a 5% (or 1 in 20) chance of
committing this type of error.
P-value
Calculation
Calculating the p-value for the binomial test
is defined by a formula which sums discrete probabilities based upon the
binomial distribution. The binomial formula is written as:
P(X=a) = [(N!)/(a!(N-a)!)] pa(1-p)N-a
where,
X is the binomial random variable (X is a
discrete random variable and 0 < X < N)
a is the actual number of mortalities for a
particular hospital's DRG
N is the number patients for a particular
hospital's DRG
p is the estimated probability of patient
death for a particular hospital's DRG
For each DRG within each hospital, p is
calculated using the expected mortality for each DRG within each hospital. For
further information regarding this computation, refer to the section
"Actual In-hospital Mortality Compared With Expected In-hospital
Mortality."
Statistical
Rating
A statistical rating is assigned to each
hospital if the difference between what was observed and what was expected in a
particular DRG is statistically significant. The p-value, calculated in terms of
a "two-tailed" test is compared to the level of significance.
If the calculated p-value is greater than 0.05, then the
conclusion is made that the difference between what was expected and what
was observed is not statistically significantly different. It cannot be
concluded that the in-hospital mortality for that particular DRG is
different from the state norm.
If the calculated p-value is less than or equal to 0.05,
then the conclusion is made that the difference between what was expected
and what was observed is statistically significant.
If the observed in-hospital mortality is less than the
statewide in-hospital mortality, the hospital is assigned the symbol
labeled "Mortality significantly less than Expected" for a
particular DRG.
If the observed in-hospital mortality is higher than
the statewide in-hospital mortality, the hospital is assigned the symbol
labeled "Mortality significantly greater than Expected" for a
particular DRG.
(pi
x ni)
