Case-Mix Adjustment of Hospital Standardized Mortality Ratios

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                                            Case-Mix Adjustment of Hospital
                                             Standardized Mortality Ratios
               Amy Mckeon; Samuel Dua Oduro
               NHS National Services Scotland, Information Services Division, Healthcare Information Group,
               1 South Gyle Crescent, Edinburgh, EH12 9EB, United Kingdom.

               1. Summary

                        Healthcare practitioners and managers responsible for delivering quality improvement in their
               institutions are interested in mortality among hospitalized patients as an overall measure of quality and safety
               in hospitals. All things being equal, hospitals with lower mortality are deemed to be performing more
               safely and more effectively than a hospital with a higher death rate.
                      However, hospitals serve different patient populations with variability in patient’s risk of death
               rendering institutional comparisons difficult to interpret without adjustment for the characteristics of such
               patient populations. Various risk-adjustment methods have been developed, including the use of logistic
               regression to estimate patients’ a priori in-hospital probabilities of death.
                      In this study we compare the case-mix adjustment of hospital standardized mortality ratios (HSMR)
               obtained by modeling deaths using the logistic regression with results obtained from decision tree analysis.
               We show in this paper that the two statistical methods give similar results. However, decision tree analysis
               provides non-statisticians, such as healthcare managers and clinicians, better visualization of patterns in the
               data and hence a clearer understanding of the process of adjusting for the various risk factors.
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               2. Data and case-mix variables
                      The data used were records of all 2,623,948 inpatient and day case discharges (excluding psychiatric
               discharges) in Scottish Hospitals for 1,169,038 patients covering the period September 2005 to August 2007.
               The hospital discharge data are then linked to death records held by General Register Office for Scotland to
               identify deaths within thirty (30) days of admission to a hospital.
                      This outcome variable therefore included in-hospital mortality and deaths following discharge. The
               covariates studied were age, sex, deprivation category, type of admission (elective/emergency), inpatient/day
               case, institution where patient was admitted from, previous emergency admissions in last year prior to the
               current admission and the Charlson index of co-morbidity .To adjust for the primary diagnosis, we developed

               twenty-six (26) diagnosis groupings based on the International Classification of Diseases (ICD 10).

               3. Model and Prediction of probability of death
                     Decision trees (sometimes called classification trees) were used to assess which of the case-mix
               variables under study explain variation in mortality and hence which variables should be used for case mix
               adjustment of the outcome variable. The approach used was essentially the same as used by Jarman and
               colleagues (1987).
                     To develop the model we divided our data set into a training and validation datasets. The SMR
               database is episode based and hence a patient could have more that one episode within a hospital stay. A
               patient could have multiple stays within the time period. To avoid double counting only one of the patient’s
               stays, the most recent was included in the analysis.
               The decision tree model successively partitions the data based on the relationships between case-mix
           T   variables and the outcome variable. We used a 5% significance level for splitting nodes of the tree and set a
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               condition that a minimum of 100 patients should remain in each terminal node. To further assess the validity
               of this model, a traditional logistic regression model was fitted to the data.

               4. Results
                     The final decision tree model estimated probability of deaths for each patient with all possible
               combinations of the case-mix variables. Aggregating these probabilities of deaths within hospitals, we were
               able to calculate the expected numbers of deaths and hence the hospital standardised mortality ratios.
               Figure 1 shows HSMR’s plotted on a funnel chart for the decision tree and logistic regression models. The

               areas under the Roc curves were respectively 0.949 and 0.946 for decision tree and the logistic regression

               model on the training data set.

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                                                                                          Lo gis t ic re gre s s io n

                                                                                          D e c is io n t re e


               Mortality rate






                                     0     5,000    10,000   15,000     20,000   25,000   30,000           35,000


                                                      Figure 1: Comparison of HSMR
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               5. Discussion
                         The decision tree model provides considerably very close estimates of the HSMR’s. This is
               advantageous because it makes no assumptions about the underlying distribution of deaths. It also provides
               non-statisticians, such as healthcare managers and clinicians, better visualization of patterns in the data and
               hence a clearer understanding of the process of adjusting for the various risk factors.

               Charlson ME, Pompei P, Ales KL, MacKenzie CR (1987). A new method of classifying prognostic co-

               morbidity in longitudinal studies: development and validation. J Chron Dis Vol. 40, No. 5, pp. 373-383

               Jarman B. et al (2005). Monitoring changes in hospital standardised mortality ratios. BMJ. 330:329-329.
               Vijaya S.,Toni H. et al (2004). New ICD-10 version of the Charlson comorbidity index predicted inhospital
               mortality Journal of Clinical Epidemiology vol. 57, No. 12