(Re)admission frequencies show substantial variations between the hospitals. For example: the overall value of the readmission frequency of hospital D equals double the value of hospital B and F. For the main CCS diagnostic group neoplasms, this value for hospital D equals even three times the value of B. We conclude that there are substantial differences in the numbers of readmissions within a given time period between the six hospitals.
Patients with higher admission frequencies bear lower predicted risks per admission, which can be explained by shifts in the casemix. For the patient view however, lowering of risks is only partly predicted by DHM-2008, since the amount of predicted deaths compared to observed deaths turned out to be relatively low for first-and-only admissions and high for readmissions. The corresponding standardised mortality ratio in the patient view is high for class P(m = 1) (127) and low for the other classes (gradually dropping to 35 for P(m > 20)) compared to the overall average of 93. In contrast to this we found that the standardised mortality ratios per nth admission view class are approximately as predicted, fluctuating around 93. DHM-2008 demonstrates quite a fair goodness of fit for the nth admission view classes. This result matches the findings of Jarman [11], where no differences in HSMR were detected by picking nth admissions for any value of n. At the same time however, a comparison of predicted and observed deaths for the patient view classes does not demonstrate a good fit for the model. The question now arises why DHM-2008 should be suited to fit the nth admission view and not be suited to fit the patient view? As we will explain below, different admission frequency classes of the patient view may incur risk differences, not detected by the known adjustment variables. In that case, comparing these classes would commit the constant risk fallacy and establishing a model fit along the lines of the patient view would be preferred to a fit along the lines of the admission view.
We will demonstrate this point by three examples that show mechanisms, lowering risks for higher admission frequencies and having nothing to do with higher quality of care:
Example 1: Admission policies may increase the number of readmissions without proportionally increasing real risks. One hospital may systematically combine the diagnosis and treatment into a single admission. Another hospital may have an admission for diagnosis and a second one for treatment, being granted a double predicted risk count, most likely without doubling of real risk, but doubling the expected risk.
Example 2: Hospitals may show different treatment practices in the frequency with which chronically ill patients are admitted for the same disease. For example readmission frequencies for the treatment of neoplasms in hospitals B and D differ on average by a factor of 3. This difference can be explained by differences in balance between inpatient versus outpatient treatments (late versus early adopters of a trend moving from inpatient toward outpatient treatment, for example [14]). The predicted risk contribution for hospital D may thus be tripled compared to B, but it is not likely that patients of D are being exposed to a tripled real risk. On the contrary, the mortality risk per patient stabilizes around 13% if admitted 10 or more times (table 3). Every incremental admission for chemotherapy further increases the denominator of the HSMR, but on average does not increase the observed mortality, the numerator, further.
Example 3: Patient referrals to tertiary care, frequently occurring in the Netherlands, may cause differences. The transfer of a patient back and forth most often is an advantage for the referring hospital, as they count a double admission, while the hospital to which the patient is being referred is at a disadvantage because they only count for one admission. On top of this the latter hospital has to deal with the risk of conducting a potentially complicated medical procedure. It is unlikely that a patient under these circumstances will experience a doubling of risk in the referring hospital.
Another plausible mechanism may be hidden in the physical condition of frequently readmitted patients. If these patients are unexpectedly resilient, they will dominate higher admission frequency groups through natural selection and consequently cause lower undetected risks, compared to lower admission frequency groups. If this hypothesis is valid, it might become visible as well in patient specific casemix properties that are known to us such as age and comorbidity (table 6). The average age of frequently admitted patients indeed is decreasing for the highest values of n, indicating a fitter population. The comorbidity is increasing however; a logical consequence of the fact that we applied the notion of readmission for any disease. So patients with more co-morbidity may be admitted more often for the various diseases they suffer from. It also indicates higher vulnerability and in that case would contradict the hypothesis. Although the hypothesis looks appealing, we cannot proof its correctness with the data currently available.
Looking back at the admission history of a frequently admitted patient, the additional risk-lowering factors just described, may have come into play already after the patient's first admission. The nth admission view constitutes a cross-section of various patient view groups, each having their own additional risks. Consequently the nth admission view cannot discriminate additional risk differences and is not suited to be used for readmission adjustment. Instead, we think the variable 'admission frequency' of the patient view should be used for this purpose. Patient views are showing why DHM-2008 predicts too high a risk for a frequently readmitted patient, as illustrated by the following case that we observed:
Patient × of hospital D contributed 3.1 predicted deaths to the denominator of the HSMR through seven successive admissions within six months. A single patient however can maximally contribute a value of 1 - in case of death - to the numerator of the HSMR.
Numerous examples alike became available in our study, for example: we found 174 patients in hospital D, each of whom contributed more than 1 predicted death to the denominator of the HSMR due to various readmissions. In total these contributions in hospital D added up to 232 predicted deaths, whereas 'only' 75 deaths were observed in this group. Clearly the number of deaths predicted by DHM-2008 for frequently admitted patients is being overestimated.
A final illustration of this phenomenon is shown in figure 3: a scatter diagram where we plotted the HSMRs as well as the SMRs of the three main CCS diagnostic groups that show the largest variations in readmission frequency - neoplasms, heart diseases and respiratory diseases - against the readmission frequency (see also figure 1). In all cases there is a downward trend: higher readmission frequencies corresponding with lower (H)SMRs.
We conclude that there is a significant association between HSMRs and numbers of readmissions per patient.
Since the study involved five consecutive years, we were not able to capture the complete patient view. Patient view sequences that started before 2003 and continued to emerge in the period 2003 - 2007 were truncated. The same happened with sequences that started during the period 2003 - 2007 and continued in the years thereafter. Consequently the picture will never be complete. For each patient being admitted at least twice, we calculated the time elapsed between the date of the first and the date of the last discharge. For 63% of these patients, the time elapsed amounted to less than one year and for 91% less than 3 years, suggesting that the larger part of the effect has been captured.
How can HSMRs be adjusted for the effects of readmissions? For that purpose, an additional adjustment variable 'admission frequency,' as used in this study in the patient view, may be applied. After adjustment, the SMRs of the patient view classes in our study will fluctuate around 93. As a consequence the goodness of fit for the admission view will be lost. However, this does not provide us with a principal problem since the division into admission frequency classes (patient view) is along the lines of identified and distinct risk classes for which adjustment is clearly needed. Nth admission classes turn out to be meaningless in terms of risk differentiation.
In particular for the higher admission frequencies, a prolonged measurement period of various years was needed in order to make visible the effects we described. For example the average time which elapsed between the first and last date of discharge for patient view class P(m > 20), amounted to 2.5 years. This does not mean however that having many patients in class P(m > 20), does not have an effect if measured for only one year. Ideally the adjustment for readmission would be based on an 'admission counter' in the file of each patient that is being increased by 1 after every new readmission. Since such counts are not being kept, an approach along the lines of this study, awkward as it might be, will be necessary.
A final remark concerns the following: (frequent) readmissions are sometimes taken to be a proxy indicator for poor quality of care. But instead of working against the hospitals with higher readmission frequencies the current HSMR seems in that case to work in favour of those hospitals, underlining the following statement: If HSMRs in the Netherlands ever will be publically reported and used to compare hospitals, then the issues raised in [4] need to be resolved and, on top of this, adjustment for readmission will be necessary. If HSMRs and particularly SMRs on diagnostic level are used by hospitals as a starting point for quality improvement [2] - a better idea for usage of the HSMR indicator - then adjustment for readmission will be necessary as well, in order to prevent misleading signals to be generated. Hospitals will in that case better be able to avoid falsely acting upon too high SMR values as well as to avoid falsely non-acting upon too low SMR values.