Objective
In this chapter we present the methods and findings of a regression to explain variation in the SAAR for geographically based systems. This was published during the course of the study.36
Methods
Identification of factors
Based on previous research on variation in emergency admission rates, and the focus here on the emergency and urgent care system, it was necessary to locate factors relating to the population, geography, health and range of emergency and urgent health services for the 150 geographically based systems. We searched national databases of routinely available data for relevant data on factors reported at PCT level. Where factors were available by financial year, we selected 2009–10, which was the mid-point year of the SAAR, or the calendar year 2009, or summed quarterly data for 2009. The source of data for factors is reported in Appendix 1.
Population factors
The SAAR was adjusted for age and sex, using 5-year age groups. We attempted to locate data on social deprivation, minority ethnic groups, density of elderly people and social isolation. The Index of Multiple Deprivation has often been identified as an explanatory factor for variation in emergency admissions. We used two domains of this index – employment and income deprivation – because the index itself includes standardised emergency admission rates.37 The employment deprivation domain reports the proportion of the working age population unable to work because of unemployment, sickness or disability. The income deprivation domain reports the proportion of the population in families who are out of work or have low earnings. We included a factor on the percentage of the population aged over 75 years old even though the SAAR was adjusted for age in case the density of older people in an area created pressure on services.
Geography
We tested one geographical factor, which was a six-category urban–rural scale. We started the analysis with a three-category scale. A patient and public involvement (PPI) representative drew attention to the effect of geography on the SAAR when we presented preliminary findings. We then sought out a more detailed scale to represent geographical differences between systems.
Health
The standardised mortality ratio has been shown to explain variation in emergency admissions overall (see Table 1). We decided not to include it because it may be an indicator of both health status of a population and performance of services for that population. Instead we used indicators of morbidity: we found data on the prevalence of three conditions included in the 14 conditions in the SAAR.
Services in an emergency and urgent care system
We located factors about key services in the emergency and urgent care system: general practice, GP OOH, EDs, acute trusts and ambulance services. We wanted to locate data on the availability, accessibility and quality of all services but could locate data on only some aspects of these services.
The Atlas of Variation was a source of health service-related factors but the authors have expressed concerns that some variation may be accounted for by data management problems.35 We replaced very high values with the median value for two factors: ED attendance rate (replaced two high values) and admissions from nursing homes rate (replaced five high values).
We calculated two factors using HES data. The first was the percentage of all emergency admissions staying less than 1 day because this had been identified as explaining the recent increase in emergency admission rates. We felt that this factor could indicate one of two things: either (1) coding differences between hospitals, for example, with patients waiting in the hospital for a few hours without using a bed coded as admissions in some hospitals and as ED discharges in another, or (2) different ways of managing patients within the hospital; for example, some hospitals may have been able to put community services in place to discharge ED attendances while others admitted patients to a hospital bed to arrange community services to allow discharge. Second, we calculated the percentage of all emergency admissions referred by GPs to identify the direct influence of general practice on emergency admissions.
Two factors about the emergency ambulance service – percentage of incidents not transported to hospital (non-conveyance) and the percentage of incidents meeting the 8-minute response target – were available only for ambulance services rather than PCTs. We allocated the ambulance service rate to each of the PCTs nested within that ambulance service, an underestimate of the variation at PCT level.
Services we could find no data for
We found no routine data for community/intermediate care, social care or system integration.
Analysis
We undertook general linear modelling in SPSS version 20 (IBM Corporation, Armonk, NY, USA) weighted for the size of the system population to account for larger uncertainty of estimates for smaller systems. The dependent variable was the SAAR for 150 systems. The independent variables were tested in a hierarchical multiple regression in two blocks, using forward stepwise regression within each block. Variables were included if the p-value for the t-test was < 0.05. The blocks were determined by the extent to which service providers could affect a factor. Block 1 was population-related factors. We used the residuals from block 1 as the dependent variable in block 2 and then tested the effect of service-related factors.
After we had completed the analysis and moved on to phase 2 of the study, we felt that this regression did not capture enough of the conceptual framework of the study. Although our conceptual framework led us to include factors which other researchers had not – that is those from services other than primary care and hospitals – we had ignored the fact that factors might operate in sequence. That is, services outside the hospital would affect numbers who turned up at the hospital. For example, difficulty getting a GP appointment has been shown to explain higher rates of attendance at EDs.26,27 We undertook a three-block analysis to reflect this:
block 1: population-related factors: population, geography, health
block 2: out of hospital service-related factors – GP access, GP quality, ambulance service performance, GP OOH service
block 3: in hospital service-related factors: ED attendance, conversion rate at ED, short length of stay in hospital.
Findings
Univariate linear regression
We display descriptions of the variables tested in the multiple regression (). It is interesting to note that two factors explained a very large amount of variation in the SAAR. Both were population factors related to deprivation: income deprivation and employment deprivation, explaining 60% and 72% of variation respectively. These are likely to be correlated. We explore correlation between factors in the next section.
Description of all factors and explanatory power in the univariate linear regression (geographically based systems)
Correlations between factors
Some of the factors were correlated with others. It is important to describe these correlations to facilitate interpretation of the final multiple regression. Employment deprivation was positively correlated with income deprivation and the prevalence of some of the 14 conditions (). Urban/rural status was positively correlated with a number of factors including the proportion of elderly people in a system and some access to general practice factors.
Correlations between factors (geographically based systems, r > 0.4)
Factors affecting standardised avoidable admissions rate in a multiple linear regression
We then undertook multiple linear regression to identify the combination of factors which predicted the SAAR (). We undertook the block 1 analysis – which tested population-related factors – and identified two factors which predicted the SAAR: employment deprivation and urban/rural status. The more deprived populations and more urban populations had higher SAARs. These two factors together predicted 75% of the variation. In the block 2 analysis – which tested service-related factors – those related to EDs, hospitals, emergency ambulance services and primary care explained further variation (r2 = 85% in a non-hierarchical analysis). Systems with higher SAARs had higher attendance rates at EDs, higher rates of conversion of ED attendances to admissions, higher proportions of very short-stay patients, higher rates of ambulance calls transported to hospital and better perceived access to general practice (see ). This last factor was in the opposite direction from the univariate linear regression and counterintuitive in the context of the conceptual framework of the study. We discuss this in Chapter 10.
Multiple linear regression (geographically based systems)
Regression metrics are reported in Appendix 2, showing that the model was a good fit. There was no evidence of multicollinearity in block 2: variance inflation factors varied between 1.1 and 1.4. Some of the factors in the multiple regression were correlated with each other even though there was no multicollinearity: employment deprivation was negatively correlated with the proportion of ambulance callers not transported to hospital; urban/rural status was correlated with perceptions of access to general practice and the proportion of ambulance callers not transported to hospital (see ). Because of the large amount of correlation between factors, it is likely that a number of regressions would fit the data equally well, so there is some uncertainty about the model presented here.
Test of a stronger system-based theoretical model
The first block was the same as block 1 in the primary analysis reported above. In block 2 – out-of-hospital factors – ambulance performance was the only factor adding to the regression. That is, factors about availability of, access to and quality of primary care did not explain further variation at this stage. In block 3 – in-hospital factors – the factors explaining further variation were those in the two-block analysis reported earlier. That is, this approach made little difference to our findings.
Conclusion
Variation in potentially avoidable emergency admissions was explained mainly by population factors. Health-care providers can reduce avoidable emergency admissions by investigating why some populations attend EDs more than others, why some EDs convert more attendances to admissions than others and why some ambulance services transport more of their calls to hospital than others. The greatest potential for reduction in avoidable emergency admissions lies with understanding more about how services can best provide care to deprived communities in ways that avoid emergency admission.
Link with phase 2: identifying residuals and potential case studies
A residual is the difference between the dependent variable for a case and its value predicted by the multiple regression. The description of qualitative residual analysis is brief28,29 and there is no guidance on which type of residual to measure or the size of a large residual. The histogram of standardised residuals from our earlier regression shows that they were normally distributed (see Appendix 2). We identified large standardised residuals as > 1.5 or < 1.5. We noted that some systems with large residuals were in geographical clusters, in that neighbouring systems had similar SAARs and similar residuals. We changed our definition of a large residual to > 1.3 or < 1.3 to include systems within each of these geographical clusters. Twenty-seven systems had large residuals ().
Systems with large residuals from regression reported in Table 6
We used purposive sampling to identify six systems for our in-depth case studies. We wanted to select cases with high, medium and low SAARs in case the way in which systems operated differed by size of SAAR. The median SAAR was 2258 with an IQR of 1808–2662. We labelled any system in the highest quartile ‘high SAAR’, any system in the lowest quartile ‘low SAAR’ and all others ‘medium SAAR’. We also wanted to select systems where the residual was positive and negative, indicating over- and underprediction of the SAAR. Some systems had predicted SAARs that were higher than the actual SAAR (overpredicted) and some had predicted SAARs that were lower than the actual SAAR (underpredicted). We categorised the 27 cases by size of SAAR and direction of residual (see ). We then grouped geographical neighbours together with the intention of selecting only one case from a cluster in order to maximise variation of selected cases.
Our intention had been to select one case from each ‘type’ (see column 1 in ). However, ‘low SAAR underpredicted’ did not have any cases and ‘high SAAR overpredicted’ was very similar to the ‘medium SAAR overpredicted’. Instead we selected cases that could represent a cluster of systems distributed across the types. We labelled selected cases using H for high SAAR, M for medium SAAR, L for low SAAR, U and O for under- and overpredicted, and 1–6 to indicate case number. Selected cases HU1, LO2, MO3, MU4, LO5 and MO6 are indicated in bold in .
