Easter 2007 in London

Defining better measures of emergency readmission Eren Demir, Thierry Chaussalet, Haifeng Xie

Who we are People  A bunch of academic staff including Christos Vasilakis  A research fellow: Haifeng Xie  A visiting professor (clinician): Peter Millard (Nosokinetics News)  Four PhD research students including Eren Demir, Brijesh Patel and Anthony Codrington-Virtue  Research collaborators in and outside the UK and academia What do we do?  Application of Decision Support, Simulation, and Data Mining applied to the process of care  Problem domain: Length of stay and cost modelling in long-term care, geriatric services; accident and emergency services  Techniques: Markov/semi-Markov models, data mining, queuing networks, simulation

Outline of presentation Definition(s) emergency readmission. The importance of emergency readmission for the National Health Service (NHS). A method for determining an appropriate time window to classify a readmission as critical readmission. Application of the methodology to the UK national dataset. Discussions and Future Work.

Emergency Readmission (ER) High level of emergency or unplanned (i.e. not scheduled) readmission is potentially associated with poor patient care “I take my car into a garage; if it needs to go back in a short time then that's obviously because they didn't do a good job“ (Clarke, 2003) Frequent readmissions are highly costly Readmission rate is an indicator in the performance rating framework for NHS hospitals in the UK Currently the NHS defines readmission as an emergency or unplanned admission (department) within 28 days following discharge Lack of consensus in the literature on the appropriate choice of time interval in defining readmission. Clarke, A. (2003). Readmission to hospital: a measure of quality of outcome. British Medical Journal 13,

Definition of ER from different sources AuthorDefinition of readmission (Anderson and Steinberg, 1984) Readmission occurred when a patient was discharged from an acute care hospital within 60 days of discharge. (Brown and Gray, 1998) The definition of readmission is ranging from 2 weeks, three months, six months or one year from index admission. (Reed et al., 1991) Readmission to the hospital soon after discharge within 14 days (Williams and Fitton, 1998) Unplanned readmission within 28 days after a discharge.

Justifying a 28 days interval? 28 day interval has been justified by constructing a graphical output for the total number of readmissions (Sibbritt, 1995) Each graph shows an exponential or lognormal shaped distribution Justification relied solely on visual inspection Too crude and does not account of variations

Modelling framework For each patient we observe the time between successive hospital admissions We assume the population of readmitted patients comprises two groups  High risk group ( )  Low risk group ( ) We do not know which group the patient belongs to Community high risk group low risk group Hospital dischargeHospital admission

Mixture distribution with probability density function (pdf) where is the probability of a patient being in group, and and are the pdf of time to admission for group and respectively. Probability of belonging to and can be determined from the posterior probability expressed via the Bayes’ theorem as Modelling framework

General Framework: “time window” Group membership of a patient with observed time to readmission : assign to if ; and to otherwise. Optimal time window can be determined by solving Or given by the time value where that is, where the two corresponding curves intersect.

Given time to admission, this approach can be expressed as a mixture distribution in terms of the rates. Where and are the pdf’s for high and low risk readmission, often assumed to be exponential. General Framework - continued Optimal time window

Modelling Framework: Alternative approach Empirical evidence suggests that risk of readmission substantially changes over time  High soon after discharge  Low after a period of time in the community Assuming that all rates ( ) are constant, time to admission follows a Coxian phase-type distribution high risk of readmission low risk of readmission Community Hospital

Application to UK National Dataset National dataset - Hospital Episode Statistics (HES)  Admissions, Discharges; Geographical, Clinical variables  Dataset ranges from 1997 – 2004 (80 million records) HES captures all the consultant episodes of a patient. First we focus our study on chronic obstructive pulmonary diseases (COPD), one of the leading causes of early readmission 962,656 episodes from patients who had the primary diagnosis code corresponding to COPD (J40-J44) After data cleansing process, a set of 696,911 completed spells were derived.

Using time window of 28 days as currently defined we observe:  Increase in number of admissions between  Decreasing trend in percentage of readmissions within 28 day interval Observations of calendar years

Strategic Health Authorities in London

Optimal time window for COPD patients Nationally, the optimal time window is computed to be about 26 days

COPD Results for SHA’s in London Fitted to COPD data from the 5 SHA’s in the London area. Marked difference in the estimated optimal time window among the regions. Estimated time window is inline with the current 28 day interval for three out five SHA’s Additional information: Probability of belonging to high risk group can be used as alternative emergency readmission “indicator”

SHA’s in London: COPD and other Fitted to data from the 5 SHA’s in the London area. Again marked difference in the estimated optimal time window among the regions Estimated time window is no longer “inline” with current 28 days Probability of belonging to high risk group is less variable English Data setNWLNCLNELSELSWL COPD 26.0 (0.26) 31.8 (0.30) 28.2 (0.28) 28.8 (0.29) 26.9 (0.27) 18.7 (0.21) Stroke 26.8 (0.193) 39.5 (0.32) 42.3 (0.34) 34.0 (0.24) 33.5 (0.22) 43.5 (0.27) Geriatrics 30.0 (0.22) 31.5 (0.24) 33.0 (0.23) 34.0 (0.22) 34.0 (0.25) 37.0 (0.26)

Summary and Future work We developed a simple modelling approach to determining an “optimal” readmission time window The approach takes account of variations across diseases, regions, etc. Suggest alternative indicators: “high risk” probability The measures are “easy” to calculate More work needed test these indicators What do we do when mixture of two-phase Coxian do not fit?  More phases…but the meaning is “lost”  Alternative: Use Mixture of Erlang and 2-phase Coxian

Model Extensions What if mixture of two exponentials does not fit?  More phases…OK if there looking for more than two readmission risk groups  Alternative: Use Mixture of Erlang and 2-phase Coxian phase 1 Hospital phase 2 phase M Hospital phase 1phase M-2 phase M-1 phase M Hospital phase 2

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