Emergency Re-admission

Nosokinetics

A Method for Determining an Emergency Readmission Time Window

Eren Demir, PhD student, HSCMG University of Westminster

The National Health Service defines re-admission (based on expert opinion) as an emergency admission to the same hospital within 28 days following discharge (Healthcare Commission, 2005). Due to lack of consensus in defining readmission time interval, we develop a modelling approach in determining an appropriate time window, within which an admission is classified as a readmission.

Figure 1 Two groups of patients in the community following discharge from hospital.

The population of patients discharged from hospital to the community can be divided generally in two groups, namely, one of patients at “high risk” of readmission (denoted as c1), and the other of patients at “low risk” (Figure 1) of readmission (c2). However, for each patient, we observe the time between successive hospital admissions (time to admission) and do not know which group the patient belongs to. Therefore, the random variable time to admission (denoted by X) can be expressed as to follow a mixture distribution with probability density function (pdf) f(x)= pf1(x) + (1-p)f2(x) where p is the probability of a patient being in group c1, f1(x) and f2(x) are the pdf of time to admission for group c1 and c2 respectively.

The optimal cut-off in time to admission that separates the high and low risk group is determined by solving, that is, where the two corresponding curves intersect.

Figure 2 Curves represent high and low risk probability density function. Vertical line represents point of intersection

Results

Using the hospital episodes statistics dataset from 1997 to 2004, we focused our study on chronic obstructive pulmonary disease (COPD), one of the leading causes of readmission. The mean time spent in the high risk and low risk group is 25 and 171 days respectively. The estimated probability of a patient being in group is 0.26 and the cut-off in time to admission, where the two curves intersect at days (Figure 2). We further estimated time window for 5 strategic health authorities in London, which clearly shows that there is a marked difference among the regions.

Strategic Health  Optimal time    Probability of belonging      
Authority         window (days)   to high risk group

North East          31.8                0.302	
North Central       28.2                0.278	
North West          28.8                0.288	
South East          26.9                0.271	
South West          18.7                0.212

Figure 3 Optimal time window for the 5 strategic health authorities and probability of being in high or low risk of readmission.

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