Improved methods for estimating incidence from linked hospital morbidity data

Kate J Brameld1, C D’arcy J Holman1, David M Lawrence1,2 and Michael ST Hobbs1

1 Department of Public Health, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia, 6009.
2 Current affiliation: TVW Telethon Institute for Child Health Research, Western Australia.

Correspondence: Kate Brameld, Centre for Health Services Research, Department of Public Health, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia, 6009. E-mail: kate{at}dph.uwa.edu.au


    Abstract
 Top
 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
Background Linked hospital morbidity data can be used to estimate the incidence of serious chronic disease. However, incidence rates calculated from first-time hospital admissions tend to be overestimated as a result of the erroneous inclusion of prevalent cases that have had previous hospital admissions prior to the study observation period. To address this problem, we have developed the backcasting method.

Method A retrograde survival model was implemented to calculate the level of over-ascertainment of incidence according to the number of years of linked data on which the estimates were based and corresponding correction factors were calculated. The method is illustrated using the example of linked hospital morbidity data on diabetes mellitus and then acute myocardial infarction, which was validated against the Perth MONICA database for cardiovascular disease.

Results Corrected estimates of the incidence of diabetes and acute myocardial infarction were produced. The incidence of diabetes was shown to be lower than in North America in accordance with prevalence estimates, whereas the incidence of acute myocardial infarction was overestimated by approximately 10%.

Conclusion A new method is presented for estimating incidence trends in disease from linked hospital morbidity data. The advantages of this method are its ease of use with routinely collected data and the relatively low cost of applying it in comparison with community surveys or maintaining formal disease registers. The method has other applications using linked data, such as the study of trends in first-time health care procedures and pharmaceutical prescriptions.


Keywords Medical record linkage, incidence, diabetes mellitus, statistical models

Accepted 4 April 2003

Examples of medical record linkage studies have appeared with increasing frequency in the literature since the 1960s, partly due to the inception of the Oxford Record Linkage Study at that time.1 Record linkage involves bringing together records derived from different sources, but relating to the same individual.2 The three basic steps are blocking of records that have a potential relationship; matching to determine if records within a block are likely to be related; and linking matched records so they can be analysed as composite or longitudinal information for the one individual.3 The process was relatively slow and cumbersome at first, but more recently the availability of affordable computing technology and the ability to process large numbers of records in a short space of time have meant that medical record linkage is no longer limited by processing power. There are now six comprehensive population-based medical record linkage systems around the world that routinely link administrative health data.1,4–8 In addition, there are numerous examples of ad hoc record linkage studies.9,10–12 The current capacity for data linkage means that linked data sets can now potentially be used to answer a diverse range of public health surveillance and health service research questions. At the same time, the use of record linkage in these studies requires corresponding developments in methods of analysis to take full advantage of the research potential of linked administrative data.

Linked hospital morbidity data can be used to estimate the incidence of serious chronic disease provided that patients with the condition are admitted to hospital at least once. In the case of incidence rates estimated from first-time hospital admissions, unless the hospital morbidity data are used in conjunction with another data source, it is common to employ a clearance period to overcome the problem of overestimation of incident cases.13–19 The problem results from the erroneous inclusion of prevalent cases that have had previous hospital admissions prior to the study observation period—the ‘prevalent pool effect’. However, enforcing a clearance period is not an ideal method. There is no guarantee it will remove all prevalent cases and it results in loss of data from the early years of observation. To address this problem, we have developed the ‘backcasting method’. It implements a retrograde survival model to calculate the levels of over-ascertainment, and corresponding correction factors, according to the number of years of linked data on which the estimates of incidence rate are based.

In this paper we explain the backcasting method for estimating incidence trends from linked hospital morbidity data. We use the example of linked hospital morbidity data on diabetes mellitus and myocardial infarction to illustrate and validate the method.


    Backcasting methods for estimation of incidence rates
 Top
 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
Correction factors for annual files
Let j = 1, 2, 3, ..., k represent a series of consecutive annual periods of observation and let dj represent the number of patients admitted to hospital at least once in the period j. If a patient has been admitted in an earlier period during the study, most recently in period i such that i < j, then the retrograde follow-up time in years is j – i. For patients with no previous event of hospital admission during the study observation period, retrograde follow-up time is censored at j.

Retrograde hazard and survival curves are produced from the data using the Kaplan-Meier estimator.20 The underlying hazard rate of a previous hospital admission at time point t, going backwards in calendar time is given by:


Equation (1)
where d(t) is the number of admissions in the interval (t, t + {delta} t) and n(t) {delta} t is the person-time at risk in that interval. In actuarial terms, survival from a previous hospital admission in reverse-time is defined by:


Equation (2)
where dl is the number of patients with previous admissions in the retrograde follow-up interval (l, l + 1), nl is the number of patients at risk at the start of each interval, and l and t are measured here as whole years.

For a chronic disease for which the retrograde hazard is monotonic and decreasing with reverse-time and where the survival function is decreasing with reverse-time, it is assumed that a point exists where {lambda}(t) = 0 i.e. the duration of retrograde follow-up where all previous admissions have been accounted for and there is no further hazard. We denote this point in reverse-time where {lambda} = 0, and the patient is risk-free, as tf.

To estimate tf, we fit a fractional polynomial regression curve to the estimates of {lambda}(t) at t = 0,1,2,...,k – 1, and solve (t) = 0 for t or the earliest reasonable approximation to zero if the fractional polynomial is asymptotic in form.21 For practical purposes, tf was taken to be the first time point when (t) <= 0.005. Retrograde survival at the point when the risk of admission is 0, S(tf), is evaluated from the retrograde survival curve at the equivalent point in time.

A correction factor for over-ascertainment of incident cases due to the prevalent pool effect is now given by the conditional probability of an admission being the true first admission, conditional on no previous admission;


Equation (3a)
and

Equation (3b)
where j effectively represents the number of years of clearance available for each annual period of observation in the study. The derivation of Equation 3aGo is given in Appendix 1.

The corrected number of first admissions is then obtained by multiplying the observed number of first admissions, Ioj, by the proportion of patients estimated to be having their true first admission, Cj, given a specified number of years data. Thus, if Ioj is the observed number of first-time hospital admissions in period j, then a corrected estimate of the number of incident cases in period j is:


Equation (4)

Correction weights for individual patients
A further refinement of the backcasting method may be used to derive correction weights for individual patients with first-time hospital admissions in a file of linked hospital morbidity data. The correction weight, Cx, is the probability that the individual case x is truly incident, as distinct from a member of the prevalent pool of previously admitted patients.

In this analysis the structure of annual files of linked hospital morbidity data is ignored. All hospital admissions are included in the model rather than just the first admission per year as with the annual method. For each admission in the study, let a denote the date of admission, b the date of the most recent previous hospital separation, and c the first date of the study observation period. The retrograde follow-up time is for cases with previous events or for censored cases. Whether or not a, b or c occur within the same annual period within the study makes no difference.

Retrograde hazard and survival curves are generated and tf and S(tf) are estimated using fractional polynomial regression as above. In this case, tf was taken to be the first time point when (t)<= 0.00001, given the different scaling in comparison to the method for annual files.

The Cx are estimated as:


Equation (5a)
and


Equation (5b)

Corrected estimates of incident cases in the study, or in different annual periods within the study, are then obtained from:


Equation (6)


    Variance estimation
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 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
It is possible to derive approximate variance measures for both the annual and individual methods and the formulas are shown below. The values given by Equations 9 and 10GoGo are virtually the same as Equations 7 and 8GoGo, and by virtue of its simplicity and ease of calculation using standard software, Equations 7 and 8GoGo are the recommended choice for calculating variance. We used SAS(r) for data management and analysis and STATAtm for the fractional polynomial regression.

Variance of the correction factor, Cj and the corrected incidence Îcj for the annual method


Equation (7)



Equation (8)

Variance of the correction factor, Cx and the corrected incidence Îc for the individual method


Equation (9)



Equation (10)


    Example of linked hospital morbidity data for diabetes mellitus
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 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
Linked data containing all records of patients admitted to hospital with any mention of diabetes mellitus, International Classification of Diseases, Ninth Revision Clinical Modification (ICD-9-CM) code 250.x22 during 1980–1995, were extracted from the Western Australian Data Linkage System on 25 September 1998.8 The data extracted included linked hospital morbidity data and death records. Use of the database for this study was approved by the University of Western Australia Committee for Human Rights and the Health Department of Western Australia’s Confidentiality of Health Information Committee.

The incidence of hospitalized diabetes was estimated using the linked hospital morbidity data and then corrected using the backcasting method, first the method for annual records and then that for individual records. Incident cases of hospitalized diabetes were defined as the first-ever admission of a patient that mentioned a diagnosis of diabetes in any of 19 diagnosis fields. The backcasting method was applied as described above, by age group and for all ages combined. The annual method requires a hospital morbidity file containing the first diabetic admission per person per year while the individual method requires a file containing all diabetic admissions.

The retrograde hazard and survival curves used in the backcasting method are shown in Figures 1 and 2GoGo. The powers and coefficients for the fractional polynomial fitted to the hazard curves are given in Appendix 2. At time zero it appears that all admissions are first admissions as there is no data available from the following year (1996, –1 years in reverse-time) that would indicate if somebody had been admitted previously, that is in reverse-time. The Figures show that the prevalent pool persisted for 13 years according to both the method for annual files and for individual patients. The hazard and survival curves for both methods have the same shape but are on a different scale. This difference is mainly due to the large number of past events in the first year of retrograde follow-up, all of which are counted in the individual method, whereas the annual method only counts zero or one event per person. The correction factors are given in Table 1Go separately for both methods and were calculated using Equations 3a and 3bGoGofor the annual method and Equations 5a and 5bGoGo for the individual method. They are similar and thus result in similar incidence estimates. An example of calculation of the correction factor using the annual method is given in Appendix 3.



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Figure 1 Retrograde hazard curves for previous diabetes-related hospital admission

 


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Figure 2 Retrograde survival curves showing the proportion of hospitalized diabetics having no previous diabetes admission

 

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Table 1 Correction factors for diabetes incidence according to the number of previous admission-free years observed in linked hospital morbidity data
 
The difference between incidence estimates when calculated using the single correction factor and using the age-specific correction factors was less than 1.3%. We report results for all ages combined in the Tables but age-specific correction factors were used to calculate age-standardized rates for the Figures. The 95% CI were calculated for the annual backcasting method and these were within the range of four to eight cases either side of the estimated incidence. The trend over time in the observed and corrected incidence rates of new cases of hospitalized diabetics in Western Australia are shown in Figure 3Go.



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Figure 3 Observed and corrected incidence rate of hospitalized diabetes, Western Australia, 1981–1995

 

    Validation of the backcasting method using the Perth MONICA data for myocardial infarction
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 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
All records of people managed in hospital for their first definite or possible myocardial infarction, with a principal diagnosis of myocardial infarction (ICD-9 and ICD-9-CM codes 410.x)22, were selected from the MONICA database. The MONICA database covers 1984–1993, for residents of the Perth Statistical Division in Western Australia who were aged 35–64 years. Perth is one of 32 WHO MONICA collaborating centres around the world that collect data to MONItor trends in CArdiovascular disease in relation to risk factor changes in the population.

Linked data containing all records of hospital admissions for myocardial infarction (ICD-9 and ICD-9-CM codes 410.x)22 during 1980–1996, for residents of the Perth Statistical Division in Western Australia who were aged 35–64 years, were selected from the WA Linked Database. After admissions involving transfers had been concatenated into single admissions, any non-fatal admission lasting less than 3 days was excluded. Cases with a length of stay of less than 3 days are generally cases being readmitted within 8 weeks for follow-up investigations and revascularization procedures and are unlikely to be genuine cases of myocardial infarction. The backcasting method was then applied.

The age-standardized incidence rate of myocardial infarction per year from 1984 to 1993, as determined using the backcasting method, was compared against the age-standardized rate from the MONICA register.

The retrograde hazard and survival curves used in the backcasting method for myocardial infarction show that the prevalent pool persisted for 13 years according to the method for individual patients. The powers and coefficients for the fractional polynomial fitted to the hazard curve are given in Appendix 2. The correction factors are given in Table 2Go. The trend over time in the observed and corrected incidence rates of new cases of hospitalized myocardial infarction in Perth, Western Australia, compared with the incidence rate as determined from the MONICA database are shown in Figure 4Go.


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Table 2 Correction factors for incident cases of myocardial infarction according to the number of previous admission-free years observed in linked hospital morbidity data
 


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Figure 4 Incidence of acute myocardial infarction Perth, Western Australia, 1981–1996

 

    Discussion
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 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
Until the present time, studies that estimated incidence from linked data relied on a choice of three methods. Studies that used hospital discharge data alone simply reported the first-time admission rate during a given time23–25 or they may have employed a clearance period to remove the prevalent pool effect.13–16 Alternatively, hospital discharge data were combined with other data sources (e.g. survey data, diabetic clinic data, primary health care records) to determine more accurately if each hospital admission represented a new incident case.26–28 The use of complementary data sources is likely to be the most accurate method to identify incident cases, but it is dependent on the availability of data from other sources and the cost may be prohibitive for routine monitoring and surveillance purposes.

The problems with the first two methods are illustrated in Figure 3Go. The ‘observed’ line represents the results of the first-time admission method. The method using a clearance period of 5 years would be illustrated if the results prior to 1985 were ignored. The ‘corrected’ lines show the results obtained from the backcasting method. Comparison of the observed and corrected lines shows that the first-time admission method substantially overestimates the incidence rate of new hospital admissions if data covering a sufficient duration of time are unavailable. The clearance period method is reasonably accurate, but results in the loss of information from the early years of observation and is dependent on an accurate decision as to the best duration of the clearance period.

The advantage of the backcasting method is that it can be used on hospital discharge data alone, it provides more accurate estimates of incidence rates than first-time admission or the use of a clearance period, and does not require any data to be discarded, which is particularly important when measuring trends over time. The backcasting method also avoids the delays and costs associated with searching through medical records and dependence on alternative data sets. The backcasting method using annual files and individual data produced very similar results and thus either could be used, although the method for annual files is the simplest.

Data on the incidence rate of diabetes in Australia and around the world are scarce. The crude community-based incidence rate in the US in 1994 was reported to be 3.7 per 1000 person-years (py), compared with 5.6/1000py in the Canadian province of Manitoba in 1991 and 2.8/1000py in 1991–1995 in Skaraborg, Sweden.29–31 Our crude estimate of the hospital-based incidence rate rose from 1.3/1000py in 1991 to 2.5/1000py in 1995. (The prevalence of diabetes in Australia is below the average for developed countries.32) Inevitably the Western Australian figures obtained from linked hospital morbidity data have not included patients with mild diabetes mellitus, who were never admitted to hospital for their condition. Nevertheless, the results suggest that either the incidence rate of moderate to severe diabetes has increased in the population or the risk of admission to hospital or the propensity for the diagnosis of diabetes to be recorded on hospital discharge abstracts has increased.

The validity of the backcasting method for removing the prevalent pool effect is demonstrated by the myocardial infarction data in Figure 4Go. The hospital morbidity data tend to overestimate the incidence of myocardial infarction. This is due to the more conservative definition of myocardial infarction using MONICA criteria compared with clinical practice. The percentage of cases coded by MONICA as ‘not acute myocardial infarction’ is less than 10% and remains fairly constant over time. Nevertheless, the prevalent pool effect is clearly visible in the earlier years. Application of the backcasting method removed the prevalent pool effect such that the percentage overestimation of the incidence of myocardial infarction when using the hospital morbidity system became approximately constant at around 15% until 1991–1993 when this dropped to 10%. In monitoring trends, the validity of relative changes in rate are also an important measure.

The accuracy of the incidence estimates presented will be effected by migration from and to WA. This averaged 3.5% from and 2.6% into WA during 1990–1998 and was most common in the younger age groups (25–40 years).33 In the future, linkage of the State Electoral Roll to the WA Linked Database should enable more accurate estimates of the effects of migration into and out of Western Australia. The accuracy of incidence measures from hospital morbidity data are also affected by trends in hospitalization patterns of patients and the propensity to record accurate information on discharge abstracts. It is important that the results of this study are interpreted in the light of changing patterns of hospital care and changing quality and completeness of morbidity data. Nevertheless, provided patterns of hospital care and the performance of information systems can be assumed to have remained fairly steady, incidence rates based on linked administrative data are reasonably construed as a reflection of underlying disease occurrence in the population.

We have quantified the effect of the introduction of case-mix funding on diabetic admissions by applying a Cox regression model to look at the effect of calendar time on time to readmission while controlling for age and sex. This showed that the risk of readmission in the 1990s was up to 15% higher than in the 1980s, suggesting that some of the increase in the incidence in hospitalization was due to the increasing proportion of patients admitted or identified in comparison to earlier years. It follows that the backcasting method is likely to overestimate the size of the prevalent pool effect and underestimate incidence in the earlier years. The size of this effect can be estimated by running the backcasting model on data for 1980–1990 only, and this suggests that the level of underestimation is less than 3%.

The advantages of this method are its ease of use with routinely collected data and the relatively low cost of applying it in comparison to community surveys or maintaining formal disease registers. The availability of primary medical care data or data on pharmaceutical prescriptions would make a further substantial contribution to improving our estimates of the numbers of incident cases. In this paper we have illustrated the method using the example of diabetes mellitus, but it can be generalized to other chronic conditions that require hospitalization, for example, severe mental illness such as schizophrenia, cerebrovascular disease, peripheral vascular disease, chronic obstructive pulmonary disease, Parkinson’s disease, multiple sclerosis, and rheumatoid arthritis; and to other applications of linked data in the field of health services research such as the study of trends in first-time health care procedures and pharmaceutical prescriptions.


KEY MESSAGES

  • A new method is described using linked hospital morbidity data to estimate the incidence of serious chronic disease.
  • Advantages of the method are its ease of use with routinely collected data and its relatively low cost of application.
  • The method is illustrated using data on diabetes mellitus and acute myocardial infarction.
  • Validation was undertaken using the Perth MONICA database for cardiovascular disease.
  • The incidence of diabetes mellitus was shown to be rising rapidly during the early 1990s in Western Australia.

 


    Appendix 1
 Top
 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
Derivation of equation 3aGo
S(t) = probability(no admission prior to time t)

1 – S(t) = probability(admission between 0 and t)

Probability(admission between 0 & tj) = 1 – S(tj) where tj is start of the study observation period

Probability(admission between 0 & tf) =*1 – S(tf)

Probability(admission between tj & tf = [1 – S(tf)] – [1 – S(tj)] =*S(tj)S(tf)

Probability(admission between tj & tf but not 0 & tj) = S(tj)S(tf)

Cj = Probability(first admission) = 1 – (the probability of admission between tj and tf but not 0 and tj)

= 1 – [Probability(admission between tj and tf but not 0 and tj)/Probability(no admission between 0 and tj)]

= 1 – [Probability(admission between tj and tf but not 0 and tj)/Probability(no admission between 0 and tj)

= 1 – {[S(tj) – S(tf)]/[1 – (1 – S(tj))

= 1 – {[S(tj) + S(tf)]/S(tj)}

Cj = S(tf)/S(tj) for tj < tfEquation (3aGo)


    Appendix 2
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 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
Go


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Powers, coefficients of time, and constants for the fractional polynomials fitted to the hazard curves
 

    Appendix 3
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 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
Calculation of the correction factor using the annual method
tf for diabetes = 13 years

S (tf) at 13 years = 0.403

S (j) at 5 years = 0.461

Cj = S (tf)/S (j)

Cj = 0.403/0.461 = 0.874


    Acknowledgments
 
The authors wish to acknowledge all staff who maintain the Hospital Morbidity Data System and the Health Services Research Linked Database. The study was funded by the National Health and Medical Research Council, Australia.


    References
 Top
 Abstract
 Backcasting methods for...
 Variance estimation
 Example of linked hospital...
 Validation of the backcasting...
 Discussion
 Appendix 1
 Appendix 2
 Appendix 3
 References
 
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