a new index of utilization of ambulatory medical care

F R A N ( ~ O I S BI~LAND, R A Y N A L D P I N E A U L T ,

A N D G R E G S T O D D A R T

A N E W I N D E X O F U T I L I Z A T I O N O F

A M B U L A T O R Y M E D I C A L C A R E

(received 5 January, 1988)

ABSTRACT. Studies of utilization of ambulatory medical care have used as indicators of utilization the number of visits or a dichotomous variable measuring whether there was at least one visit in a period of time. Recently, these measures have been criticized on the ground that they do not distinguish between visits initiated by the patients and the follow-up visits prescribed by the physician within an episode of care. Taking into account the fact that delineation of episodes of care is intractable in most research endeavours, an index of utilization of ambulatory care is proposed here to measure the pattern of care. Using as data the date at which visits occured within a period of time, the index takes into account these criticisms. The validity of the index is also assessed.

Most of the research dealing with office-based visits to physicians has generally used, as indicators of utilization, measures such as total number of visits or the occurrence of at least one visit over a period of time. These studies have generally failed to explain variations in the utilization of office-based visits partly because the measure of utilization itself is inappropriate to the research question [1--8].

Recent studies on utilization have focused on the occurrence of episodes of care rather than on visits as such [9--12]. An episode of care has been defined as the care required by an individual over a period of time for a medical condition [13--15]. Although the medical condition of a patient sets the general boundaries of the episode of care, an observed episode of care can begin before or after a medical condition is identified by the patient or by the physician, and it can end before or after the medical condition has disappeared. A major contribution in this regard is the work of Hornbrook and his colleagues [16]. They propose the general term "health care episode" which is "the period of time during which a specific disease process, illness, health care problem, or treatment process is present" [16]. A health care episode can be broken down into the following: episode of disease,

Social Indicators Research 21: 409--439, 1989. �9 1989 KluwerAcademic Publishers. Printed in the Netherlands.

410 FRAN(~OIS BI~LAND ET AL.

episode of illness, health maintenance episode and episode of care. The distinction between episode of disease and episode of illness is particularly interesting. The former represents the provider's perspective as it "begins with clinical specification that a disease is present and ends with specification that it is resolved" [16]. The latter, representing the patient's perspective, "is defined as a single, unbroken interval of time during which the patient suffers from a continuous spell of signs and/or symptoms that are perceived as sickness or ill-health" [16]. In this sense, episodes of disease may exist almost independently of episodes of illness.

An episode of care "designates a series of temporally continuous health care services related to the treatment of a given spell of illness or provided in response to a specific request by the patient or other relevant entity" [16]. An episode of care can refer to the services rendered by a single or multiple providers and it can include a single or multiple hospitalizations during a defined period of time [14]. An episode of care can coincide with one episode of illness or embrace several of them. The boundaries of episodes of illness are often difficult to draw. Hence, from an operational standpoint, the onset of an episode of care can be the initial contact with the medical care system. Conversely, the ending point is represented by the last medical care encounter which was followed by a sufficient lapse of time before the next one. Of course, the term "sufficient" has yet to be operationally defined. Physician episodes of care have also been defined to take into consideration the contribution of each provider when more than one is involved in an episode of care tT. Finally, health maintenance episodes involve a series of contacts with the health care system which "do not involve a disease or illness" [16].

This article addresses the overall question of the relationship between utilization and episodes of care. Specifically, the objectives are: (1) to develop a measure of utilization based on the view that medical care is rendered within the context of episodes of care, and (2) to assess the validity of this new measure.

1. THE EPISODE OF CARE AND THE DISTRIBUTION OF VISITS

Studies concerned with utilization of ambulatory medical care generally tend to explain this phenomenon by referring to social, psychological,

INDEX OF USE OF MEDICAL CARE 411

organizational and economic factors [18, 19]. The model usually states that health or illness influences utilization given predisposing and enabling factors [1, 3]. But neither the number of visits, nor even the number of episodes of care, as a measure of the dependent variable in such model, takes into account the way that utilization is patterned through time. For example, a sequence of visits covering many episodes of care does not have the same meaning as a sequence of visits over the same period but confined to one episode of care. Thus, an appropriate measure of utilization should ideally try to translate, through the construction of an appropriate index, the intensity of utilization found in different patterns of care. Though the number of episodes alone does not seem to be an adequate measure of utilization, it must be taken into account in a composite measure of utilization. This index should also consider the fact that part of the follow-up visits within an episode of care depend on the compliance behavior of the patient.

For some problems, the researcher is less interested in the actual number of services than in the way they are rendered, their sequence and the lapse between them. In other words, what is needed is not a summative measure, but a measure that reflects the process of render- ing these services, that is the lapse between them, their relationships to one or more episodes of care, etc. This measure should be consistent with the generally accepted view that utilization results from the interaction between characteristics of the physician and those of the patient. Within this interaction, patients have relatively more influence on the initiation of episodes of care while physicians have relatively more influence on the number and patterns of services used during an episode [20].

Medical encounters within an episode of care can be numerous and distributed over time in many ways. Furthermore, within a given period of time, an individual can experience many episodes of care that will either be distributed evenly or clustered in an uneven way. That is, the utilization of ambulatory medical care tends to form a particular pattern in time for each individual. This modeling in time is a two-stage process whereby utilization depends on (1) the number of episodes of care and (2) the number of encounters within each episode of care. This process can be translated into probabilistic language. Encounters or visits over a period of time are not independent events; some of them are correlated because they are part of the same episode of care.

412 FRANI~OIS Bt~LAND ET AL.

The purpose of our measure of index is precisely to control for this intercorrelation of events over time.

One way of representing this intercorrelation is to construct a typology that cross-tabulates the number of episodes with the volume of utilization. If each of these dimensions is dichotomized into high and low levels, a table is obtained (Table I).

On the one hand, the two cells that are most relevant for medical care are I and II, that is high utilizers. In terms of the model of utilization, these two types are different. In cell I, the number of episodes is high. This indicates a high propensity for patients to initiate episodes of care. Cell II contains the high utilizers of services who have probably experienced a single episode of intense utilization of health services, involving a serious disease or overprescribing by the physician or both. On the other hand, cell III may represent a "reservoir" of unmet needs. For example, low utilizers of services coupled with a high number of episodes may well represent individuals who are sick, that is, who have had several episodes of illness and, consequently, of care, and who use medical care insufficiently. Cell IV seems to reflect a different phenomenon. Indeed, utilizers may represent healthy people who have very few contacts with the medical care system, these being for minor problems of short duration.

Clearly, the meaning of utilization differs for each combination of frequency of episode of care and volume of visits. A measure based

TABLE I Typology of utilizers of health services according to the volume of visits and the number of episodes of care during a period

of time

Volume of visits

high low

Number of high I Ill episodes of care low II IV

INDEX OF USE OF M E D I C A L CARE 413

exclusively on the number of episodes or on the number of visits, is thus an incomplete indicator of total utilization, although such specific measures may be appropriate for certain types of studies [19]. Inves- tigations of total utilization require a measure which combines both sources of variations in the utilization pattern. The index of utilization proposed here attempts to satisfy this requirement.

2. D E L I N E A T I O N OF E P I S O D E S OF CARE

As mentioned earlier, precise delineation of episodes of care is a very difficult task for both conceptual and practical reasons [16, 21]. Conceptually, delineation algorithms must allow for the possibilities of concurrent or interleaved episodes, and the former may involve situa- tions in which a specific service addresses two or more concurrent, but distinct problems of the patient. For successive episodes of care for the same illness, it is necessary to specify some appropriate period of elapsed time between the episodes in order to delineate them. Yet, at least in principle, this period is illness-specific. Further, such episodes of care may be part of one prolonged or chronic illness, or may be generated by different illness episodes for the same condition. When delineating episodes of care for ostensibly different illnesses, care must be taken to label each illness appropriately in order to avoid mistaking individual illnesses for episodes of care.

Practical problems of measurement can also be formidable. The utilization data that are typically available have not been generated or stored for research purposes, but rather for administrative, often reimbursement-related, activities. They often do not contain sufficient detail or accuracy for episode delineation. Diagnostic information, critical to episode delineation exercices, is frequently imprecise or unreliable, and the typical levels of missing data on key items such as date of care, procedures provided, or diagnosis can easily prohibit meaningful delineation. In the absence of generalizable algorithms for the delineation of episodes of ambulatory care that require a minimum of precise, reliable information, or until improvements in data systems will routinely support more demanding algorithms, an index of utilization consistent with episodic principles may be an extremely useful addition to methods of analyzing utilization data.


An example will convince the reader. The file of the Quebec National Health Insurance Board (R6gie de l'assurance-maladie du Qu6bec -- RAMQ) includes information on the following: the sex and age of the patient, the physician claiming the fees, his/her specialty, the code of the service claimed, the amount of the fees, the place where the service was rendered and finally the diagnosis according to ICDA-9 codes. Unfortunately, the diagnosis is coded by the RAMQ for a random sample of claim forms, corresponding to 60% of the total. However, as claim forms represent charges, rather than encounters, and as there can be more than one charge for a single encounter, it may be possible to link a diagnosis to a sufficient number of charges to be able to make up episodes of care [21]. For this purpose, the 1981 RAMQ file on the ambulatory care of patients 15 years old and over, from the Island of Montreal, has been thoroughly examined. Seven cases have been extracted here for illustration, and are shown in Table II.

The diagnoses in Table II are ICDA-9 codes classified according to the Schneeweiss et al categorization scheme for ambulatory medical care. It is clear from this Table that any hope of systematically recon- structing an episode of care on the basis of diagnosis alone should be abandoned.

The episode of care for patient # 7 consists of one visit with two charges claimed by physician # 35173. A diagnosis of low back pain was made. This is an example of a fully documented episode of care. In the case of patient # 8, we have been less lucky, as the only claim made on her behalf does not include the diagnosis.

The first case of obesity is fully documented (patient # 11), while only one of the visits is documented for the second case. For patient #55, the diagnosis of the visit on day 119 in 1981 is not coded, although we know that an ECG was made on this occasion. A hundred days later, a complete examination was made by a GP with a diagnosis of adverse effects of medical agents. Who prescribed these agents? Or were non-prescribed drugs involved?

The other case is much more complex, but leaves us even less comfortable. For patient # 10, the diagnosis on the 41 st day of 1981 is not documented. Some 60 days later, two diagnoses are made by two different GPs, one being on a night call and giving a diagnosis of mononucleosis. This diagnosis was not confirmed by the second GP,

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416 F R A N ( ~ O I S BI ~L A N D E T AL.

seen the very same day, most probably during day time. Because no visit occurs until 40 days later, the diagnosis of mononucleosis can most probably be discarded. Then three other visits follow. One may conclude that as there are forty to a hundred days between each visit, there is the same number of visits and episodes. But, we do not need the information on the diagnosis to reach this conclusion!

This study of seven cases indicates that despite an incomplete set of data, episodes of care can be delineated in a number of cases. However, this would require that each record on the RAMQ file be examined.

Formal rules for attributing a visit to an episode are very difficult to devise here [21, 12]. This task of going through all cases is almost an impossible one, even with a medium sized sample, as is the case here. The 2241 cases in the file generated 14634 visits and a total of 17195 medical procedures. Thus a measure based on the pattern of care received by a patient should be devised using an approximation of the mixture of episodes of care and the number of visits within the episodes. This measure should also be an approximation of the way

episodes are distributed throughout the time period observed. The utilization index developed here will be based on the information generated by the administrative file available to us. As the structure of this file is not unique but can be found in many other administrative files on health care utilization, our index will have potential use for other researchers.

3. T H E R A T I O N A L E F O R C O N S T R U C T I N G

AN I N D E X O F U T I L I Z A T I O N

The major task in the construction of an index of utilization is to weigh adequately visits within one episode of care. Two assumptions will be made to describe the functional relations between visits and episodes of care:

1. Visits that occur in clusters have a higher probability of being due to a small number of episodes than visits that are thinly spread over time. Thus the former should have less weight than the latter in an index of utilization in order to reflect accurately the occurence of episodes of care.


2. The probability is higher that visits which are distributed over a long period of time are due to more episodes of illness than visits that are distributed over a shorter period of time. The latter should then weigh less than the former in the computation of an index score for a given patient.

These two assumptions concern (a) the distribution of visits over time and (b) the period over which the visits are made. They derive from the following considerations of the links between visits and episodes of care:

1. Different forms of the distribution of the same number of visits over a period of time can be observed for different individuals. For instance, individuals with three visits over a period of time can have a sequence of clustered visits or a sequence of visits sparsely distributed over time; and the period of time over which the visits are distributed can be more or less extensive.

2. The period of time over which a fixed number of visits extends varies within a sample or a population. Thus the meaning of the distribution of the visits, clustered or not, varies with the number of visits considered and with the total time over which the period extends. Hence, three visits made over a period of 15 days are already clustered and probably come from the same episode. But three visits to a physician in a period of six months can be grouped either in two episodes, with respectively one and two visits each, or in three independent episodes.

3. Because, in any given time period, there is a limit to the number of ways in which a high number of visits is distributed, while the distribution of a small number of visits is less limited, the variation of the index of utilization for a high number of visits should be smaller than the variation for a low number of visits. Thus, the index of utilization should increase the variation for a small number of visits in a sample or a population, allowing, at least theoretically, a better distinction among patients with different patterns of care, but with an equally low number of visits. Simi- larly, an index of utilization should decrease the variation for observations with a high number of visits. As these observations represent utilization patterns with fewer episodes than visits, this


should increase the reliability of the index of utilization, since patients with the same pattem of utilization, but with a different number of visits, should get nearly the same score on the index.

4. AN INDEX OF UTILIZATION

a. Some Operational Considerations

The synthetic utilization index (UI) of office visits to physicians which we propose is based on explicit assumptions about the components of utilization and the way these components are functionally related. These assumptions and their functional relations can be translated into mathematical functions. In many instances, the mathematical functions used here to represent these elements and their relations will be arbitrary. Functions other than these could have been chosen. However, we felt that these functions were realistic. When using only the number of visits over a period of time as an indicator of utilization, one is making implicit assumptions that are never made clear, or justified, or examined in any small or great detail. Here we start with the notion that utilization is a function of episodes of care within which one or more visits might occur. These assumptions will be translated into parameters linked by mathematical functions which describe the way episodes of care vary within a period of time, given the range of that period.

The task before us is not to weigh explicitly visits within an episode (although the index of utilization should approximate the effect of episodes of care on the utilization score of an individual) but rather to define the parameter of the UI index in such a way that it uses the partial information on patterns of medical care use available in most data sets. This information should be easily collected within the format of an interview or a questionnaire or should be available from second- ary sources.

b. The Unit of Measurement

When the number of visits is used as an indicator of the pattern of utilization, the distance between each visit is equal to one. By contrast, the distribution of the number of days for each patient between a fixed


point in time and the date of each visit, takes into account the pattern of the distribution of visits in one period. For each patient in a data set, this fixed point (to) is defined here at the first occurrence of a visit. The time at which another event occurs is time I~ and is equal to the number of days elapsed from t o . This definition follows the general usage in longitudinal analysis.

It is appropriate to use this definition for a number of ieasons: (1) the number of days is a continuous measure and can be submitted legitimately to all the usual mathematical operations, (2) the occurrence of each visit is identified by one value that clearly distinguishes it from all other visits, (3) these values increase with the rank of the visit in the distribution, (4) the values associated with the distribution of visits describe the pattern of visits through time, and (5) the distances between visits are not uniformely one. These distances vary as a function of the pattern of visits in a period. Visits that occur in clusters have short distances between them, while visits that are sparsely distributed over time are separated by larger distances.

c. The Functional Form of the Index

An index of utilization should reflect, as defined above, (1) the way visits are clustered over time and (2) the time range of the occurrences of visits. The global assumption is that the location of visits over a period of time depends on the occurrence of episodes of care. As the variations in these locations and their time range are functions of these occurrences, an index of utilization can be based on the former to measure the latter.

The first assumption is concerned with the variation in the location of visits over a period of time. The standard deviation is precisely a measure of the variation of events. However the standard deviation of the location of visits that are highly clustered will have a larger value than the standard deviation of a pattern of utilization with less clustered visits. The standard deviations will have a larger value because, given the same period of occurrence of visits, highly clustered patterns imply more variations in the distribution of days of visits than patterns with a more uniform distribution of days. This behavior of the standard deviation is the inverse of what is required by the first assumptions described above. Thus an index of utilization should be an inverse


function of the standard deviation of the pattern of visits of each patient.

The goal of the index of utilization is to score the utilization of individuals. Thus, the index should use a parameter that is measured in comparable units over a whole set of individuals. In statistical literature, the coefficient of variation (CV) is used to define the behavior of a distribution of events between samples [23]. This coefficient is simply the ratio of the standard deviation to the mean. Here we want to measure the variations in the distribution of events (visits to physicians) occuring to each individual registered in a data set. The standard deviation usually measures the extent of the variations in a sample, and its absolute value varies as to the mean of the distribution. As the mean of the distribution of events differs from one sample to another, the standard deviation is adjusted, in the coefficient of variation, by taking the ratio of the standard deviation to the mean. The mean of the distribution of visits through time is simply the mean time elapsed in a period before the occurrence of an event. In the case of two specific patients with the same number of visits arranged in patterns which mirror one another, the mean will be higher for the pattern with the visits concentrated at the end of the period, and lower for the pattern of visits concentrated at the beginning of the period. This is not appropriate as both of these patterns should have an equal score on an index of utilization. Patterns of visits are said to mirror each other if the distances between the number of days are the same over the period, but arranged in reverse order.

The mean is used in the CV to standardize for the unit into which the standard deviation is measured. The range of the distribution of visits for a patient can play this role because it is an indicator of the unit into which the standard deviation is measured. Thus the range can standardize the values of the standard deviation of the distribution of visits for each patient, making these standard deviations comparable among individuals.

The inverse of the ratio of the standard deviation to the range will be used here as the parameter in the index of utilization which takes into account the clustering of visits within episodes of care.

The second assumption is concerned with the range over which the visits occur. The R is introduced in the R/s ratio to standardize the

I N D E X OF U S E OF M E D I C A L C A R E 421

score (the inverse of the standard deviation) for each individual. Now the range should be introduced explicitly in the indicator of utilization. The number of episodes should be proportional to the range because, given an equal number of visits, the probability is higher that they will come from a higher number of episodes if the range is large. Thus, the R/s ratio should be multiplied by a function of the range. An arbitrary transformation of the value of the range is proposed here to measure the effect of the range on the estimation of a monotonic function of the number of episodes weighted for the number of visits within episodes: the square root of the range. This function reduces the effect of the range on the value of the indicator of utilization. We feel that extreme values -- 365 days for a period that extends over a year -- are too high and should be reduced.

If the two results obtained thus far are merged by a product, the index of utilization is:

UI -- ,~- • R R 3/2

s s

This index is thus defined as inversely proportional to the standard deviation of the distribution of days at which the visits occur over a period of time and as directly proportional to the distance in days between the first and the last visit in the same period.

Each of the characteristics of utilization in the assumptions given at the beginning of this paper has been considered. The behavior of this index will be described, and its usefulness will be assessed through (1) an analysis of the form of its distribution (normality and skewness), (2) an analysis of its relation to an indicator of intensity of care received in 1981 by the patients in the sample and (3) a study of groups of patients with different levels of care.

5. AN E M P I R I C A L S T U D Y OF U T I L I Z A T I O N B E H A V I O R S OF

A S A M P L E OF P A T I E N T S IN M O N T R E A L

a. The Data

The data used in this study are representative of the patients living on Montreal Island and seen by general practitioners and specialists in

422 FRANCOIS BI~LAND ET AL.

ambulatory care in 1981. The sample was drawn from the 1981 file of the "Rrgie de l'assurance-maladie du Qurbec" (RAMQ), the adminis- tration responsible for the payment of physician claims. In the Province of Quebec, each citizen is fully covered for medical care costs, without direct charges or co-insurance payments.

The RAMQ file represents the total utilization of physician services paid for on a fee for service basis in the Province of Quebec. A total of 17197 charges were claimed for 14634 office-based visits by physicians on behalf of the 2241 patients in our sample. The charges claimed by physicians who do not give office-based ambulatory care are excluded from our sample (pathologists are a case in point). Furthermore, the only patients included in the sample were those old enough either to make the decision to visit the physician or to have a say in that decision. Consequently, children younger than 15 years old were excluded from this study. Visits to an obstetrician-gynecologist were explicitly excluded because medical care to pregnant women, with its specific pattern, can bias the results of the analysis. Well-baby care and pregnancy care are not studied here.

The data represent the utilization of office-based visits by a group of patients over a one year period. The visits occurred either in private clinics, in ambulatory care hospital clinics or in a hospital emergency room. Emergency room visits for patients admitted to hospital within the process of the care were excluded from the data base. The beginning (1st of January 1981), and the end (31st of December 1981) of the period are arbitrarily chosen. The data are left and right censured: an episode of care could have started in 1980 or could have ended in 1982. Thus the data set is truncated and the utilization patterns of some patients are not fully covered here. However as utilization is observed over a period of one year, and as the truncation occurs over the same season (winter), this should not have an immediate impact on the assessment of the validity of the UI index.

b. The Distribution of the Index Scores

Figure 1 shows the plot of the logarithm of the number of visits for our sample of 1981 Montreal patients. In Figure 2, the logarithm of the scores on the index of utilization (UI) are plotted for the same sample. The plot of the log of the number of visits is as expected. Similar

I N D E X O F U S E O F M E D I C A L C A R E 423

Frequencies

450

400

350

300

250

200

i50

t00

50

0 I I I | I I I I I I I I I I I I I I I I N ~ ' - - ' - - - I

. . . . ~ . ~. ~ . ~. ~ . ~ . ~ . ~ . ~ . ~ . ~ . ~ . ~ . ~ . ~ . ~. ~.

LOG (number of v i s i t s )

Fig. 1. Plot of the distribution of the log of the number of visits for a sample of patients Montreal, 1981.

Frequencies

4O0

35O

3OO

25O

2OO

150

iO0

5O

0

LOG (UI}

Fig. 2. Plot of the distribution of the scores of a sample of patients on the logarithm of UI Montreal, 1981.


distributions have been found in the United States, Great Britain and Quebec. The distribution is extremely skewed to the left. The distribution of the number of visits has often been approximated by a truncated negative binomial (TNB) rather than by a normal distribution. The hypothesis that the distribution of visits is reproduced by a TNB cannot be rejected here at the 0.05 level (X 2 = 34.6 with 29 degrees of freedom). Even the log transformation of this distribution cannot efficiently be used to approximate a normal distribution. In Figure 2,

the distribution of the log of the UI scores is shown to be approximately normal with a skewness of - 0 . 8 5 and a kurtosis of 1.31 exclud- ing the patients with one visit only. The mean and the median are approximately equal with X = 4.27 and MED = 4.39. The distribution

of the log of the UI scores is thus slightly skewed to the right. Patients with only one visit in the 1981 data file have the same UI

score of zero if "log 0" is defined as zero, because they have a standard deviation of the distribution of the days in the period equal to zero. This is a consequence of the fact that the observed distribution of visits is censured. In these censured cases the real value of the patient score on the index of utilization cannot be evaluated. It can take any value from a real zero, if the visit in 1981 is really their first visit in their life, to another value representing the time elapsed since their last, but unrecorded visit. It is a matter of speculation to attribute to individuals with only one visit a score of zero or a missing value on the index of utilization. Also, one can speculate on the possibility that these individuals have a higher than average probability of being low users of health services, and thus of being positioned in the left part distribution of the log of the UI scores. This would decrease the skewness of the distribution in Figure 2.

c. A Study of the Criterion Validity of the UI Index

The validity of a measuring device is best ascertained by a comparison with a criterion measuring exactly what the instrument intends to measure. Here we suggest that the UI index is a better device than the number of visits to measure the total utilization pattern of an individual. If a criterion measure were readily available, this criterion by itself should be used and there would be no need to search for a utilization index.


Although no suitable criterion measures are available, information on physician charges in the RAMQ data set can be used as a proxy measure for intensity of service in tests of criterion validity of the UI index. A patient's total charges are the sum of the claims from physicians on behalf of a patient over the 1981 period. Within the data base available here, these physician claims are based on a fee schedule negotiated by the physician unions (one for the specialists, another for the GP's) with the Ministry of Health and Social Services of the Quebec Government. The claims made by the physicians are charges for very general categories of care (general examination for example), or rather precise diagnostic or therapeutic actions (anti-allergic injections is a case in point). More than one charge can be claimed by the physician for one visit. On the one hand, the charge for each physician activity represents a mix of the time required to accomplish it, the physician competence involved, the importance the government and the physicians attach to it, and the negociating strategies and political goals pursued by each of them. On the other hand, the total charges generated by the care for one patient represent a mix of the needs of the patient, the interpreta- tion physicians give to these needs, and the physician claim strategies. The total charges are thus an imperfect indicator of the intensity of medical care delivered in the physician's office, but they represent the value a society attaches to specific professional activities at one moment in time, weighted by the amount of money the political authority and the professionals themselves have agreed to settle for, over a bargaining table.

The charges claimed by a physician on behalf of a patient are made on the basis of the procedures the physician applies during a visit. Many procedures can be applied during a visit, but their number is in fact limited. Most of the claims are made for an ordinary or a complete examination; of course only one of these can occur in one visit. As a consequence there is a strong correlation between the number of visits made by a patient and the total charges claimed by a physician on his behalf. But there should also be a correlation between a measure of utilization that tries to integrate the variations in utilization patterns due to an episode of care, and the total charges. The first visit in an episode of care should be more costly than the follow-up visits, as the physician will provide more comprehensive services (complete examination rather than an ordinary one) to investigate the case, and could apply

426 FRANCOIS Bt~LAND ET AL.

more procedures to ascertain the diagnosis. The follow-up visits can consist of less complicated procedures or in a routine and limited check on the evolution of the illness. Thus, there is a rationale for expecting a significant correlation between the index of utilization (UI) and the total physician charges.

When the log of the annual charges is regressed, first on the number of visits, and second, on the UI scores, 64.3% of the variance of the charges is explained in the first case, and 75.7% in the second case, when the quadratic term is included in both regression equations. But, if the log of the number of visits is entered in the regression equation with its quadratic term, 83.6% of the variance of the charges is explained, while 78.2% of the variance is explained by the log of the UI scores. However, the quadratic term is not significant in the former case, although it remains significant in the latter.

The charges are clearly correlated with the number of visits and with the index of utilization proposed here. The logarithmic tranformation has more impact on the number of visits than on the UI score. In the latter case, the transformation has almost no impact on the variance of the charges explained. The index of utilization (UI) tries to take into account the effect of pattern of care on utilization; the results of the regression analysis show that this operationalization of the pattern is related to the charges made by physicians on behalf of a patient. The analysis of the logarithmic transformation of the dependent variable in the two regression models does not provide clear guidelines for choosing between the log number of visits or the log of UI as an adequate indicator of utilization. However these results show that the net number of visits is the measure that has the least in common with our criterion of external validity. But as the log of the UI index is almost normally distributed, and as the regression of the total annual changes on the UI index or on its logarithmic transformation yielded the same result, we propose that this transformation be made on the UI scores. Thus the index should be named the log UI index.

d. A Study of the Internal Consistency of the Log Ul lndex

The log UI index is a measure of the intensity of utilization found in a pattern of medical ambulatory care. It is thus postulated that the


pattems are ordered along a continuum on which individual patients are classified according to the amount of care they use. Each point on the continuum indicates (1) that a patient located at that point has a greater propensity to use than a patient positioned at a lower point and (2) that a patient at this one point has the same pattern of care as all the patients with the same value on the log UI scale. The internal validity of the UI index will be assessed here, testing for this second property.

As the log UI index is a continuous measure, categories of patients have been designed using a set of arbitrary cut points as boundaries. The homogeneity of the groups so obtained will not be perfect, but these groups should provide for an adequate approximation if enough categories are defined.

Ten categories of patients were created. A first set of nine cutting points was selected from a study of the graph showing the regression of the total annual charges on the log UI scores, adding the significant quadratic terms in the regression model. Corrections to the cutting point values were made, after a preliminary analysis, in order to achieve a better homogeneity within the groups.

Some statistics on each group of patients are given in Table III. Of course the log of UI scores increases with the ordering of the group. The number of visits increases also, but much more rapidly than the log of UI scores. This essentially means that the differences between users are proportionally greater at the lower end of the log UI index than at the lower end of the number of visits scale, while this difference is proportionally smaller at the higher end of the log UI index than at the higher end of the number of visits scale. The variation on the log UI index is thus greater among low users than among higher users com- pared with the variation obtained on the number of visits. This is to be expected from the very construction of the tog UI index. The range in the number of days between the first and the last visits increases from group 1 to group 10. The low figure in group 1 shows that this group is essentially made up of individuals with only one visit, or of individuals with visits occuring in very small time lapses. The standard deviations in the distribution of days increase from group 1 to group 5, and diminish thereafter. This reflects the fact that as the number of visits increases, the ways in which it can be arranged in a calendar year decreases.

4~

b

o

Gc

TA

BL

E I

II

Sta

tist

ics

on t

en g

roup

s of

pat

ient

s

~r~

Stat

isti

cs

1 2

3 4

5 6

7 8

9 10

T

otal

> Z

L

og U

I sc

ores

0.

08

2.51

3.

29

3.76

4.

17

4.69

5,

15

5.36

5.

63

6.01

3.

42

# of

vis

its

(mea

ns)

1.08

2.

25

2.65

3.

07

4,05

6.

53

11.0

5 14

.39

21.4

4 41

.79

6.53

# of

vis

its

(min

imum

) 1

2 2

2 3

4 8

8 13

17

1

# of

vis

its

(max

imum

) 4

5 8

9 18

19

31

37

14

15

7 15

7 t-

rang

e of

the

# of

day

s > Z

be

twee

n th

e 1 s

t and

la

stvi

sit

0,12

6 19

.42

70.8

7 14

3.31

19

8.23

25

4.02

29

8,70

29

1.09

31

8.35

32

7.45

16

0.86

stan

dard

dev

iati

on o

f "4

th

e di

stri

buti

on o

f > t--

' da

ys o

f occ

urre

nce

of v

isit

s 0.

044

6.53

20

.03

42.4

1 44

.60

38.0

7 29

.31

23.6

6 20

.61

14.8

1 25

.36

Num

ber

of c

ases

48

5 15

6 14

2 26

1 24

7 56

1 12

3 10

7 78

80

22

40

INDEX OF USE OF M E D I C A L CARE 429

Table III also shows that the number of visits in each group is not fixed, varying within limits that differ and generally increase from group 1 to group 10. This distribution of visits can be used to study the homogeneity of patterns of utilization within the groups. Distributions of visits by American, English and Canadian patients have been studied in the literature to assess the diversity or the homogeneity of these respective populations of patients. The findings of these studies usually indicate that the patients have heterogeneous patterns of utilization. To arrive at this conclusion, these studies compare the fit of the observed distribution of visits to a model postulating homogeneity (a Poisson model for example), and to another model postulating heterogeneity (usually a negative binomial model). Here we will use the fit of the distribution of visits of the ten groups to a Poisson model to test for their homogeneity. This model will be tested on three distributions: (1) the distribution of visits in the ten groups for the whole of 1981, (2) the distribution of visits in a 14-day period, taking as an estimate of the average number of visits during this period the proportion of visits that should have occured within 14 days, given the annual average of visits, and (3) the distribution of the number of times two consecutive visits occur, not more than 14 days apart. The choice of 14 days is rather arbitrary here, but corresponds to one criterion that has been used to delineate between episodes of care [12]. These three types of distribution should be reproduced by a Poisson model.

In Table IV, the distribution of visits within group 1 to 9 are listed. The distribution of visits in group 10 is not given because it is too sparse to be analyzed and goes well over the 33rd visit.

To test for the l~oisson model, a distribution of events should start at the zero level. Here, the distribution starts at very different levels, from one visit to thirteen visits. A quasi-Poisson model has been defined much like the quasi-independence model in a contingency table where the cells with no observations are cells with fixed zero (structural zero). These cells cannot contain information as individuals in the sample cannot, by definition, be classified in them. Working from the usual definition of the Poisson model:

e-;ri - - ( r - - - - 0 , 1 , 2 ..) P ' = r,!

430 F R A N C O I S BI~LAND ET AL.

'7.

t5

09

t ~

r

z

Tab

le IV

(Con

tinu

ed)

GR

OU

PS

OF

PA

TIE

NT

S

Num

ber

of v

isit

s 1

2 3

4 5

6 7

8 9

Tot

al(l

)

21

1(2)

1

8 12

22

1

4 7

23

7 10

24

5

7 25

3

7 26

4

5 27

5

9 28

1(

2)

0 3

29

0 4

30

1(2)

0

4 31

1(

2)

0 3

32

2 4

33+

1(

2)

3(2)

52

Stat

isti

cs f

or th

e qu

asi-

Poi

sson

mod

el

G 2

3.

84

2.81

8.

58

6.07

2.

42

22.6

2 26

.43

20.1

5 22

.58

5675

.08

D.F

. 2

2 4

3 4

14

10

13

19

36(4

)

O

Ct~

�9

> r"

t~

(1)

Incl

udes

gro

up

10;

(2)

excl

uded

fro

m e

stim

atio

n pr

oced

ure;

(3)

add

ed

for

com

puta

tion

of

G2;

(4)

bey

ond

the

38th

vis

it,

the

dist

ribu

tion

is to

o sp

arse

to

be a

naly

sed.

4~

432 FRAN(~OIS Bt~LAND ET AL.

where Pi is the expected probability, 2 the mean of the distribution and ri the i th level of the distribution of visits, the quasi-Poisson model can be written as a log-linear model:

(rfi)F~ = 6~(-~. + N) + 6ir , (i = 0 , . . . , I)

where ,~ is an estimated mean, ri is the ith level. The 6; takes the value 1 or 0 whether the cell contains a structural zero or an observation. The 17. are the estimated log frequency and the N the number of observations in the sample. A Newton--Raphson procedure has been used here to estimate the parameters of the model [24].

The G 2 statistic is used to assess the fit of the quasi-Poisson model to the distribution found in Table IV. The G 2 is the likelihood ratio statistic and is distributed as X 2. This statistic has in practice given less weight to the deviation of small cells from the estimated frequencies than the usual goodness of fit statistic X 2. This is a desirable property here as it prevents the model from being rejected because of the inevitable bad fit of the cells situated at the tail end of the distribution of visits.

The results in Table IV show that the distribution of visits in groups 1 to 9 closely follow a quasi-Poisson model, except in the very few cases where the the level of significance reaches the 0.03 or the 0.01 level. In any case, these statistics are nearer to statistical significance than any of the other distributions of visits that can be found in the literature. It must be said that these results are obtained on grouped data, and as such are coming from groups of patients that are only approximately homogeneous. Also, the quasi-Poisson model holds better in groups with the lowest average number of visits. Further division of the groups with the highest average number of visits would not have been proper as these groups count rather small numbers of individuals (see Table III). Finally, the distribution of visits for the whole sample does not follow a quasi-Poisson model. It has already been noted that this distribution was approximated with a truncated negative binomial distribution. In conclusion, there is some evidence that each of the nine groups of patients is homogeneous with respect to the pattern of care, while the whole sample of patients is heterogeneous. This first result conforms to expectations.

The second criterion examined the homogeneity of the utilization of

TA

BL

E V

S

moo

thed

dis

trib

utio

ns o

f vi

sits

ove

r a

14-d

ay p

erio

d

GR

OU

PS

# of

vis

its

1 2

3 4

5 6

7 8

9 10

T

otal

(a)

Sm

ooth

ed o

bser

ved

dist

ribu

tion

s 0

462

144

131

1 22

11

9

2 1

1 2

3 4 5 6 7 (b)

esti

mat

ed d

istr

ibut

ion

(Poi

sson

Mod

el)

0 46

5.32

14

3.10

12

8.28

1

19.6

8 12

.35

13.0

4 2

0.40

0.

53

0.66

3 4 5 6 7 (C

) an

nual

ave

rage

num

ber

of v

isit

s 1.

08

2.25

2.

65

(Gdl

sta

tist

ics

0.12

0.

53

4.03

Deg

rees

of

free

dom

1

1 1

231

213

440

80

62

33

20

1816

27

28

10

3 33

33

32

22

31

9 3

6 16

8

7 9

23

75

2 1

4 3

6 17

1

1 1

3 7

3 3

2 2

1 1

232.

01

211.

46

436.

70

80.5

1 61

.61

34.2

7 16

.10

1743

.70

27.3

2 32

.85

109.

38

34.1

2 34

.01

28.1

8 25

.81

436.

74

1.61

2.

55

13.7

0 7.

23

9.39

11

.54

20.6

9 54

.79

1.14

1.

02

1.73

3.

18

11.0

5 4.

57

0.11

0.

24

0.65

4.

43

0.29

1.

42

0.01

0.

38

0.00

0.

09

0.00

3.07

4.

05

6.53

11

.05

14.3

9 21

.44

41.7

9 6.

53

1.08

4.

41

1.46

2.

77

4.24

1.

60

12.8

0 15

0.41

1 1

2 3

3 3

6 5

m

X

�9

�9

> O

> 4~

434 FRANCOIS Bt~LAND ET AL.

the ten groups over a 14-day period. As the utilization pattern within each group follows a quasi-Poisson model, except the tenth where the hypothesis was not tested, the distribution of visits in any sub-period should theoretically follow a Poisson model. To test for this consequence, four periods of 14 days were randomly selected using a random number table. The distributions of visits were obtained for the next fourteen days for each of the ten groups. As the observations at the tail end of these distributions were rather erratic, the four distributions in each of the groups were added and the result divided by four. The resulting frequencies were rounded to the nearest integer. Cells with less than a mean of 0.5 were deleted. The ten distributions found in Table V are called smoothed distributions here to take into account this transformation. The Poisson distribution is [24]:

--2t e ri

- - ( i - - - 0 , 1 , 2 , ..) P ' - - ri!

where t is the proportion of time the sub-period represents. The other terms are already known. The estimated frequencies in Table V have been obtained from this equation by setting t -- 14/365 and 2 is the average number of visits in a 365-day period. It should be clear from the comparison of the observed and the expected distribution and from the G 2 statistics, that the distribution of the ten groups of patients is homogeneous over a 14-day period. Even the number of observations at the tail end of the distribution are surprisingly well estimated by the model. But, as expected, the distribution of visits over a 14-day period for the whole sample is heterogeneous.

The third and last test of homogeneity of the pattern of care in the 10 groups does not involve the distribution of visits. Rather, the frequencies of the occurence of one pattern of utilization over a one year period is observed. The number of times 2 visits occur in less than fifteen days defines one of the ways utilization can be patterned. If the diagnoses made during these 2 consecutive visits are the same, there is ground to identify one episode of care that includes two visits. In a homogenous group of patients, the episodes with the same number of visits should be independent events. The distribution of these episodes should follow a Poisson law. But as shown at the beginning of this paper, the proportion of diagnoses missing in the data set is too high to


t ~

O

t-q

"6

Z

[-

O~

O

v

~ r -"q "~t"

Tab

le V

1 (C

onti

nued

)

4~

GR

OU

PS

(a

) ex

pect

ed u

nd

er a

Poi

sson

mo

del

1

2 3

4 5

6 7

8 9

10

Tot

al

0 --

93

.41

100.

56

173.

88

148.

30

1 --

47

.90

34.7

0 70

.62

75.6

5 2

12.2

8 5.

99

14.3

4 19

.30

3 0.

69

1.94

3.

28

4 0.

20

5 6 7 8 9 10

11

12

13

14

15

16

G 2

--

10

.34

0.47

7.

85

1.42

D

.F.

--

1 2

3 2

186.

11

205.

35

113.

29

41.6

7 11

.49

2.54

0.

47

0.07

18.3

0 6

14.9

8 31

.54

33.2

0 23

.30

12.2

7 5.

17

1.81

0.

55

11.1

1 6

7.67

20

.21

26.6

4 23

.40

15.4

2 8.

13

3.57

1.

34

0.44

12.4

6 7

0.41

2.

14

5.62

9.

84

12.9

4 13

.60

11.9

1 8.

95

5.88

3.

43

1.80

0.

86*

0.38

* 0.

15"

0.06

* 0.

02*

0.01

"

19.0

0 10

0.29

1.

62

4.56

8.

56

12.0

4 13

.54

12.6

9 10

.20

7.17

4.

48

2.52

1.

29"

0.60

* 0.

26*

0.11

" 0.

04*

0.01

"

66.8

3 10

761.

78

821.

64

443.

10

159.

30

42.9

6 9.

27

1.67

0.

26

0.03

0.

00

0.00

0.

00

0.00

0.

00

0.00

0.

00

0.00

1599

.86

15

> Z

�9

>

Z

>

* T

hese

cel

ls h

ave

bee

n a

dd

ed f

or th

e co

mp

uta

tio

n o

f th

e G

2 st

atis

tics

.


identify episodes. Nonetheless, as long as the hypothesis of homogeneity holds within each group of patients, the Poisson model should reproduce the observed frequencies of the number of times 2 visits are not separated by more than 14 days.

In Table VI, the tests of the Poisson models are not as successful as in the former two cases. The distributions in group 2, 6 and 10 are particularly problematical. However, in none of these cases are the discrepancies between the observed and the expected frequencies as large as in the total sample. There is no doubt that there is more homogeneity within the 10 groups than within the sample taken as a whole.

6. DISCUSSION

Hulka and Wheat have suggested that the measure of utilization used in a study should correspond to the specific aspect of utilization examined [18]. For example, a study explaining utilization in terms of a decision- making process will choose to observe the occurrence of a specific visit and try to link factors describing and explaining the decision-making process that leads to this visit in particular. Gortmaker, Eikenrode and Gore [26] have found that explaining the occurrence of one visit rather than the number of visits in one period does not yield the same results. The percentage of variance explained is lower in the former case and the variables entering the model are not necessarily the same.

Studies which observed the total utilization behavior of a group of patients over a period of time try to explain a set of events. It should be clearly recognized in these studies that it is the behavior observed over a period of time which is the subject of the explaining and that some of these behaviors are correlated because they come from the same episode, while others are independent from one another.

The log UI scale proposed here is based on the hypotheses that utilization is pattemed over a period of time, that these different patterns are classifiable on a continuum indicating the amount of care used and that, at each point on the log UI scale, the patterns are homogeneous. We have shown here that the log UI score predicts the variations in the intensity of care measured by the total annual charges made by physicians on behalf of a patient, and that within 10 groups of

4 3 8 FRAN(~OIS BI~LAND ET AL.

patients there is some evidence of homogeneity of the patterns of utilization. Insofar as the 10 groups are further subdivided, the homogeneity of the subgroups should increase. At the limit, there is the same number of groups as log UI scores in a sample. These represent the smallest homogeneous entity observable. Although the log UI scores are correlated with the number of visits, individuals with the same UI score can have a different number of visits. However, this different number of visits comes from homogeneous patterns of utilization, which means that individuals having the same log UI score have an identical propensity to use ambulatory care services. Put another way, individuals with equal log UI scores have an equal probability of visiting a physician x times in a period. Thus, when using the log UI scale in a study, it should be clear that one is predicting or explaining the distribution of these probabilities.

The scale proposed here is one of many that can be built to measure total utilization over a period of time: (1) premises other than the one made here may be more realistic, (2) different statistics than the range and the standard deviation of the days of occurence of visits can be proposed, and (3) other functions relating them to one another may be more appropriate. However, the proposed log UI index is a way of measuring the total utilization of ambulatory care that makes explicit its assumptions and that recognizes that visits to physicians are not random phenomena.

A C K N O W L E D G M E N T S

This research was supported in part by a scholarship awarded to the first author by the Fonds de la recherche en sant6 du Qurbec, by the Ministry of Health and Social Affairs, Quebec and by a grant from the National Health Research and Development Program of Health and Welfare Canada. Editorial assistance was provided by Louise Valois.

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a new index of utilization of ambulatory medical care

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