# Estimating relative complexity of care provided in ambulatory settings

# Estimating relative complexity of care provided in ambulatory settings

##### By David Katerndahl, M.D., M.A., and Robert Wood, Dr.P.H.

Since the days of the Resource-Based Relative Value Scales, primary care physicians have been fighting for a system of compensation that recognizes the complexity of the primary care encounter. In a system where “sicker” equals “more difficult to treat,” the struggle has been an uphill fight. Ultimately, this mentality has its roots in the reductionistic, cause-and-effect view of illness taught in specialty-oriented medical education. In ambulatory care settings, however, things are different. Here you find multiple “agents” (patient, family, friends, physician, office staff) interacting with the patient’s multiple, less-defined illnesses, which display the unpredictability of chaotic or random dynamics, less specific diagnostic tests, and variable patient behavior. No longer is the system simply the sum of its parts (Wilson & Holt, 2001).

### Method for estimating the complexity of ambulatory care

The focus of such a measure should be on relationships because relationships are far more important to the complexity of a system than are its components (Plsek & Wilson, 2001). Thus, the clinical encounter should be the focus of the measure of complexity because it represents the point of decision-making (Wilson & Holt, 2001). However, because a specialty is not defined by a single encounter and because complexity in relationships often reflects the frequency with which change occurs, the measure of complexity needs to include inter-encounter variation as well. Thus, whereas the complexity of an encounter includes the number of events occurring and the amount of information transferred, the complexity of a specialty or practice needs to include the diversity and variability of events across encounters. Just as the complexity of a situation is the sum of the complexity of the event and the average complexity encountered (Shannon, 1963; Reza, 1994), our measure of complexity should reflect the complexity of the typical encounter and the complexity across encounters.

### Computation of complexity of each input/output

The complexity of each input/output is defined as the mean input/output per clinical encounter weighted by its inter-encounter diversity and variability. Thus, the complexity of diagnoses seen in family practice would be the product of the mean number of diagnoses seen in family practice encounters (1.75 diagnoses using the 2000 NAMCS data), the inter-encounter diversity of diagnoses weighting, and the inter-encounter variability of diagnoses weighting. The diversity of an input/output is defined as the proportion of the number of categories needed to include 95 percent of the input/output reported out of the total possible categories. The 95 percent proportion was chosen to minimize the impact of a rare or miscoded input/output. The variability was defined as the coefficient of variation (COV) of the input/output, which is calculated as the standard deviation divided by the mean. The COV was chosen over other measures of variation because it is a unit-free measure (Armitage & Berry, 1987). To standardize the weightings and limit the impact of low diversity or variability on complexity, the weightings used are the Z-transformations of the diversity proportion and the COV, and range between 0.5 and 1.0.

Using the 2000 NAMCS database (National Center for Health Statistics, 2000), the diversity of 95 percent of the diagnoses seen is 0.48 and the COV of diagnoses seen is 0.49. These Z-transform into weights of 0.68 and 0.69 respectively. Thus, the complexity of family practice diagnoses is:

Mean Diagnoses | x | Diversity | x | Variability | = | |

Per Encounter | Weighting | Weighting | Complexity | |||

1.75 | x | 0.68 | x | 0.69 | = | 0.82 |

Because some inputs/outputs (i.e., patient characteristics, disposition) could not be represented in this manner, those variables were handled in a different but analogous way. For these variables, Z-transformations were performed on each component. Thus, patient characteristics are represented by three components (gender-race/ethnicity, age variability, and proportion of patients previously unknown to the physician). Gender and race/ethnicity were combined in a two-way table. As with diversity, this combined gender-race/ethnicity is the proportion of possible categories that represents 95 percent of the patients seen. Similarly, age variability is measured as the COV for the ages of the patients seen. Finally, the proportion of patients previously unknown to the physician is also assessed. Previous work suggests that previously unknown patients represent situations of higher complexity (Fraser & Greenhalgh, 2001), supporting the belief that continuity of care reduces complexity. Once these three components are represented by their proportions or COV, Z-transformation is performed to convert them to scores ranging from 0.5 to 1.0 and these scores are then summed to provide an estimate of patient characteristics complexity. Using the 2000 NAMCS data, this results in a patient characteristics complexity for family practice as follows:

Proportion/COV | Z-Transformation | |

Gender-Race/Ethnicity | 0.63 | 0.74 |

Age Variability | 0.52 | 0.70 |

Previously Unknown Patients | 0.09 | 0.53 |

PATIENT CHARACTERISTICS COMPLEXITY | 1.97 |

### Computation of total complexity

Once the complexity of each component has been calculated, the total input and total output complexities are calculated by summing the component complexities (Bar-Yam, 1997). However, calculation of the total specialty complexity is not merely the sum of the input and output complexities. A fundamental principle of complex systems is that there is a logarithmic relationship between input and output, so that, as the information in the input increases linearly, the complexity of the system increases exponentially. Thus, for binary data, the total system complexity is determined by the following formula (Bar-Yam, 1997):

System Complexity | = | Output Complexity | x | 2 | ^{(Input Complexity)} |

Table 1 presents the complexity of family practice using the 2000 NAMCS data. Notice that the total input complexity is the sum of the complexities of reasons-for-visit (0.78), diagnoses (0.82), examination/testing (0.83), and patient characteristics (1.97). Using the formula presented above, we calculate the total specialty complexity as:

System Complexity | = | Output Complexity | x | 2 | ^{(Input Complexity)} |

45.46 | = | 2.15 | x | 2 | ^{(4.40)} |

### Characteristics of calculated complexity

There are no particular units to this calculated complexity; they are “units of complexity.” The value of the estimated complexity is in its relationship relative to the complexity of another system measured in the same way. Thus, its value is in comparing the complexity of ambulatory care provided by two or more specialties or changes in complexity of care provided by one specialty over time. In addition, the more complex the system, the more universal are its estimates (Bar-Yam, 1997). This suggests that estimates of complexity are generalizable in complex systems. Thus, we would expect that the patterns seen in our estimate of relative complexities would hold to similar estimates using other databases and other physicians of the same specialties. Finally, we can determine confidence intervals around estimates using bootstrap methods.

### Complexity density

The estimate of complexity of ambulatory care presented above is a measure of the complexity of the clinical encounter based on the quantity of information and events, diversity, and variability. However, just as the capacity of a channel to deal with the amount of transmitted information is related to the transmission time (Reza, 1994), so too dealing with complexity is time-dependent (Boisot & Child, 1999); the more time you have, the more likely you are to observe any cyclic behaviors, which decrease complexity (Bar-Yam, 1997). Thus, the shorter the duration-of-visit, the more complex the encounter will seem and the greater the burden felt by the physician. Duration-of-visit inversely correlates with the complexity of the medical problem seen (Greenwald, et al., 1984). In fact, inadequate time is often cited as the cause of medical errors (Ely, et al., 1995; Leclere, et al., 1990; Croskerry, et al., 2004), one measure of the complexity of a system (Bar-Yam, 1997).

If we are to assess the impact of the complexity of the encounter on the physician, we need to adjust the estimated complexity for the duration-of-visit. Temte, et al. (2007) have suggested the encounter problem density (number of clinical problems addressed per hour) as a measure of complexity. Although simpler to measure, such assessments do not address the diversity and variability of patients and problems, which also contribute to the mental burden to the physician. For our purposes, the estimated complexity is divided by the duration-of-visit to obtain the complexity per minute. An hourly complexity density estimate (Temte, et al., 2007) is derived by multiplying the complexity per minute by 60 (see Table 2). The complexity density represents the complexity burden on the physician.

### Conclusion

There is increasing recognition that the complexity of medical care has important implications for health policy. Although risk adjustment methods exist, measures of complexity relevant to clinical care have not been developed. A new method to estimating relative complexity of clinical encounters appropriate for use with national databases was developed to estimate complexity based on the amount of care provided weighted by its diversity and variability. Such estimates of clinical complexity could have broad use for inter-specialty comparisons as well as longitudinal applications.

This study was funded in part by a research grant from the Texas Academy of Family Physicians Foundation.

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