INDUSTRIAL ENGINEERING APPLICATIONS IN HEALTH CARE SYSTEMS:APPLICATION OF STATISTICAL METHODS

APPLICATION OF STATISTICAL METHODS

Several statistical methods have been used in the analysis and improvement of health care systems. Variability is the fact of life in any kind of data collected in health care, and statistical methods are the tools needed to understand this data. In this section, some common examples of the use of statistical analysis and modeling in health care will be presented.

As stated above, use of queuing and simulation models requires collection of data regarding the probability distribution of interarrival times for customers and service times. Use of a specific queuing model requires that the assumptions regarding the probability distributions in the model are valid. Industrial engineers must be able to verify that the collected data fit the assumed probability distri- bution. Similarly, simulation models need the data regarding various service times and other proba- bilistic elements of the model. Statistical methods have also been used to study and manage variability in demand for services (Sahney 1982).

Use of Regression Models

Regression models can be used to predict important response variables as a function of variables that could be easily measured or tracked. Kachhal and Schramm (1995) used regression modeling to predict the number of primary care visits per year for a patient based upon patient’s age and sex and a measure of health status. They used ambulatory diagnostic groups (ADGs) encountered by a patient during a year as a measure of health status of the patient. All the independent variables were treated as 0–1 variables. The sex variable was 0 for males and 1 for females. The age of the patient was included in the model by creating ten 0–1 variables based on specific age groups. The model was able to explain 75% of the variability in the response variable. Similar models have been used to predict health care expenses from patient characteristics.

Determination of Sample Size

Industrial engineers frequently encounter situations in health care systems where they need to deter- mine the appropriate amount of data needed to estimate the parameters of interest to a desired level of accuracy. In health care systems, work-sampling studies are frequently done to answer questions such as ‘‘What percentage of a nurse’s time is spent on direct patient care?’’ or ‘‘What fraction of a clinic service representative’s time is spent on various activities such as answering phones, checking- in the patients, looking for medical records, and the like?’’ In work-sampling studies, the person being studied is observed a predetermined number of times at random time intervals. For each observation, the task being performed is recorded. The estimate of the fraction of time spent on an activity is obtained by dividing the number of occurrences of that activity by the total number of observations.

The number of observations needed for a work-sampling study can be calculated from the fol- lowing formula:

where N = number of observations

Z = normal probability distribution factor, based on confidence level

p = unknown fraction to be estimated

I = desired margin of error in estimation

It is common to use a 95% confidence level for which the value of Z in the equation is 1.96. The value of I needs to be selected based upon the situation. For example, if the fraction being estimated is in 0.4–0.6 range, a value of I as ±0.02 may be acceptable, but ±0.05 may be too high. The value of p to be used in the equation poses a problem because this is the unknown fraction one is attempting to estimate from the data. If, from past experience or from literature, an approximate value of p is known, it can be used in the calculation of N. Another approach is to use p = 0.5 because it results in the largest value of N for fixed values of Z and I. If the computed value of N is too large to observe due to time and cost constraints, the only choice is to tolerate a larger possible error or a lower level of confidence.

A similar formula is also available for determining the sample size in situations that require determination of actual time to perform a task. For example, for a staffing study in a call center, one may need to estimate average time needed to service a phone call.

Use of Control Charts

Control charts have been used in health care as visual tools to observe the performance of a process over a period of time and alert the managers when an investigation may be necessary to identify an external cause that may have affected the performance. Individual (X) and moving range (MR) charts have been used for measurement data such as patient wait time, turnaround time for a test, number of times an error is made during a day, and length of stay for a particular diagnostic related group (DRG). P-charts have been used for fractions or percentages. Examples include patient satisfaction data, percentage utilization of a resource, bed occupancy expressed as % of total beds, and fraction of patient transport requests handled within 15 minutes of request. Cumulative sum charts have been used to detect small but significant changes in the mean. Kachhal and Schramm (1995) describe a bed model where auto regressive integrated moving average was used on a control chart with eco- nomic control limits to manage bed capacity at a hospital.