Geometric-Based g-Type Statistical Control Charts for Infrequent Adverse Events: New Quality Control Charts for Hospital Infections

New "g" and "h" type statistical control charts are developed and illustrated for monitoring hospitalacquired infections and other low frequency adverse events, such as heart surgery complications, catheterrelated infections, surgical site infections, contaminated needle sticks, and other iatrically induced outcomes. These new charts, based on inverse sampling from geometric and negative binomial distributions, are simple to use and can exhibit significantly greater detection power over conventional methods. Several interesting properties and design modifications of these new charts also are illustrated that can significantly improve power to detect process changes over conventional methods. INTRODUCTION Possible approaches for detecting changes in the rate of low defect processes, hospital infections, and other adverse events range from standard Shewhart control charts to more complex alternatives. While some options require more detailed data availability and involved calculations than others, one option of particular interest due to ease of use, low occurrence (e.g., infection or defect) rates, and the immediate availability of each observation is the number of events between occurrences, such as between infections, adverse events, or defects. Appropriate control charts for such scenarios, especially useful when the occurrence rate is low, were developed in 1989 by the author [7], investigated, and partially disseminated via several unpublished reports and conference papers [3-6] in circulation. A primary purpose of this article therefore is to summarize the use of this type of control chart and illustrate their application to healthcare and other concerns. These new charts, called g and h charts, are based on inverse sampling from underlying geometric and negative binomial distributions and are particularly useful in certain cases over conventional charts in terms of significantly improved detection performance. After a brief review of the general concepts and use of statistical process control (SPC) within health care, several approaches to applying SPC to infection control, adverse events, and other healthcare data are described and illustrated, with particular emphasis on the use of g control charts. Some interesting properties and design issues of these new charts then are illustrated that can significantly improve the power to detect important process changes over conventional approaches, including use of supplementary rules, redefined Bernoulli trials, and a new supplementary rule. Probability-based limits, more advanced chart types, possible transformation approaches, other extensions, and results of ongoing work also are briefly discussed. The intended audience includes healthcare managers, clinical practitioners, hospital epidemiologists, and quality control and infection control personnel. The article assumes only a basic familiarity with statistical process control (SPC), with the main emphasis being on illustrating the general approach rather than on mathematical derivations. HEALTHCARE EPIDEMIOLOGY AND INFECTION CONTROL Hospital epidemiologists routinely study infection control, with several surveillance methods having been proposed [14]. These programs tend to be concerned with both epidemic (outbreaks) and endemic (sysInstitute of Industrial Engineers Society for Health Systems 1999 Conference Proceedings Benneyan: Statistical g Control Charts 176 temic) infections, which in SPC terminology equate to unnatural and natural variability, respectively, and both of which can be effectively studied with control charts. Many traditional descriptive methods, however, do not fully consider, in the classic SPC sense, infection as a longitudinal process with inherent natural, and perhaps unnatural, variation. At least one epidemiologist [8] has proposed monitoring infection rates over time, rather than "statically", in a manner which is quite similar in nature and philosophy to SPC. Nosocomial infections basically are any infections that are acquired or spread as a result of a patient being hospitalized, rather than being present as an admitting condition at the time of hospitalization. Some examples include surgical wound infections, pneumonia, bacteremia, urinary tract infections, cutaneous wound infections, bloodstream infections, catheter infections, and gastrointestinal infections. National costs of nosocomial infections have been estimated at approximately 8.7 million additional hospital days and 20 thousand deaths per year [11], and hospital accrediting bodies therefore are urging quality improvement methodology be applied to this process defect. For example, the Joint Commission on Accreditation of Healthcare Organizations (JCAHO), among others, requires hospitals be engaged in continuous quality improvement (CQI) activities, including the application of statistical methods such as statistical process control (SPC) to infection control. This article therefore focuses on approaches to applying SPC to infection control data, with particular emphasis on the design and use of g control charts for the number of events, surgeries, or days between infections, although these same methods are equally applicable for monitoring other types of low defect processes, such as in manufacturing and service settings. A recent more extensive series of articles [2] also elaborates on and compares various alternate approaches in greater detail. Because significant differences can exist between service-specific infection rates, such as for adult and pediatric intensive care units, surgical patients, and high-risk nursery patients, separate control charts might be applied to each of these categories. Additionally, infection rates generally are more representative if based on the number and/or duration at-risk, such as the number of patient days, surgeries, and devise-use/devise-days, rather than simply on number of admissions, discharges, etc. [17]. Of course, to study each category separately and adjusted in an appropriate manner requires more detailed data availability and additional calculations. For whatever denominator method, stratification, or at-risk adjustment used, some of the general approaches to SPC discussed in this article can be applicable. Subgroup Number Subgroup Statistic (e.g., average, rate, number, Centerline = Central Tendency Upper Control Limit