Research Papers

Statistical Control Charts Based on a Geometric Distribution

Journal of Quality Technology 1992;24(2):63-69

In some production and administrative processes, the occurrence of certain count events is best described by a shifted geometric distribution. Control charts are developed for the total number of events and the average number of events in a fixed number of units of process output. These charts also are appropriate for monitoring binary processes when the Bernoulli defect rate is low. Several examples illustrate the consequences of applying standard c or u charts when the geometric model is appropriate.

Statistical Models for Analysis and Optimal Design of Laboratory Screening Policies for Cervical Cancer

Annals of Operations Research 1996;67:235-285

This paper develops several statistical and economic models to analyze the accuracy and total cost of laboratory procedures commonly used to examine Pap smears for early indications of cervical cancer. The expected values, variances, and probability distributions are derived for the overall system sensitivity, specificity, and cost of several possible screening policies. These models are useful for analytically comparing alternate screening policies and identifying the optimal minimal societal cost policy. Results show that the overall process can never have higher sensitivity nor lower specificity than the confirming pathologist and that a rescreening rate of either 0% or 100% always must be optimal. Significant improvements in sensitivity and costs are shown to be possible by changing the policy currently required under the congressional Clinical Laboratory Improvements Amendments Act.

Mathematical Models for Evaluating Automated Rescreening in Cervical Cytology

Acta Cytologica 1997;41(1):209-223

We develop mathematical models that determine the overall sensitivity, specificity, and expected cost of automated rescreening systems in order to assist decision makers with the difficult task of evaluating their use in the process of screening cervical smears. Results show that the optimal screening policy is highly dependent on assumptions on screening costs and disease incidence, but that an automated system can significantly increases the overall system cost without significantly improving accuracy.

Use of Mathematical Programming in Analysis of Constrained and Unconstrained Industrial Experiments

Quality Engineering 2000;12(3):395-406

This article illustrates three approaches for using mathematical programming in the analysis of experimental design results in order to identify the overall optimal process settings. Results of these approaches are compared to more conventional methods. Use of the proposed methods also is illustrated to map out the optimal tradeoff frontier between nonconformance and total costs and to conduct sensitivity analysis when accurate cost estimates are not easily to obtain.

Use of Moving Averages and Binary Cumulative Sums in Nosocomial Cluster Detection

Emerging Infections Diseases 2002; 8(12), 1426 - 1432

We investigate the performance of cumulative sum and moving average methods for automated surveillance of resistant organisms and detection of nosocomial infection clusters, which often occur undetected at significant cost to the medical system and individual patient. All nosocomial outbreaks of resistant bacteria from 1995-200 were analyzed using Cusums and MAs for which genotyping data were available: methicillin-resistant Staphylococcus aureus surgical site infections and vacomycin-resistant Enterococcus in a bone marrow transplant unit and an ICU.

Performance of Number-Between Charts

Health Care Management Science 2001;4:319-336

This article investigates the statistical properties and operating characteristics of new g and h Shewhart control charts, based on inverse sampling from geometric and negative binomial distributions, for monitoring the number of cases between hospital-acquired infections and other adverse events. Several design considerations are illustrated that significantly can improve the operating characteristics and sensitivity of these charts, including the use of within-limit rules, a new in-control rule, redefined Bernoulli trials, and probability-based limits.

Optimal Cervical Cancer Screening Policies

IEMS International conf. proceedings 2000;1-7

This paper summarizes several recent studies of cervical cancer screening policies commonly used to examine Pap smears for early detection. We investigate and compare the policy mandated by the Clinical Laboratory Improvement Amendments Act (CLIA), recently proposed automated rescreening approaches, and possible alternatives to CLIA similar to multiple 100% inspection policies to eliminate nonconforming manufactured product in the presence of inspection error. Using mathematical and expected cost models, significant improvements in early detection and total costs are shown possible by revising the policies currently required by CLIA. Use of automated rescreening devices recently approved by the FDA in many cases can be a move in the wrong direction in terms of accuracy and cost, despite widespread marketing by manufacturers to the contrary.

Statistical Quality Control Methods in Infection Control and Epidemiology: Introduction

Infection Control and Hospital Epidemiology 1998;19(3):194-214

A fairly thorough discussion of the application of statistical process control to processes often examined by hospital epidemiologists, with emphasis on the basic philosophical and theoretical foundations of SPC and their relation to the field of epidemiology. The focus is on underlying concepts and is mostly non-mathematical.

SQC Methods in Infection Control and Epidemiology: Performance and Research Issues

Infection Control and Hospital Epidemiology 1998;19(4):265-283

Continues the above discussion on the use of SPC in epidemiology and infection control, with emphasis on the statistical properties of control charts, issues of chart design, optimal control limit widths, and more advanced types of control chart schemes. Numerous references are provided in both articles for readers seeking further information.

Number-Between Quality Control Charts

Health Care Management Science 2001;4:305-318

Alternate Shewhart-type statistical control charts, called "g" and "h" charts, are developed for monitoring the number of cases between hospital-acquired infections and other adverse events, such as heart surgery complications, catheter-related infections, surgical-site infections, contaminated needle sticks, and other iatrically induced outcomes. These new charts are based on inverse sampling from geometric and negative binomial distributions, are simple for practitioners to use, and in some cases can exhibit significantly greater detection power over conventional binomial-based approaches, particularly for infrequent events and low defect rates.

Design and Use of g Charts (Overview)

Inst. Industrial Engineers SHS conf. proc. 1999;175-186

This article examines approaches to the design and application of statistical control charts to low defect processes such as high yield manufacturing systems and various adverse healthcare events (hospital infections, contaminated needle sticks, heart surgery complications), with particular emphasis on the development of events-between g and h control charts, design issues, and their statistical operating characteristics. 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.

Development of a Web-Based Multifacility Healthcare Surveillance Information System

Jrnl Healthcare Information Mgmt 2000;14(3):19-26

This article describes recent work to develop a Web-based statistical surveillance system to monitor in real-time disease and symptom occurrence rates across the U.S. Air Force's worldwide healthcare network. The approach incorporates statistical and related methods in order to identify unusual events and patterns of concern in large, highly distributed data streams, work that resulted in an award from Vice President Gore.

Another View on How to Measure Health Care Quality

Quality Progress 1995;28(2):120-124

Provides an alternative viewpoint on issues discussed in a previous guest column on applying statistical methods to health care, infection control, hospital epidemiology, clinical laboratories, and outcome metrics, primarily from the perspective of the Deming philosophy and of statistical quality control.

Some Control Chart Caveats

Infection Control and Hospital Epidemiology 1999;20(8);526-527

A brief discussion of common errors and pitfalls frequently made in the use of statistical process control.

Examining Health Systems from Engineering Economy and Cost of Quality Perspectives

Managed Care Quality (St Lucie Press) 1998;181-206

This chapter explores the application of engineering economy principles to the cost and quality of health systems.

An Approach to Controlling Methicillin-Resistant Stapylococcus Aureus Using Annotated Statistical Control Charts

Infection Control and Hospital Epidemiology 2002; 23(1): 13-18

The benefits of a MRSA feedback program using annotated SPC charts were studied via retrospective and prospective analyses of MRSA monthly rates at 24 medical, medical specialties, surgical, intensive care, and cardiothoracic wards and units at 4 hospitals over a 46 month period. Results were fed back monthly to medical staff, managers, and hotel services. MRSA rate reductions started 2 months after starting this program, with current rates approximately 50% lower and more consistent than when the program began. Staff report finding this the most positive form of MRSA feedback they have received, helping to detect rate changes and manage resources more effectively.

Risk-adjusted Sequential Probability Ratio Tests and Longitudinal Surveillance Methods

International Journal for Quality in Healthcare 2003; 15:5-06

Incorporating risk-adjustment into statistical process control methods can significantly improve their effectiveness for monitoring clinical and other healthcare processes. Examples include surgical site infections for patients who can be stratified into one of several risk categories and coronary artery bypass graft patients who each have a different prior likelihood of survival based on activity, family history, and other predictors. Appropriate SPC methods for such application are discussed, along with some important statistical issues that arise when incorporating risk adjustment and the resultant sensitivity to detect changes in the underlying rate.

Working Papers

Alternate Dispersion Measures in Replicated Factorial Experiments

citation

Any of several statistics traditionally are used to detect dispersion effects in the analysis of replicated factorial experiments, including the within-run standard deviation s, the natural logarithm ln(s+1), various signal-to-noise ratios, and others. This study examines the relative performance of these conventional approaches and an alternate type of dispersion measure motivated by a desire to improve power by increasing associated degrees of freedom. Two alternate measures, the absolute deviation from each within-run mean and a normalized tranform of this statistic, can increase significantly the probability of detecting dispersion effects if the false alarm rate could be controlled

Exponentially Weighted Moving Average and Probability Limit g-Charts in Modeling Nosocomial Outbreaks

in review

Exponentially-weighted moving average and probability-limit event-interval statistical process control charts were applied to 5 years of nosocomial data from Pseudomonas aeruginosa sepsis in a neonatal intensive care unit, methicillin-resistant Staphylococcus aureus surgical site infections, and vacomycin-resistant Enterococcus in a bone marrow transplant unit and an ICU. Sensitivity and false-positive rates were determined empirically for various values of the chart design parameters k, l, and a.

On the Sensitivity of Desirability Functions for Multi-response Optimization

citation

summary t.b.d.

Design, Use, and Performance of Statistical Control Charts for Clinical Process Improvement

in review

This article provides an overview of the different types and uses of SPC charts, their statistical performance, and methods for determining appropriate sample sizes. Empirical examples illustrate appropriate applications of each chart type, sample size determination, and chart performance. Sensitivities are calculated and tabulated for a wide range of scenarios to aid practitioners in designing control charts with desired statistical properties. Implications on the type of data collected, format, and sampling frequency are discussed, as well as methods for dealing with rare events. The intended audience includes practitioners and healthcare researchers seeking either an introduction to these methods or further insight into their design and performance.

Lab Reports

Summary of Pap Smear Screening Models Research

QPL Report Series, No. MIM-98-3, AHCPR Grant Executive Summary (ROS HSO93229-01)

This research is concerned with the overall sensitivity, specificity, and cost of laboratory processes for screening Pap smears for early indications of cervical cancer or its precursors, with particular focus on the policy required by the Clinical Laboratory Improvement Amendments Act (CLIA). Mathematical and economic models are developed that prove CLIA is never optimal by any criteria and always increases total costs, overall sensitivity under CLIA never can be improved beyond certain mathematical bounds, no amount of partial screening ever is optimal, and multiple evaluations of each smear in some cases is optimal. The proposed use of automated rescreening technology as recently approved by the FDA also can dramatically increase overall costs without significantly improving sensitivity. Improvements by switching to the optimal policy range from 90,000 to 165,000 fewer false-negatives and $250 to $750 million savings per year nationwide.

Alternate Dispersion Measures in Replicated Factorial Experiments

QPL Report Series, No. MIM-00-2

Any of several statistics traditionally are used to detect dispersion effects in the analysis of replicated factorial experiments, including the within-run standard deviations the natural logarithm ln(s+1), various signal-to-noise ratios, and others. This study examines the relative performance of several conventional and alternate approaches in several recent experimental designs, with ln(s+1) typically producing the best results. An alternate approach based on a normalized transform of the absolute deviations from each within-run mean also can increase the probability of detecting dispersion effects, but at the expense of uncontrolled false alarm rates.

Tutorials

Use and Interpretation of Statistical Quality Control Charts

International Journal for Quality in Health Care 1998;10(1):69-73

This article provides a brief introduction to the use of statistical quality control charts for analyzing, monitoring, and improving health care processes. Examples illustrate appropriate chart use and interpretation, and the article concludes with some common pitfalls to avoid and references for further exploration.

Introduction to Using Computer Simulation in Healthcare

Journal of the Society for Health Systems 1997 : 5(3):1-15

This paper discusses the use of simulation analysis for studying and improving health systems. A pediatric case study illustrates the steps involved in a simulation analysis and the use to assess tradeoffs between resource utilisation and waiting times.

Moment Generating Functions

citation

This monograph reviews the meaning, uses, and calculation of moment generating functions for discrete and continuous random variables. Moment generating functions serve several practical uses in probability and statistics, are used to prove many important results, and can help determine the probability distribution, mean, and variance of random variables and functions of random variables. We illustrate these principles through several examples and summarize several important results that have been proven via their use.

A Tutorial on Using g and h Control Charts

citation

summary