A Unified Approach to Patient Classification and Nurse Staffing for Long-Term Care Facilities

A UNIFIED APPROACH TO PATIENT CLASSIFICATION AND NURSE STAFFING FOR LONG-TERM CARE FACILITIES Lawrence J. Cavaiola DUDLEY KNOX LIBRARY NAVAL POSTGRADUATE SCHOOL MONTEREY. CAUFORMA f A Unified Approach to Patient Classification and Nurse Staffing for Long-Term Care Facilities by Lawrence J. Cavaiola A dissertation submitted to The Johns Hopkins University in conformity with the requirements for tne degree of Doctor of Philosophy. Baltimore, Maryland 1975 WMO SoNTCREY CALIFORNIA ABSTRACT In order to assist administrators of long-term facilities in responding to the changing environment of and demand for institutional care of the elderly and chronically infirm, a unified approach to patient classification and nurse staffing has been developed. The approach is essentially structure oriented and is directed toward the presentation of alternative nurse staffing strategies; its basis is the quantification of patient nursing needs through intermediate steps of assessment and classification. The classification system, in turn, has been related to the demand for nursing services, as categorized by care area, for each of three homogeneous patient groupings. Effective allocation and assignment of patient nursing care activities have been modeled by use of techniques of mathematical programming. The ability to predict, with reasonable confi- dence, the level of care to which a patient would most appropriately be assigned based on an assessment of various functioning status items, psycho-social status indicators, and medically defined conditions was considered initially. Application of an existing nonlinear multiple regression technique to patient assessment data drawn from a comprehensive assessment i , 11 instrument yielded a means by which patients could be classified according to 37 health status indicators. The regression method was chosen for its specific applicability to problems of fitting a polychotomous ordered response, analogous to the level of care. In order to achieve a classification system of reasonable size for use in typical long-term care facilities, various subsets of the original 37 variables were tested for their prediction and recognition powers; a subset of 12 variables was shown to possess adequate capabilities in this regard. This subset was synthesized into an implementable patient classification system procedure. The determination of an optimal staff mix,- allocation of nursing time, and assignment of nurses to patient care demands was captured in the Basic Staffing Model (BSM) , a mixed-integer linear program. The BSM maximizes an objective function that combines the concepts of the appropriate assignment of nursing personnel to specific patient care activities and the satisfaction of high priority demands at greater than minimum levels, if possible. Model constraints include the availability of nursing resources, budgetary limitations, legal staffing requirements, and adherence to bounded representations of patient nursing care activities. Two extensions to the BSM, Model I and Ill Model II, were developed to facilitate the exploration of alternative staffing policies. Model I allows for the parametric representation of changes in the total patient-centered services provided and personnel budget, while Model II enables parametric alterations in upper and lower bounds on staff and patient demands to be examined. Two algorithms were derived for the efficient solution of both BSM extensions. Recognizing the forms of the models, branch and bound methods incorporating post-optimality analysis in specialized linear programming routines were developed. These methods were based on the Upper Bounded Dual Simplex algorithm of Wagner; their computational characteristics for both general parametric mixed-integer linear programs and specific examples of applications to nurse staffing problems were investigated. ACKNOWLEDGEMENTS First and foremost, I would like to thank my principal advisor, Dr. John P. Young, for his patient guidance and encouragement throughout this endeavor. Having originally kindled my interest in the application of operations research to problems of health care delivery, Dr. Young later suggested the topic of this dissertation to me. His continuing interest and support are gratefully acknowledged. I also thank my second reader, Dr. R. Rao Vemuganti, for his many hours of assistance, especially in the development of the mathematical programming aspects of this work. To Eleanor M. McKnight, R.N. , M.P.H. I extend my grateful thanks for sharing her data and expertise in the long-term care field. Certainly this study would not have been as complete without her assistance I would also like to acknowledge the contributions made by Dr. David B. Duncan, Dr. Charles A. Rohde, and Dr. Rodger Parker to the application of statistical theory to problems of patient classification. In addition, I thank Mary E. Campion, R.N., M.S.N, for the many hours of her time spent in discussions of the psychosocial and human aspects of long-term care. I extend my gratitude to Mr. Arnold Richman, iv Vice President, Operations of the Medical Services Corporation of Towson, Maryland for his assistance. The support of my graduate studies by the United States Navy through its Junior Line Officer Advanced Education (Burke) Program is most gratefully acknowledged. This study was supported in part under grant R18-HS-01250, "Health Manpower for Long-Term Care," National Center for Health Services Research, Health Resources Administration, U.S. Public Health Service, DHEW. My appreciation is expressed to Mrs. Louise Lieu for her diligent typing of the drafts of this work, and to Mrs. Doris Stude for her painstaking preparation of the final copy. Finally, to my wife, Maureen, and my son, Michael, I extend my deepest thanks for their love and encouragement throughout the preparation of this dissertation. To my family 1546723 TABLE OF CONTENTS Page LIST OF TABLES ix LIST OF FIGURES xi CHAPTER I. Introduction: The Need for Research 1 1.1 General Discussion 1 1.2 The Need for Research at the Facility Level 4 1.3 The Proposed Research 10 CHAPTER II. A Review of Existing Methodologies for Patient Classification and Nursing Resource Allocation 14 11. Introduction 14 11. Patient Classification in an Acute Care Setting 15 11. Nurse Staffing in an Acute Care Setting 23 11. Patient Classification in a Long-Term Care Setting 33 11. Nurse Staffing in a Long-Term Care Setting 43 11. Work of the "Four University" Group 51 11. Summary 53 CHAPTER III. Development of the Methodology 54 111.1 Introduction 54 111. The Administrator's Problem 55 111. A Patient Classification System 58 111. A Basic Staffing Model 73 111. Extensions to the Basic Staffing Model 83 111. Data Requirements and Availability 89 CHAPTER IV. Patient Classification for Long-Term Care 101 VI. 1 Introduction 101 VI. 2 The Pattern Recognition Problem 103 VI. 3 A Review of Multivariate Statistical Techniques 110 VI. 4 The Method of Walker and Duncan 126 VI. 5 The Variable Subset Selection Problem 143 VI. 6 Results 146 VI. 7 Final Remarks 163 CHAPTER V. Mathematical Programming Solution Methodology: Parametric Mixed-Integer Linear Programming 171 V.l Introduction 171 V.2 Parametric Linear Programming 17 5 vii Vlll TABLE OF CONTENTS, cont'd. Pa9 e V.3 Parametric Integer and Mixed-Integer Linear Programming 180 V.4 A Proposed MILP Parametric Programming Algorithm 197 V.5 The Upper Bounded Dual Simplex Algorithm 202 V.6 Postoptimality Analysis of the Requirements Vector 211 V.7 Postoptimality Analysis of the Upper and Lower Bounds 2 20 V.8 Conclusion 232 CHAPTER VI. An Application of the Methodology 238 VI. 1 Introduction 238 VI. 2 Problem Construction and Computational Considerations 239 VI . 3 Example of Model I for Service Level Variation 244 VI. 4 Example of Model I for Budget Variation 247 VI. 5 Example of Model II 254 VI . 6 Conclusion 260 CHAPTER VII. Summary, Recommendations, and Extensions 262 VII. 1 Introduction 262 VII. 2 Previous Work 26 3 VII. 3 The Proposed Methodology 266 VII. 4 Recommendations and Extensions 2 ?1 APPENDIX A 275 BIBLIOGRAPHY 280 VITA 288 7681342 7246398 LIST OF TABLES Table Title Page 11. Young's Classification of Pediatric Patients 21 11. Task Complexes Identified by Wolfe 25 11. PETO Elements of Care 29 11. PETO Conversion of Points into Hours of Care 31 II. 5 Katz, et aJL. Classifications of Indepen- dence in ADL 35 11. Definitions of the Indicators and Categories Used by Parker 39 11. Key Variables Determined by Discriminant and Cluster Analysis by Parker and Boyd 43 11. The "Four University" Research Group 52 111.1 CPAI Classification Descriptors 62 111. CPAI Sample Categorized by Level of Care and Research Group 6 4 111. CPAI Sample Categorized by Appropriate Level of Care and Research Group 65 111. Nursing Care Areas Identified by McKnight 68 111. 5 Mean Time Needed to Complete Each of the Nursing Care Areas by Personnel Level and by Patient Ambulatory Status and Nursing Need as Found by McKnight 6 9 111. Average Required Performance Times per Day (in Minutes) by Care Area and Patient Classification (Based on McKnight 's Colorado Study Data) 7 2 111. Ordinal Skill Level Preferences by Care Area and Nursing Need, Based on the Study of McKnight and Steorts 94 111. Percentages of Time (Averaged Over Three Shifts) and Number of Hours Available per 8-Hour Shift for Patient-Centered Activities 96 111. Upper and Lower Bound on 6-,^ (in minutes), Percentage of Patients in Each Category Receiving Care, and Priority Constants p^ 99 111. 10 Average and Extreme Daily (24-hour) Patient Staffing Requirements (in hours) by Patient Classification 100 IV. 1 Derived Sample for Classification Study 148 IV. 2 Variables Selected for Classif ication Study 150 IV. 3a Results of Application of Walker and Duncan Method for 37 Variables 151 ix 4 4 LIST OF TABLES, cont'd. Table Title Page IV. 3b ANOVA for Application with 37 Variables 151 IV. 3c Classification Matrix for Application with 37 Variables 152 IV. 4 Subsets of the Original Variables Chosen for Analysis 153 IV.

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