# Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint(2012)

## Chapter: Appendix A: Mathematical Functions

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Page 121
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×

A

Mathematical Functions

TABLE A-1

Stationary Population Process Model for Population Age j at Year i

 Measure Formulation 1. Population Size (N) For year i = 1: Nij = age – specific population size For year i > 1: Nij = Ni-1,j-1 – DWi-1,j-1 – CPi-1,j-1 2. Target Population (T) No Vaccine: Tij = Nij × Proportion Targetij where Proportion Targetij = 0 Vaccine Steady State for year i = 1: Tij = Nij × Proportion Targetij where Proportion Targetij = 1 Vaccine Introduced: Tij = Nij × Proportion Targetij with Proportion Targetij = Input (% of N)ij 3. Vaccinated Immune (V) Vij = Tij × coverage rateij × effectivenessij 4. Vaccinated Susceptible (VS) VSij = Tij × coverage rateij × (1 – effectivenessij) 5. Not Vaccinated Immune (B) Bij = (Vij / herd immunityij) – Vij 6. Not Vaccinated Susceptible (BS) BSij = Nij – Vij – VSij – Bij 7. Total Cases (C) Cij = (VSij + BSij) × incidence rate 8. Deaths by Disease (D) Dij = Cij × case fatality rate
Page 122
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×
 Measure Formulation 9. Cases: Impairment (CP) CPij = (Cij – Dij) × proportion cases impaired 10. Cases: Morbidity (CM) CMij = Cij – Dij – CPij 11. Vaccine Complications (A) Aij = (Vij + VSij) × vaccine complications rate 12. All Cause Deaths (DA) Including Disease No Vaccine: DAij = Nij × all cause mortality rate Vaccine Steady State: DAij = (Nij × all cause mortality rate) – Deaths averted by vaccine * Deaths averted by vaccine = Vaccine Steady State Dij – No Vaccine Dij Vaccine Introduced: DAij = (Nij × all cause mortality rate) – Deaths averted by vaccine * Deaths averted by vaccine = Vaccine Introduced Dij – No Vaccine Dij 13. Cause Deleted Deaths (DE) Excluding Disease DEij = DAij – Dij
Page 123
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×

TABLE A-2

Health and Economic Values for Population Age j at Year i

 1. Premature Deaths Averted per Year 2. Incident Cases Prevented per Year 3. Quality-Adjusted Life Years (QALYs) Gained 4. Disability-Adjusted Life Years (DALYs) Gainedaa 5. Net Direct Costs 6. Delivery Costs 7. Health Care Costs (HC) Averted 8. Workforce Productivity (WP) Gained per Year 9. One-Time Costs Cost Research + Cost Licensure + Cost Start Up

aFox-Rushby, J. A., and Hanson, K. 2001. Calculating and presenting disability-adjusted life years (DALYs) in cost-effectiveness analysis. Health Policy and Planning 16(3):326-331.

Page 124
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×

TABLE A-3

Detailed Expressions (in Reference to Table A-1 and Table A-2)

 Measure Formulation All Cause Mortality Rate (Derived by Life Table Over Interval)a QALYsDeath QALYsImpairment by disease or complication QALYsMorbidity by disease or complication Disability-Adjusted Life Years (DALYs) Generalizationb Years of Life Lost (YLL) + Years of Life Lived with Disability (YLD) YLD or YLL (W = 1) DALYs Variables K = age weight modulation factor (0 = off, 1 = on) F = constant (0.1658) r = discount rate j = age of death (YLL) or age of onset of disability (YLD) G = parameter form the age weighting function (0.04) L = standard expectation of life at age a (YLL) or duration of disability (YLD) W = disability weight (YLD) DALYsDeath DALYsImpairment by disease or complication DALYsMorbidity by disease or complication Health Care Costs (HC)Death HCImpairments by disease or complication HCMorbidity by disease or complication
Page 125
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×
 Measure Formulation Workforce Productivity (WP) Gained DeathDeath WPImpairment by disease or complication WPMorbidity by disease or complication

aPreston, S., P. Heuveline, and M. Guillot. 2000. Demography: Measuring and modeling population processes. Chapter 3: The Life Table and Single Decrement Process. P. 46.

bFox-Rushby, J. A., and K. Hanson. 2001. Calculating and presenting disability adjusted life years (DALYs) in cost-effectiveness analysis. Health Policy and Planning 16(3):326–331.

Page 126
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×

Page 121
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×
Page 122
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×
Page 123
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×
Page 124
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×
Page 125
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×
Page 126
Suggested Citation:"Appendix A: Mathematical Functions." Institute of Medicine. 2012. Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint. Washington, DC: The National Academies Press. doi: 10.17226/13382.
×
Next: Appendix B: Candidate Disease Profiles and Data »
Ranking Vaccines: A Prioritization Framework: Phase I: Demonstration of Concept and a Software Blueprint Get This Book
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As a number of diseases emerge or reemerge thus stimulating new vaccine development opportunities to help prevent those diseases, it can be especially difficult for decision makers to know where to invest their limited resources. Therefore, it is increasingly important for decision makers to have the tools that can assist and inform their vaccine prioritization efforts.

In this first phase report, the IOM offers a framework and proof of concept to account for various factors influencing vaccine prioritization-demographic, economic, health, scientific, business, programmatic, social, policy factors and public concerns. Ranking Vaccines: A Prioritization Framework describes a decision-support model and the blueprint of a software-called Strategic Multi-Attribute Ranking Tool for Vaccines or SMART Vaccines. SMART Vaccines should be of help to decision makers. SMART Vaccines Beta is not available for public use, but SMART Vaccines 1.0 is expected to be released at the end of the second phase of this study, when it will be fully operational and capable of guiding discussions about prioritizing the development and introduction of new vaccines.

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