Maximizing the effectiveness of a pediatric vaccine formulary while prohibiting extraimmunization
Tóm tắt
The growing complexity of the United States Recommended Childhood Immunization Schedule has resulted in as many as five required injections during a single well-baby office visit. To reduce this number, vaccine manufacturers have developed combination vaccines that immunize against several diseases in a single injection. At the same time, a growing number of parents are challenging the safety and effectiveness of vaccinating children. They are also particularly concerned about the use of combination vaccines, since they believe that injecting a child with multiple antigens simultaneously may overwhelm a child’s immune system. Moreover, combination vaccines make it more likely that extraimmunization (i.e., administering more than the required amount of vaccine antigens) occurs, resulting in greater concerns by parents and vaccine wastage costs borne by an already strained healthcare system. This paper formulates an integer programming model that solves for the maximum number of vaccines that can be administered without any extraimmunization. An exact dynamic programming algorithm and a randomized heuristic for the integer programming model is formulated and the heuristic is shown to be a randomized ξ-approximation algorithm. Computational results are reported on three sets of test problems, based on existing and future childhood immunization schedules, to demonstrate their computational effectiveness and limitations. Given that future childhood immunization schedules may need to be solved for each child, on a case-by-case basis, the results reported here may provide a practical and valuable tool for the public health community.
Từ khóa
Tài liệu tham khảo
Bazaraa MS, Jarvis JJ, Sherali HD (1990) Linear programming and network flows. Wiley, New York
Burden RL, Faires JD (1997) Numerical analysis, 6th edn. Brookes-Cole, New York
CDC Vaccine Price List (2006) Center for disease control and prevention, national immunization program website. Retrieved August 3, 2006, from www.cdc.gov/nip/vfc/cdc_vac_price_list.htm.
Centers for Disease Control and Prevention (2006) Recommended childhood and adolescent immunization schedule—United States. Morb Mort Wkly Rep 54(52):Q1–Q4
Centers for Disease Control and Prevention (2007) Recommended childhood and adolescent immunization schedule—United States. Morb Mort Wkly Rep 55(51):Q1–Q4
Centers for Disease Control and Prevention (2003) Prevention and control of infections with hepatitis viruses in correctional settings. Appendix hepatitis A and B vaccines. Morb Mort Wkly Rep 52(RR-1):34–36
Centers for Disease Control and Prevention (2002) General recommendations on immunization. Morb Mort Wkly Rep 51(RR-2)
Centers for Disease Control and Prevention (1999) Combination vaccines for childhood immunization. Morb Mort Wkly Rep 48(18)(RR-5)
Centers for Disease Control and Prevention (1995) Recommended childhood and adolescent immunization schedule—United States. Morb Mort Wkly Rep 44(RR-5):1–9
Chen RT, DeStefano F, Pless R, Mootrey G, Kramarz P, Hibbs B (2001) Challenges and controversies in immunization safety. Infect Dis Clin North Am 15(1):21–39
Cochi SL (2005) 2005 National immunization survey. Presentation to National Press Club, July 27, 2005
Diekema DS (2005) Responding to parental refusals of immunization of children. Pediatrics 115(5):1428–1431
Edwards KM, Decker MD (2001) Combination vaccines. Infect Dis Clin North Am 15(1):209–230
Flanagan-Klygis EA, Sharp L, Frader JE (2005) Dismissing the family who refuses vaccines: A study of pediatrician attitudes. Arch Pediatr Adolesc Med 159(10):929–934
Garey MR, Johnson DS (1979) Computers and intractability: A guide to the theory of NP-completeness. W.H. Freeman, New York
Hall SN (2006) The design and analysis of pediatric vaccine formularies: theory and practice. University of Illinois, Urbana, Illinois Ph.D. Dissertation
Hochbaum DS (ed) (1997) Approximation algorithms for NP-hard problems. PWS, Boston, Massachusetts
Infectious Diseases in Children (2002) Almost 200 new drugs in development for use in children. 15(10):41–44
Jacobson RM, Targonski PV, Poland GA (2007) Meta-analyses in vaccinology. Vaccine 25:3153–3159
Jacobson SH, Karnani T, Sewell EC (2003a) Analyzing the economic value of the hepatitis B-Haemophilus influenzae type B combination vaccine by reverse engineering a formulary selection algorithm. Vaccine 21:2169–2177
Jacobson SH, Karnani T, Sewell EC (2004) Assessing the impact of wastage on pediatric vaccine immunization formulary costs using a vaccine selection algorithm. Vaccine 22:2307–2315
Jacobson SH, Sewell EC (2002) Using Monte Carlo simulation to determine combination vaccine price distributions for childhood disease. Health Care Manage Sci 5:135–145
Jacobson SH, Sewell EC, Allwine DA, Medina EA, Weniger BG (2003b) Designing pediatric vaccine formularies and pricing pediatric combination vaccines using operations research models and algorithms. Expert Rev Vaccines 2(1):15–19
Jacobson SH, Sewell EC, Deuson R, Weniger BG (1999) An integer programming model for vaccine procurement and delivery for childhood immunization: a pilot study. Health Care Manage Sci 2:1–9
Jacobson SH, Sewell EC, Karnani T (2005) Engineering the economic value of two pediatric combination vaccines. Health Care Manage Sci 8(1):29–40
Jacobson SH, Sewell EC, Proano RA (2006) An analysis of the pediatric vaccine supply shortage problem. Health Care Manage Sci 9(4):371–389
Nemhauser GL, Wolsey LA (1999) Integer and combinatorial optimization. Wiley, New York
Srinivasan A (1999) Improved approximation guarantees for packing and covering integer programs. SIAM J Comput 29(2):648–670
Sewell EC, Jacobson SH (2003) Using an integer programming model to determine the price of combination vaccines for childhood immunization. Ann Oper Res 119:261–284
Sewell EC, Jacobson SH, Weniger BG (2001) Reverse engineering a formulary selection algorithm to determine the economic value of pentavalent and hexavalent combination vaccines. Pediatr Infect Dis J 20(11):S45–S56
Weniger BG (1996) Economic analysis to meet the challenges of new combination vaccines. Presented at Vaccine Economics: Planning a Research Agenda for the Challenge of New and Improved Vaccines, Atlanta, GA
Weniger BG, Chen RT, Jacobson SH, Sewell EC, Deuson R, Livengood JR, Orenstein WA (1998) Addressing the challenges to immunization practice with an economic algorithm for vaccine selection. Vaccine 16(19):1885–1897