Attack ratios

First: No vaccine is 100% effective.

For each vaccine, there is a proportion of people who will not develop immunity to the disease from the vaccine. Some vaccines are more effective than others. The effectiveness of pertussis vaccines is complicated by the fact that immunity to pertussis (whooping cough) wanes, so a person becomes more susceptible to Bordetella pertussis infection with the amount of time since the last dose of a pertussis-containing vaccine.

I know the last thing that U.S. taxpayers want to think about on April 15^th is math, but I found this sentence about the 2010 pertussis epidemic in California in the news recently: "Of the 132 patients under age 18, 81 percent were up to date on recommended whooping cough shots and eight percent had never been vaccinated. The other 11 percent had received at least one shot, but not the complete series."

Does that mean that pertussis vaccine is only 19% effective? Does that mean that children who have not been vaccinated are less likely to get pertussis?

The first thing to realize is that those are percentages of cases of pertussis, not percentages of vaccinated versus unvaccinated children who got pertussis.

The question is: what is the denominator?

To know how effective a vaccine is, the denominator we need is the number of vaccinated and unvaccinated people who were exposed to a vaccine-preventable disease.

In 2010, 95% of children 19 to 35 months of age had received at least 3 doses of pertussis-containing vaccine and 68% of children 13 – 17 years of age had received a dose of tetanus, diphtheria, and acellular pertussis vaccine (Tdap). In California, 93.1% of kindergarten students had received at least 3 doses of DTP/DTaP/DT.

The reason why more vaccinated children got pertussis than unvaccinated children is that most children are vaccinated against pertussis. The percent of vaccinated children who got pertussis (attack ratio) is smaller than the percent of unvaccinated children who got pertussis.

In large outbreaks, like the California pertussis epidemic and our current pertussis epidemic in Washington State, knowing the total number of people exposed to the infecting pathogen can be difficult, so let's look at some smaller outbreaks of another vaccine-preventable disease:

There was an outbreak of measles in a high school in Utah in 1996. Of the 17 cases of measles, 8 were in students who had received measles, mumps, and rubella vaccine (MMR) and 9 were in unvaccinated children. So, 47% of cases were vaccinated students and 53% of cases were unvaccinated students.

Does that mean that the vaccine was not effective?

Not when we consider that the denominators were 852 vaccinated students and 27 unvaccinated students in the school. So, the measles attack ratio* was 1% of vaccinated students (8 ÷ 852) and 33% of unvaccinated students (9 ÷ 27).

Vaccine effectiveness (VE) is calculated as:

[(ARU – ARV) ÷ ARU] x 100

where ARU is the attack ratio in unvaccinated individuals and ARV is the attack ratio in vaccinated individuals. In the Utah outbreak, the effectiveness of MMR at preventing measles was:

[(33 – 1) ÷ 33] x 100 = 97%

This outbreak occurred before the Advisory Committee on Immunization Practices (ACIP) recommended 2 doses of MMR rather than one. None of the 72 students who had received 2 doses of MMR got the measles, so the vaccine effectiveness for 2 doses of MMR was 100%.

Similar attack ratios and vaccine effectiveness has been seen in other measles outbreaks:

In an outbreak in a German public school, the measles attack ratio was:

·       53% of unvaccinated students

·       1.4% of vaccinated students

Vaccine effectiveness was:

·       98.1% for one dose of measles-containing vaccine

·       99.4% for two doses

In a primary school in Singapore, the measles attack ratio was:

·       52.8% of unvaccinated students

·       1.2% of vaccinated students

Vaccine effectiveness was 97.8%

What about pertussis?

In an outbreak in the Virgin Islands, the attack ratio for pertussis was:

·       18% of unvaccinated students

·       6% of vaccinated students

Vaccine effectiveness was 65.6%

Among pertussis cases ages 6 months to 5 years in an outbreak in an Amish community:

·       88 (72%) had no record of pertussis immunization

·       6 (5%) had received one or two doses of DTP/DTaP

·       29 (24%) had received ≥3 doses of DTP/DTaP

We don't know the denominators for this outbreak (the number of children exposed to B. pertussis), so we can't calculate the attack ratios or vaccine effectiveness.

Obviously, pertussis vaccines are not as effective as measles vaccine, but people vaccinated against pertussis that become infected with B. pertussis less likely than people who are not vaccinated to have severe disease and less likely to transmit the bacteria to others (Baptista et al., 2006; Préziosi & Halloran, 2003).

Why use a vaccine that is not 100% effective?

Would you stop locking your doors because burglars can still break into your house when the doors are locked? Would you stop wearing a seatbelt because you can still be injured in a motor vehicle accident while you are wearing a seatbelt?

Seatbelts reduce the risk serious injuries.

Locked doors reduce the risk of being robbed.

Vaccines reduce the risk of vaccine-preventable diseases.

Please drive carefully.

Road Crash Fatalities on US Income Tax Days

ማቴዎስ ጳውሎስ

*The term "attack rate" is commonly used, but a rate is an incidence over time.

References:

Baptista, P. N., Magalhães, V., Rodrigues, L. C., Rocha, M. A. W., & Pimentel, A. M. (2006). Pertussis vaccine effectiveness in reducing clinical disease, transmissibility, and proportion of case with positive culture after household exposure in Brazil. Pediatric Infectious Disease Journal, 25(9), 844-846. http://www.ncbi.nlm.nih.gov/pubmed/16940847.

Centers for Disease Control and Prevention. (1997). Measles outbreak, southwestern Utah, 1996. Morbidity and Mortality Weekly Report, 46(33), 766-769. http://www.cdc.gov/mmwr/preview/mmwrhtml/00049048.htm.

Centers for Disease Control and Prevention. (1998). Measles, mumps, and rubella – vaccine use and strategies for elimination of measles, mumps, rubella, and congenital rubella syndrome and control of mumps_ recommendations of the Advisory Committee on Immunization Practices (ACIP). Morbidity and Mortality Weekly Report, 47(8), 1-57. http://www.cdc.gov/mmwr/preview/mmwrhtml/00053391.htm.

Centers for Disease Control and Prevention. (2006). Pertussis outbreak in an Amish community – Kent County, Delaware, September 2004 – February 2005. Morbidity and Mortality Weekly Report, 55(30), 817-821. http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5530a1.htm.

Centers for Disease Control and Prevention. (2011). National and state vaccination coverage among adolescents aged 13 through 17 years – United States, 2010. Morbidity and Mortality Weekly Report, 60(33),1117-1123. http://www.cdc.gov/mmwr/preview/mmwrhtml/mm6033a1.htm.

Centers for Disease Control and Prevention. (2011). National and state vaccination coverage among children aged 19 – 35 months – United States, 2010. Morbidity and Mortality Weekly Report, 60(34), 1157-1163. http://www.cdc.gov/mmwr/preview/mmwrhtml/mm6034a2.htm.

Centers for Disease Control and Prevention. (2011). Vaccination coverage among children in Kindergarten – United States, 2009 – 2010 school year. Morbidity and Mortality Weekly Report, 60(21), 700-704. http://www.cdc.gov/mmwr/preview/mmwrhtml/mm6021a4.htm.

Grens, K. (April 3, 2012). Whooping cough vaccine fades in pre-teens: study. Reuters Health Information. Retrieved April 14, 2012 from http://www.nlm.nih.gov/medlineplus/news/fullstory_123698.html.

Ong, G., Rasidah, N., Wan, S., & Cutter, J. (2007). Outbreak of measles in primary school students with high first dose MMR vaccination coverage. Singapore Medical Journal, 48(7), 656-661. http://smj.sma.org.sg/4807/4807a10.pdf.

Préziosi, M-P. & Halloran, M. E. (2003). Effects of pertussis vaccination on disease: vaccine efficacy in reducing clinical severity. Clinical Infectious Diseases, 37(6), 772-779. http://cid.oxfordjournals.org/content/37/6/772.long.

Wei, S. C., Tatti, K., Cushing, K., Rosen, J., Brown, K., Cassiday, P., Clark, T. et al. (2010). Effectiveness of adolescent and adult tetanus, reduced-dose diphtheria, and acellular pertussis vaccine against pertussis. Clinical Infectious Diseases, 51(3), 315-321. http://cid.oxfordjournals.org/content/51/3/315.long.

Wichmann, O., Hellenbrand, W. Sagebiel, D., Santibanez, S., Ahlemeyer, G., Vogt, G. et al. (2007). Large measles outbreak at a German public school, 2006. Pediatric Infectious Disease Journal, 26(9), 782-786. http://www.ncbi.nlm.nih.gov/pubmed/17721371.