# Modes of Action and Time-Varying VES

• M. Elizabeth Halloran
• Ira M. LonginiJr.
• Claudio J. Struchiner
Chapter
Part of the Statistics for Biology and Health book series (SBH)

## Abstract

Suppose you have just been vaccinated against an infectious agent. Your physician or health practitioner tells you that the protective efficacy of the vaccine is 90%. You might then wonder if that means that the vaccine reduces your probability of contracting the infection (or disease) by 0.90 at each exposure to infection. In other words, you still might have a finite probability of contracting the infection or disease each time you were exposed, but it would be much less than it would have been if you had not been vaccinated. Alternatively, you might think that it means that you have a 0.90 probability of being completely protected against the disease, but still a 0.10 probability that you received absolutely no protection against infection or disease compared to what it would have been had you not been vaccinated. That is, the vaccine fails to elicit a protective immune response in 10% of the vaccinated people. Would you behave differently if you knew which of these possibilities were actually true? Would it make a difference if the vaccine were against a disease with a high case fatality ratio?Would it make a difference if the efficacy were 60% rather than 90%?

In Chapter 6, vaccine efficacy results were reported simply based on relative cumulative incidence or rates without any further interpretation of the meaning of the efficacy estimate. In 1984, Smith et al published a paper that grew out of a student exercise that altered the discussion about interpreting and evaluating protective efficacy of vaccines. They considered two models of vaccine mechanism they called Type I and Type II. In the Type I mechanism, vaccination is assumed to reduce the instantaneous disease rate in all the vaccinated people by a constant proportion. That is, Type I assumes that protection is multiplicative on the baseline hazard of infection. The effect is homogeneous in the vaccinated population. In the Type II mechanism, vaccination is assumed to provide a constant proportion of individuals with complete immunity from the disease. That is, it completely protects a portion of the vaccinated people, but completely fails to protect in the other portion. Under the Type II mechanism, the distribution of protection is heterogeneous in the vaccinated population.

## Keywords

Attack Rate Transmission Probability Frailty Model Cholera Vaccine Vaccine Effect
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag New York 2010

## Authors and Affiliations

• M. Elizabeth Halloran
• 1
• Ira M. LonginiJr.
• 1
• Claudio J. Struchiner
• 2
1. 1.Center for Statistics and Quantitative Infectious DiseasesUniversity of Washington, and Fred Hutchinson Cancer Research CenterSeattleUSA
2. 2.Escola Nacional de Saúde Pública Fundação Oswaldo CruzRio de JaneiroBrazil