Vaccine effectiveness

In the medical statistics and epidemiology of infectious diseases to determine the part of vaccine efficacy ( IW ), and vaccine efficacy , protection , ( English vaccine efficacy ) or vaccination effect called, in addition to the cost-efficiency and the vaccine safety the most important prerequisites for the recommendation of a vaccine . The vaccine efficacy is not to be confused (usually by the observational studies measured) vaccine effectiveness ( English vaccine effectiveness ).

The vaccine effectiveness is the direct effect of the vaccine, which is used for the evaluation of a program of measures in the case of infectious diseases and is calculated as the relative reduction in the risk of developing the target disease among those who were vaccinated compared to those who were not. At best, vaccine effectiveness is determined in randomized controlled trials under “optimal conditions”. “Optimal conditions” means that certain criteria are met, such as B. an appropriate selection of (usually healthy) subjects or the verified and timely administration of the vaccine and a functioning cold chain .

The formula for vaccine effectiveness was established in 1915 by statisticians Major Greenwood and George Udny Yule in their The Statistics of Anti-Typhoid and Anti-Cholera Inoculations, and the Interpretation of Such Statistics in General. Developed for assessing the effectiveness of cholera and typhoid vaccines . It provides a rough but quick estimate of the effectiveness of a vaccination in the target population . Vaccine effectiveness is derived from the relative risk of infection in vaccinated and unvaccinated individuals. To calculate the effectiveness of the vaccine, it is sufficient to determine the percentage of vaccinated people in the target population and the percentage of vaccinated people among all sick people.

Formula for vaccine effectiveness

It is assumed that the risk of infection for vaccinated and unvaccinated individuals is the same and that vaccinations in the population are carried out according to the randomization principle (random allocation). Vaccine effectiveness is generally expressed as a proportional reduction in the incidence rate (IR) of the target disease among vaccinated ( ) compared to unvaccinated individuals ( ). The incidence rate indicates the ratio of newly infected or sick people to the total number of people at risk. Let the number of sick people be among those who were vaccinated and the number of people who got sick among those who were not vaccinated (see incidence ). The vaccine effectiveness (IV) can be calculated as the ratio of the disease rate in vaccinated people to that in non-vaccinated people: ${\ displaystyle IR_ {v}}$ ${\ displaystyle IR_ {u}}$ ${\ displaystyle c_ {v}}$ ${\ displaystyle n_ {v}}$ ${\ displaystyle c_ {u}}$ ${\ displaystyle n_ {u}}$

{\ displaystyle IW_ {IR} = {\ frac {IR_ {u} -IR_ {v}} {IR_ {u}}} \ cdot 100 \, \%}

,

in which

${\ displaystyle AR_ {v} = c_ {v} / n_ {v}}$ : Incidence rate among vaccinated persons ( incidence rate among vaccinated persons)

{\ displaystyle AR_ {u} = x_ {u} / n_ {u}}

: Incidence rate among unvaccinated persons (incidence rate among non-vaccinated persons)

Equivalently, the vaccine effectiveness can also be calculated directly from the   relative risk (RR) of the vaccinated with regard to the target disease compared to the unvaccinated:

{\ displaystyle RR = {\ frac {c_ {v} / n_ {v}} {c_ {u} / n_ {u}}} = {\ frac {R_ {1}} {R_ {0}}}}

.

The vaccine effectiveness is then its complement:

{\ displaystyle IW_ {RR} = 1-RR = 1 - {\ frac {c_ {v} / n_ {v}} {c_ {u} / n_ {u}}} = 1 - {\ frac {c_ {v } n_ {u}} {c_ {u} n_ {v}}} = {\ frac {{\ frac {n_ {v}} {n_ {u} + n_ {v}}} - {\ frac {c_ { v}} {c_ {u} + c_ {v}}}} {{\ frac {n_ {v}} {n_ {u} + n_ {v}}} \ left (1 - {\ frac {c_ {v }} {c_ {u} + c_ {v}}} \ right)}} = {\ frac {pc} {p (1-c)}}}

,

where the two parts and are given by: ${\ displaystyle p}$ ${\ displaystyle c}$

{\ displaystyle p = {\ frac {n_ {v}} {n_ {u} + n_ {v}}} \; \;}

and with

{\ displaystyle \; \; c = {\ frac {c_ {v}} {c_ {u} + c_ {v}}}}

${\ displaystyle p}$ : Proportion of vaccinated persons in the target population
${\ displaystyle c}$ : Proportion of vaccinated among all sick people

The above formula approximates the complement of the odds ratio that can be obtained from case-control studies . As such, the formula can be used to estimate the effectiveness of the vaccine based on the incidence density ratio (IDR). Let and be the number of vaccinated and non-vaccinated cases identified and and the number of vaccinated and non-vaccinated control cases that come from the reference population. In this case it can be shown that ${\ displaystyle a}$ ${\ displaystyle b}$ ${\ displaystyle d}$ ${\ displaystyle f}$

${\ displaystyle IW_ {IDR} = 1-IDR \ approx 1 - {\ frac {a / b} {d / f}} = {\ frac {pc} {p (1-c)}}}$ .

An alternative calculation is the proportion of people in the placebo group of a vaccine study who would not have gotten sick if they had received the vaccine.

Differences between vaccine effectiveness studies and vaccine effectiveness studies

The vaccine effect (vaccine effectiveness) refers to vaccination protection, which is determined by randomized controlled trials under optimal conditions, where the storage and administration of the vaccine is monitored and the participants are usually healthy. Vaccine effectiveness refers to vaccine protection measured in observational studies of people with underlying diseases who were given vaccines under real-world conditions by various health care providers.

The vaccination effect shows how effective the vaccine can be under ideal circumstances and with one hundred percent vaccine uptake. In contrast, vaccine effectiveness measures how well a vaccine performs when used in routine community conditions. If the vaccine effectiveness study is based on a population that is in a particular controlled environment, the vaccine effectiveness study will be more effective. If the criteria were to change, e.g. For example, if they were based on a larger population that is not as restricted and in a more natural setting, it would be equivalent to a vaccine effectiveness study. What makes vaccine efficacy studies applicable is that they also display infestation rate as well as a follow-up on vaccination status. Vaccine effectiveness studies are much easier to track than vaccine effectiveness studies given the allowance for environmental differences.

The advantages of vaccine efficacy studies are the possible control of confounding factors by means of randomization , as well as prospective, active monitoring of the infestation rates and careful follow-up of the vaccination status for a study population. The main disadvantages of vaccine efficacy studies are their high complexity and the cost of carrying them out, especially in the case of relatively rare infection outcomes from diseases where it is necessary to increase the sample size in order to achieve clinically relevant discriminatory power .

Vaccine effectiveness in COVID-19

Hypothetical vaccine effectiveness scenarios indicated that a vaccine with at least 70% effectiveness would have been sufficient to contain the spread of COVID-19 in South Africa.

Individual evidence

↑ Wolfgang Kiehl : Infection protection and infection epidemiology. Technical terms - definitions - interpretations. Ed .: Robert Koch Institute, Berlin 2015, ISBN 978-3-89606-258-1 , p. 64, keyword vaccine effectiveness
^ Matthias Egger, Oliver Razum et al .: Public health compact. Walter de Gruyter, (2017), p. 473.
↑ John M. Last: A Dictionary of Epidemiology. , 4th edition, 2001 International Epidemiological Association , Oxford UP 2001, p. 184. Keyword: vaccine efficacy .
↑ Lothar Sachs , Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 .
↑ Standing Vaccination Commission: Innovations in the current recommendations of the Standing Vaccination Commission (STIKO) at the RKI from August 2013. Ed .: Robert Koch Institute, Berlin 2013, p. 353.
↑ Major Greenwood and George Udny Yule : The statistics of anti-typhoid and anti-cholera inoculations, and the interpretation of such statistics in general. (1915), 113-194.
↑ Lothar Sachs , Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 , p. 198
^ Matthias Egger, Oliver Razum et al .: Public health compact. Walter de Gruyter, (2017), p. 442.
^ Matthias Egger, Oliver Razum et al .: Public health compact. Walter de Gruyter, (2017), p. 473.
↑ Wolfgang Kiehl: Infection protection and infection epidemiology. Technical terms - definitions - interpretations. Ed .: Robert Koch Institute, Berlin 2015, ISBN 978-3-89606-258-1 , p. 64, keyword vaccine effectiveness
↑ Lothar Sachs , Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 , p. 199
↑ Halloran, M. Elizabeth, et al .: Direct and indirect effects in vaccine efficacy and effectiveness. American journal of epidemiology (1991), p. 325
↑ John M. Last: A Dictionary of Epidemiology. , 4th edition, 2001 International Epidemiological Association , Oxford UP 2001, p. 184. Keyword: vaccine efficacy .
↑ National Center for Immunization and Respiratory Diseases: How do vaccine effectiveness studies differ from vaccine efficacy studies? (2011), accessed March 23, 2020.
↑ Zindoga Mukandavire et al .: Quantifying early COVID-19 outbreak transmission in South Africa and exploring vaccine efficacy scenarios. (2011), PLOS ONE (2020). P. 5

[1] Wolfgang Kiehl : Infection protection and infection epidemiology. Technical terms - definitions - interpretations. Ed .: Robert Koch Institute, Berlin 2015, ISBN 978-3-89606-258-1 , p. 64, keyword vaccine effectiveness

[2] Matthias Egger, Oliver Razum et al .: Public health compact. Walter de Gruyter, (2017), p. 473.

[3] John M. Last: A Dictionary of Epidemiology. , 4th edition, 2001 International Epidemiological Association , Oxford UP 2001, p. 184. Keyword: vaccine efficacy .

[4] Lothar Sachs , Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 .

[5] Standing Vaccination Commission: Innovations in the current recommendations of the Standing Vaccination Commission (STIKO) at the RKI from August 2013. Ed .: Robert Koch Institute, Berlin 2013, p. 353.

[6] Major Greenwood and George Udny Yule : The statistics of anti-typhoid and anti-cholera inoculations, and the interpretation of such statistics in general. (1915), 113-194.

[7] Lothar Sachs , Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 , p. 198

[8] Matthias Egger, Oliver Razum et al .: Public health compact. Walter de Gruyter, (2017), p. 442.

[9] Matthias Egger, Oliver Razum et al .: Public health compact. Walter de Gruyter, (2017), p. 473.

[10] Wolfgang Kiehl: Infection protection and infection epidemiology. Technical terms - definitions - interpretations. Ed .: Robert Koch Institute, Berlin 2015, ISBN 978-3-89606-258-1 , p. 64, keyword vaccine effectiveness

[11] Lothar Sachs , Jürgen Hedderich: Applied Statistics: Collection of Methods with R. 8., revised. and additional edition. Springer Spectrum, Berlin / Heidelberg 2018, ISBN 978-3-662-56657-2 , p. 199

[12] Halloran, M. Elizabeth, et al .: Direct and indirect effects in vaccine efficacy and effectiveness. American journal of epidemiology (1991), p. 325

[13] John M. Last: A Dictionary of Epidemiology. , 4th edition, 2001 International Epidemiological Association , Oxford UP 2001, p. 184. Keyword: vaccine efficacy .

[14] National Center for Immunization and Respiratory Diseases: How do vaccine effectiveness studies differ from vaccine efficacy studies? (2011), accessed March 23, 2020.

[15] Zindoga Mukandavire et al .: Quantifying early COVID-19 outbreak transmission in South Africa and exploring vaccine efficacy scenarios. (2011), PLOS ONE (2020). P. 5