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Press the
**Calculate**
button in the lower left corner to perform the sample size calculations

## Introduction

This web application performs sample size calculations for cohort and test negative design studies on brand-specific vaccine effectiveness (VE), and relative VE of one vaccine over another. The sample size calculations are adjusted for confounders, and subject dropout. For sample sizes in test negative design studies, this application also provides the size of the catchment that is required to obtain the required sample size.

This web application performs sample size calculations for cohort and test negative design studies on brand- and strain-specific vaccine effectiveness (VE).

## Definition of vaccine effectiveness (VE)

### Cohort study (incidence risk ratio)

We define absolute VE of a vaccine as
*1 - Relative risk of being a case in vaccinated subjects over unvaccinated subjects*
. Similarly, we define relative VE as
*1 - Relative risk of being a case in subjects vaccinated with one vaccine over another vaccine*
.

#### References

The calculations for minimum detectable VE are done using the
*epi.sscohortc*
function of the R package
*epiR*
which internally uses the approach described in
*Woodward M (2005). Epidemiology Study Design and Data Analysis. Chapman & Hall/CRC, New York, pp. 381 - 426.*

The calculations for expected lower and upper limits of confidence intervals for VE are based on simulations. The confidence intervals are obtained using the approach described in
*Morris, J. A., & Gardner, M. J. (1988). Statistics in medicine: Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates. British medical journal (Clinical research ed.), 296(6632), 1313.*
Please note that this method does not use an exact confidence interval.

### Cohort study (incidence rate ratio)

We define absolute VE of a vaccine as
*1 - Ratio of incidence rate of being a case in vaccinated subjects over unvaccinated subjects*
. Similarly, we define relative VE as
*1 - Ratio of incidence rate of being a case in subjects vaccinated with one vaccine over another vaccine*
.

#### References

The calculations for minimum detectable VE are done using the
*epi.sscohortt*
function of the R package
*epiR*
which internally uses the approach described in
*Lwanga S, Lemeshow S (1991). Sample Size Determination in Health Studies. World Health Organization, Geneva.*

The calculations for expected lower and upper limits of confidence intervals for VE are based on simulations. The confidence intervals are obtained using the approach described in
*Rothman KJ (2012) Epidemiology: An Introduction. 2nd Ed., Oxford University Press, Oxford.*
Please note that this method does not use an exact confidence interval.

### Test negative design studies (odds ratio)

We define absolute VE of a vaccine as
*1 - odds of being vaccinated among cases divided by the odds of being vaccinated among control subjects*
. Similarly, we define relative VE as
*1 - odds of being vaccinated with a particular vaccine versus the reference vaccine among cases divided by odds being vaccinated with a particular vaccine versus the reference vaccine among controls*
.

#### References

The calculations for minimum detectable VE are done using the
*epi.sscc*
function of the R package
*epiR*
which internally uses the approach described in
*Dupont WD (1988) Power calculations for matched case-control studies. Biometrics 44: 1157 - 1168.*

The calculations for expected lower and upper limits of confidence intervals for VE are based on simulations. The confidence intervals are obtained using the approach described in
*Morris, J. A., & Gardner, M. J. (1988). Statistics in medicine: Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates. British medical journal (Clinical research ed.), 296(6632), 1313.*
Please note that this method does not use an exact confidence interval.

### Questions or Suggestions?

Please contact: anirudh.tomer@p-95.com