papciUI {papci}

papciUI

Description

This function will automatically launch the PA interactive user interface in a web browser. The user interface can also be accessed by https://kate-yueyi-li.shinyapps.io/shiny . Neither R nor any packages are required in this online version.

Usage

papciUI()

Details

The definitions of PPA, NPA, PPV and NPA in this package are

• PPA= Pr(comparator+|baseline+), NPA= Pr(comparator-|baseline-)

• PPV= Pr(baseline+|comparator+), NPV= Pr(baseline-|comparator-)

The point estimations are x/m for PPA and and (n-y)/n for NPA. By ignoring enrollment biases, PPV and NPV are estimated as x/(x+y) and (n-y)/(m+n-x-y), respectively. When samples are not enrolled randomly or selected based on baseline results, PPV and NPV are obtained by the Bayes theorem and not binomially distributed. They are defined as

PPV = prev*PPA / [ prev*PPA + (1-prev)*(1-NPA) ]

NPV = (1-prev)*NPA / [ (1-prev)*NPA + prev*(1-PPA) ]

Nine methods are allowed for constructing the confidence interval(s) for PPA and NPA referring to binom.confint. Six methods are allowed for constructing the confidence interval(s) for PPV based on the risk-ratio R1=(1-NPA)/PPA.

• Koopman (1984) - derived the (1-\alpha)100% CI for R1 by using Chi-squared method.

• Katz et al.(1978) - derived the (1-\alpha)100% CI for R1 by assuming that the log(R1) is approximately normally distributed.

• Noether (1957) - developed the (1-\alpha)100% CI for R1 using an explicit solution.

• Gart and Nam (1988) - improved Koopman's method by correcting the asymptotic skewness.

• Bootstrap - derived the risk ratio CI using Bootstrap method from multiple random samples.

• Plug-In - derived the 95% CI for PPA and NPA as (PPA_l,PPA_u) and (NPA_l,NPA_u). Applied all four combinations (i.e., (PPA_l, NPA_l); (PPA_l, NPA_u); (PPA_u, NPA_l); (PPA_u, NPA_u)) into above PPV formulas by Bayes theorem, and the minimum and maximum values are determined as the lower and upper bound of 95% CIs of PPV.

Given the CIs for the risk-ratio R1, denoted as [R1_l, R1_u], the CIs for PPV can be directly contained by

[p/(p + (1-p)*R1_u), p/(p + (1-p)*R1_l)]

CIs of NPV can be derived in the same way.

Value

A list of data.frame containing the estimated agreements (ppa, npa, ppv, npv) and the lower and upper bounds of the confidence interval for all the methods in methods_pa or methods_pv.

Author(s)

Lei Yang, Cui Guo, Kate Li, Chang Xu ([e-mail])

References

1. Gart John J and Nam Jun-mo (1988). Approximate interval estimation of the ratio of binomial parameters: a review and corrections for skewness, Biometrics, 323-338.

2. Katz DJSM, Baptista J, Azen SP and Pike MC (1978). Obtaining confidence intervals for the risk ratio in cohort studies, Biometrics, 469-474.

3. Koopman PAR (1984). Confidence intervals for the ratio of two binomial proportions, Biometrics, 513-517.

4. Noether Gottfried E (1957). Two confidence intervals for the ratio of two probabilities and some measures of effectiveness, Journal of the American Statistical Association, 52: 36-45.

See Also

binom.confint for different methods to obtain a confidence interval on the binomial probability like PPA and NPA.

Examples

agreement(x = 90, y = 10, m = 100, n = 80, prev = 0.3)
agreement(x = 84, y = 0, m = 84, n = 97, prev = 0.096)