R/estimation.R
conditional_mle.RdProportion estimated using the MLE and confidence intervals based the asymptotic distribution of the estimator.
conditional_mle(
R1 = NULL,
R2 = NULL,
R3 = NULL,
R4 = NULL,
n = R1 + R2 + R3 + R4,
pi0,
gamma = 0.05,
alpha0 = 0,
alpha = 0,
beta = 0,
V = NULL,
...
)A numeric that provides the number of participants in the survey sample that were tested positive with both (medical) testing devices (and are, thus, members of the sub-population).
A numeric that provides the number of participants in the survey sample that are tested positive only with the first testing device (and are, thus, members of the sub-population).
A numeric that provides the number of participants in the survey sample that are tested positive only with the second testing device.
A numeric that provides the number of participants that are tested negative with the second testing device (and are either members of the sub-population and have tested negative with the first testing device or are not members of the sub-population).
A numeric that provides the sample size. Default value R1 + R2 + R3 + R4. If this value is provided it is used to verify that R1 + R2 + R3 + R4 = n.
A numeric that provides the prevalence or proportion of people (in the whole population) who are positive, as measured through a non-random,
but systematic sampling (e.g. based on medical selection).
A numeric that is used to compute a (1 - gamma) confidence region for the proportion. Default value is 0.05.
A numeric that corresponds to the probability that a random participant
has been incorrectly declared positive through the nontransparent procedure. In most applications,
this probability is likely very close to zero. Default value is 0.
A numeric that provides the False Negative (FN) rate for the sample R. Default value is 0.
A numeric that provides the False Positive (FP) rate for the sample R. Default value is 0.
A numeric that corresponds to the average of squared sampling weights. Default value is NULL.
Additional arguments.
A cpreval object with the structure:
estimate: Estimated proportion.
sd: Estimated standard error of the estimator.
ci_asym: Asymptotic confidence interval at the 1 - gamma confidence level.
gamma: Confidence level (i.e. 1 - gamma) for confidence intervals.
method: Estimation method (in this case mle).
measurement: A vector with (alpha0, alpha, beta).
beta0: Estimated false negative rate of the official procedure.
ci_beta0: Asymptotic confidence interval (1 - gamma confidence level) for beta0.
boundary: A boolean variable indicating if the estimates falls at the boundary of the parameter space.
pi0: Value of pi0 (input value).
sampling: Type of sampling considered ("random" or "weighted").
V: Average sum of squared sampling weights if weighted/stratified is used (otherwise NULL).
n: Sample size.
avar_beta0: Estimated asymptotic variance of beta0
...: Additional parameters.
# Samples without measurement error
X = sim_Rs(theta = 3/100, pi0 = 1/100, n = 1500, seed = 18)
conditional_mle(R1 = X$R1, R2 = X$R2, R3 = X$R3, R4 = X$R4, pi0 = X$pi0)
#> Method: Conditional MLE
#>
#> Estimated proportion: 3.2061%
#> Standard error : 0.3792%
#>
#> Confidence interval at the 95% level:
#> Asymptotic Approach: 2.4629% - 3.9494%
#>
#> Assumed measurement error: alpha = 0%, beta = 0%,
#> alpha0 = 0%
#>
#> Estimated false negative rate of the
#> official procedure: beta0 = 68.81%
#> CI at the 95% level: 61.58% - 76.04%
#>
#> Estimated ascertainment rate:
#> pi0/pi = 31.19%
#> CI at the 95% level: 23.96% - 38.42%
#>
#> Sampling: Random
# With measurement error
X = sim_Rs(theta = 30/1000, pi0 = 10/1000, n = 1500, alpha0 = 0.001,
alpha = 0.01, beta0 = 0.05, beta = 0.05, seed = 18)
conditional_mle(R1 = X$R1, R2 = X$R2, R3 = X$R3, R4 = X$R4, pi0 = X$pi0)
#> Method: Conditional MLE
#>
#> Estimated proportion: 3.6736%
#> Standard error : 0.4164%
#>
#> Confidence interval at the 95% level:
#> Asymptotic Approach: 2.8574% - 4.4899%
#>
#> Assumed measurement error: alpha = 0%, beta = 0%,
#> alpha0 = 0%
#>
#> Estimated false negative rate of the
#> official procedure: beta0 = 72.78%
#> CI at the 95% level: 66.73% - 78.83%
#>
#> Estimated ascertainment rate:
#> pi0/pi = 27.22%
#> CI at the 95% level: 21.17% - 33.27%
#>
#> Sampling: Random
conditional_mle(R1 = X$R1, R2 = X$R2, R3 = X$R3, R4 = X$R4, pi0 = X$pi0,
alpha0 = 0.001, alpha = 0.01, beta = 0.05)
#> Method: Conditional MLE
#>
#> Estimated proportion: 2.6929%
#> Standard error : 0.4434%
#>
#> Confidence interval at the 95% level:
#> Asymptotic Approach: 1.8238% - 3.5619%
#>
#> Assumed measurement error: alpha = 1%, beta = 5%,
#> alpha0 = 0.1%
#>
#> Estimated false negative rate of the
#> official procedure: beta0 = 66.48%
#> CI at the 95% level: 55.69% - 77.26%
#>
#> Estimated ascertainment rate:
#> pi0/pi = 33.52%
#> CI at the 95% level: 22.74% - 44.31%
#>
#> Sampling: Random