conditional_mle: Compute MLE based on the full information R1, R2, R3 and R4.
In pempi: Proportion Estimation with Marginal Proxy Information

conditional_mle

R Documentation

Compute MLE based on the full information R1, R2, R3 and R4.

Description

Proportion estimated using the MLE and confidence intervals based the asymptotic distribution of the estimator.

Usage

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,
  ...
)

Arguments

`R1`	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).
`R2`	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).
`R3`	A `numeric` that provides the number of participants in the survey sample that are tested positive only with the second testing device.
`R4`	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).
`n`	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.
`pi0`	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).
`gamma`	A `numeric` that is used to compute a (1 - gamma) confidence region for the proportion. Default value is `0.05`.
`alpha0`	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`.
`alpha`	A `numeric` that provides the False Negative (FN) rate for the sample R. Default value is `0`.
`beta`	A `numeric` that provides the False Positive (FP) rate for the sample R. Default value is `0`.
`V`	A `numeric` that corresponds to the average of squared sampling weights. Default value is `NULL`.
`...`	Additional arguments.

Value

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.

Author(s)

Stephane Guerrier, Maria-Pia Victoria-Feser, Christoph Kuzmics

Examples

# 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)

# 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$pi0)
conditional_mle(R1 = X$R1, R2 = X$R2, R3 = X$R3, R4 = X$R4, pi0 = X$pi0,
alpha0 = 0.001, alpha = 0.01, beta = 0.05)

pempi documentation built on Oct. 9, 2023, 5:10 p.m.