conditional_mle {pempi}

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)