phm {mada}

Diagnostic Meta-Analysis with the proportional hazards model approach of Holling et.al (2012)

Description

The function fits the model of Holling et al. (2012). The adjusted profile maximum likelihood estimator (APMLE) is implemented for homogeneity and heterogeneity of primary studies.

Usage

phm(data, ...)
## Default S3 method:
phm(data = NULL, subset=NULL, 
    TP="TP", FN="FN", FP="FP", TN="TN",  
    correction = 0.5, correction.control = "all", 
    hetero = TRUE, estimator = "APMLE", l = 100, ...)

Arguments

data

any object that can be converted to a data frame with integer variables TP, FN, FP and TN, alternatively a matrix with column names including TP, FN, FP and TN.

subset

the rows of data to be used as a subset in all calculations. If NULL (the default) then the complete data is considered.

TP

character or integer: name for vector of integers that is a variable of data or a vector of integers. If data is not NULL, names are expected, otherwise integers are.

FN

character or integer: name for vector of integers that is a variable of data or a vector of integers. If data is not NULL, names are expected, otherwise integers are.

FP

character or integer: name for vector of integers that is a variable of data or a vector of integers. If data is not NULL, names are expected, otherwise integers are.

TN

character or integer: name for vector of integers that is a variable of data or a vector of integers. If data is not NULL, names are expected, otherwise integers are.

correction

numeric, continuity correction applied if zero cells

correction.control

character, if set to "all" (the default) the continuity correction is added to the whole data if only one cell in one study is zero. If set to "single" the correction is only applied to rows of the data which have a zero.

hetero

logical, should heterogeneity of studies be assumed? Will fit model for homogeneity otherwise.

estimator

character, determines estimator used. Currently only APMLE is available.

l

interger, number of iterations for fixed point algorithm

...

arguments passed on to other functions (currently not used)

Details

The model of Holling et al. (2012) assumes that the relationship between false positive rates u and and sensitivities p can be described by

u^\theta = p,

where \theta is the diagnostic accuracy parameter. If homogeneity of the studies can be assumed, \theta is estimated as a fixed effect. Under heterogeneity a random effect with variance \tau^2 describes the variation of the diagnostic accuracy parameter in the population of studies. Since the error of each observed \theta depends only on the sample size and \theta the model has only one parameter in the case of homogeneity and two parameters under heterogeneity, making it suitable for diagnostic meta-analysis with low sample size. Estimation proceeds by a fixed point algorithm derived from the adjusted profile likelihood. More details on the computational approach can be found in Holling et al. (2012).

Value

An object of the class phm for which many standard methods are available. See phm-class for details.

Author(s)

Philipp Doebler <[e-mail]>, Walailuck Boehning (original implementation of estimation algorithm)

References

Holling, H., Boehning W., Boehning, D. (2012) “Meta-Analysis of Diagnostic Studies based upon SROC-Curves: a Mixed Model Approach using a Proportional Hazards Model.” Statistical Modelling, 12, 347???-375.

See Also

phm-class

Examples

data(AuditC)
(fit <- phm(AuditC))
summary(fit)
plot(fit)