Package {dtametaTMB}

dtametaTMB: Diagnostic Test Accuracy Meta-Analysis using Template Model Builder

Description

Functions for fitting diagnostic test accuracy (DTA) meta-analysis models using Template Model Builder (TMB).

Details

Implemented methods

• Reitsma model

• Rutter-Gatsonis HSROC model

• Hoyer multiple-threshold model

Main workflow

• fitReitsma() -> plot() -> forest()

• fitReitsmaSubgroup() -> plot() -> forest()

• fitRutterGatsonis() -> plot() -> forest()

• fitRutterGatsonisSubgroup() -> plot() -> forest()

• fitHoyer() -> plot() -> forest()

Included datasets

• anaemia

• anticcp

• diabetes

• FENO

• RF

• schuetz

See the package vignettes for worked examples and model descriptions.

Author(s)

Maintainer: Claus Nowak claus.nowak@donau-uni.ac.at

Authors:

• Claus Nowak claus.nowak@donau-uni.ac.at

FENO dataset

Description

This is the FENO data set from Schneider (2017) from a review of fractional exhaled nitric oxide (FeNO) for diagnosis of asthma.

Usage

FENO

Format

A data frame with 150 rows and 7 variables:

study

Study identifier

study_id

Study identifier (numeric)

cutoff

Threshold for FeNO measured in ppb

TP

Number of true positives

FN

Number of false negatives

FP

Number of false positives

TN

Number of true negatives

Note

The data are reproduced from the original source and the supplementary material accompanying the Cochrane Handbook. However, the study 'Schneider 2013' contains inconsistent diseased counts (TP + FN). To illustrate the Hoyer analysis in the vignette, we modify the TP counts in rows 118–120 from 39 to 38. Other corrections restoring internal consistency are also conceivable.

Source

Schneider, A. et al. (2017). A novel statistical model for analyzing data of a systematic review generates optimal cutoff values for fractional exhaled nitric oxide for asthma diagnosis. Journal of Clinical Epidemiology, 92, 69-78. doi:10.1016/j.jclinepi.2017.09.001

RF dataset

Description

This is the RF data set from Nishimura (2007) from a review of rheumatoid factor (RF) to diagnose rheumatoid arthritis.

Usage

RF

Format

A data frame with 50 rows and 8 variables:

study

Study identifier

year

Year of the study

TP

Number of true positives

FP

Number of false positives

FN

Number of false negatives

TN

Number of true negatives

cutoff

Threshold used in U/mL for test positivity

method

Different methods used to perform the test

Source

Nishimura, K. et al. (2007). Meta-analysis: diagnostic accuracy of anti-cyclic citrullinated peptide antibody and rheumatoid factor for rheumatoid arthritis. Annals of Internal Medicine, 146(11), 392-403. doi:10.7326/0003-4819-146-11-200706050-00008

Anaemia (synthetic data set)

Description

This is a synthetic data set where haemoglobin was measured by a point-of-care device, with laboratory measurement acting as the reference standard. Lower values indicate disease (anaemia).

Usage

anaemia

Format

A data frame with 81 rows and 11 variables:

study

Study identifier

threshold

Haemoglobin in g/dL

TP

Number of true positives

FN

Number of false negatives

FP

Number of false positives

TN

Number of true negatives

D

Number of diseased individuals

H

Number of healthy individuals

sens

Sensitivity

fpr

False positive rate

testdirection

Smaller values indicate disease (=less)

Source

Synthetic dataset.

Likelihood Ratio Tests for Diagnostic Test Accuracy Models

Description

Compare nested diagnostic test accuracy meta-analysis models using likelihood ratio tests (LRTs).

Usage

## S3 method for class 'Reitsma'
anova(object, ..., test = "Chisq")

## S3 method for class 'ReitsmaSubgroup'
anova(object, ..., test = "Chisq")

## S3 method for class 'RutterGatsonis'
anova(object, ..., test = "Chisq")

## S3 method for class 'RutterGatsonisSubgroup'
anova(object, ..., test = "Chisq")

## S3 method for class 'RutterGatsonisReg'
anova(object, ..., test = "Chisq")

Arguments

Details

These methods compute likelihood ratio statistics from the fitted model log-likelihoods and compare models ordered by increasing numbers of estimated parameters. The test statistic is

-2(\ell_0 - \ell_1)

where \ell_0 and \ell_1 are the log-likelihoods of two nested models. Under standard regularity conditions, the statistic follows a chi-squared distribution with degrees of freedom equal to the difference in the numbers of estimated parameters.

The models supplied should be nested and fitted to the same dataset. Warnings are issued when models have identical numbers of parameters or when the log-likelihood decreases for a more complex model, suggesting that the nesting assumptions may be violated.

Value

An object of class "anova" inheriting from "data.frame" with the following columns:

Df

Number of estimated parameters in the model.

logLik

Model log-likelihood.

Df.diff

Difference in parameters compared with the previous model.

Chisq

Likelihood ratio chi-squared statistic.

Pr(>Chisq)

P-value from the chi-squared test.

See Also

logLik(), anova()

Anticcp dataset

Description

This is the anticcp data set from Nishimura (2007) from a review of anti-cyclic citrullinated peptide antibody (anti-ccp) to diagnose rheumatoid arthritis.

Usage

anticcp

Format

A data frame with 37 rows and 7 variables:

study

Study identifier

year

Year of the study

TP

Number of true positives

FP

Number of false positives

FN

Number of false negatives

TN

Number of true negatives

generation

First generation (CCP1) or second generation (CCP2) assay

Source

Nishimura, K. et al. (2007). Meta-analysis: diagnostic accuracy of anti-cyclic citrullinated peptide antibody and rheumatoid factor for rheumatoid arthritis. Annals of Internal Medicine, 146(11), 392-403. doi:10.7326/0003-4819-146-11-200706050-00008

Export Model Results for RevMan

Description

Converts fitted model objects (Reitsma, ReitsmaSubgroup, RutterGatsonis, RutterGatsonisSubgroup) into a format suitable for manual entry into the Diagnostic Test Accuracy module of Review Manager (RevMan).

Usage

as_revman(x, ...)

## S3 method for class 'Reitsma'
as_revman(x, ...)

## S3 method for class 'RutterGatsonis'
as_revman(x, ...)

## S3 method for class 'ReitsmaSubgroup'
as_revman(x, ...)

## S3 method for class 'RutterGatsonisSubgroup'
as_revman(x, ...)

Arguments

Value

A data frame with columns:

Subgroup

Only returned for ReitsmaSubgroup and RutterGatsonisSubgroup objects.

Externally_Calculated_Parameters

Revman model/parameter types.

Parameter

RevMan parameter name.

Estimate

Parameter estimate.

The returned table contains the model parameters displayed by RevMan:

• E(logitSe)

• E(logitSp)

• Var(logitSe)

• Var(logitSp)

• Cov(logits)

• Corr(logits)

• Lambda

• Theta

• beta

• Var(accuracy)

• Var(threshold)

• SE(E(logitSe))

• SE(E(logitSp))

• Cov(Es)

• Studies

Note

For Rutter and Gatsonis models SE(E(logitSe)), SE(E(logitSp)), and Cov(Es) are not computed.

Diabetes dataset

Description

This is the diabetes data set from the supplementary material in Hoyer (2018).

Usage

diabetes

Format

A data frame with 124 rows and 9 variables

study

Study identifier

threshold

Threshold HbA1c used to derive TP, FN, FP, TN

TP

Number of true positives

TN

Number of true negatives

FP

Number of false positives

FN

Number of false negatives

D

Number of diseased individuals

H

Number of healthy individuals

originally_published

Whether the data threshold/row was used in the original publication (1=yes, 0=no)

Source

Hoyer, A., Hirt, S., Kuss, O. (2018). Meta-analysis of full ROC curves using bivariate time-to-event models for interval-censored data. Research Synthesis Methods, 9(1), 62-72. doi:10.1002/jrsm.1273

Fit Threshold-Based Bivariate Time-to-Event Model (Hoyer)

Description

This is a high-level wrapper that performs the full workflow for fitting the Hoyer AFT model:

1. Restructuring of threshold-based data into interval format

2. Estimation of initial parameter values

3. Model fitting via likelihood maximization

The input data must contain cumulative counts for true positives, false positives, false negatives, and true negatives at multiple thresholds within each study.

Usage

fitHoyer(
  data,
  TP,
  FP,
  FN,
  TN,
  study,
  threshold,
  smallest,
  largest,
  testdirection = c("greater", "less"),
  eval_threshold = NULL,
  conflevel = 0.95,
  dist = "loglogistic",
  verbose = FALSE,
  ...
)

Arguments

Details

Fits the threshold-based bivariate accelerated failure time (AFT) model for diagnostic test accuracy (DTA) meta-analysis as described by Hoyer et al. (2018). The model is estimated using interval-censored likelihoods via Template Model Builder (TMB).

The function internally calls:

• restructure_data to convert cumulative counts into interval-censored data

• initHoyerAFT to estimate starting values

• fitHoyerAFT to fit the model

Missing values in the input data are removed prior to analysis. A message is issued listing the affected studies.

Value

An object of class "HoyerAFT" as returned by fitHoyerAFT, containing:

data

Processed original data

restructured

Interval-formatted data

fit

Optimization output

sdreport

TMB report object

sdreport2

Summary of reported parameters

sensspec

Sensitivity and specificity estimates

Note

Requires a compiled TMB model named "Hoyer".

References

Hoyer, A., Hirt, S., Kuss, O. (2018). Meta-analysis of full ROC curves using bivariate time-to-event models for interval-censored data. Research Synthesis Methods, 9(1), 62-72. doi:10.1002/jrsm.1273

Examples

data("diabetes")
fit <- fitHoyer(
  data = diabetes,
  TP = TP,
  FP = FP,
  FN = FN,
  TN = TN,
  study = study,
  threshold = threshold,
  testdirection = "greater",
  smallest = 2,
  largest = 10
)
summary(fit)

Fit Threshold-Based Bivariate Time-to-Event Model (Hoyer AFT)

Description

Fits a bivariate accelerated failure time (AFT) model for diagnostic test accuracy (DTA) data using interval-censored likelihoods as described in Hoyer et al. (2018). The model is estimated using Template Model Builder (TMB) with study-specific random effects.

Usage

fitHoyerAFT(
  data,
  init,
  conflevel = 0.95,
  eval_threshold = NULL,
  verbose = FALSE
)

Arguments

Details

The model reports logit-survival quantities, which correspond to sensitivity and false positive rate for testdirection = "greater", and to false negative rate and specificity for testdirection = "less".

Model fitting is performed using nlminb, and uncertainty estimates are obtained via TMB::sdreport. Parameter transformations include log-scale parameters and Fisher's Z-transform for correlations.

Value

An object of class "HoyerAFT" containing:

data

Processed original data

restructured

Interval-formatted data

fit

Optimization output from nlminb

sdreport

TMB report object from sdreport

sdreport2

Summary of reported parameters

distcode

Distribution code used in the model

sensspec

Sensitivities and specificities at the chosen thresholds

Note

Requires a compiled TMB model named "Hoyer".

References

Hoyer, A., Hirt, S., Kuss, O. (2018). Meta-analysis of full ROC curves using bivariate time-to-event models for interval-censored data. Research Synthesis Methods, 9(1), 62-72. doi:10.1002/jrsm.1273

Examples

data("diabetes")
res <- restructure_data(
  data = diabetes,
  TP = TP,
  FP = FP,
  FN = FN,
  TN = TN,
  threshold = threshold,
  study = study,
  smallest = 2,
  largest = 10
)
init <- initHoyerAFT(res$restructured)
fit <- fitHoyerAFT(res, init)
summary(fit)

Fit Reitsma Model

Description

Fits the Reitsma bivariate random-effects model for diagnostic test accuracy (DTA) meta-analysis using a binomial-normal likelihood via glmmTMB.

Usage

fitReitsma(data, TP, FP, FN, TN, study, constrain = NULL, conflevel = 0.95)

Arguments

Value

A list of class "Reitsma" with components:

• data: the original data set with derived quantities

• glmmTMB: fitted model object.

• estimates: parameter estimates with SE.

• vcov: variance-covariance matrix.

• sensspec: sensitivity and specificity estimates.

• LRDOR: Diagnostic odds ratio and likelihood ratios.

• RutterGatsonis_recovered: Recovered parameters in the Rutter-Gatsonis (HSROC) parameterization.

• constrain: Random effects parameters fixed at zero.

References

Reitsma, J. B., et al. (2005). Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. Journal of Clinical Epidemiology, 58(10), 982–990. doi:10.1016/j.jclinepi.2005.02.022

Rutter, C. M., & Gatsonis, C. A. (2001). A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations. Statistics in Medicine, 20(19), 2865–2884. doi:10.1002/sim.942

Harbord, R. M., Deeks, J. J., Egger, M., Whiting, P., & Sterne, J. A. C. (2007). A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics, 8(2), 239–251. doi:10.1093/biostatistics/kxl004

Examples

data("anticcp")
fit <- fitReitsma(
  data = anticcp,
  TP = TP,
  FP = FP,
  FN = FN,
  TN = TN,
  study = study
)
fit$estimates

Fit Reitsma Subgroup Model

Description

Fits the Reitsma bivariate random-effects model with a single categorical covariate for diagnostic test accuracy (DTA) meta-analysis using a binomial-normal likelihood via glmmTMB. The model is fitted twice, once with dummy/reference cell coding, and once with central-mean parameterization.

Usage

fitReitsmaSubgroup(
  data,
  TP,
  FP,
  FN,
  TN,
  study,
  subgroup,
  constrain = NULL,
  sensspec_constrain = NULL,
  variances = c("common", "unequal"),
  conflevel = 0.95
)

Arguments

Value

A list of class "ReitsmaSubgroup" with components:

• data: the original data set with derived quantities

• glmmTMB_mu: fitted model object with cell means parameterization.

• estimates_mu: parameter estimates with SE with cell means parameterization.

• vcov_mu: variance-covariance matrix with cell means parameterization.

• sensspec: sensitivity and specificity estimates.

• glmmTMB_nu: fitted model object with dummy/reference-cell parameterization

• estimates_nu: parameter estimates with SE with dummy/reference-cell parameterization.

• vcov_nu: variance-covariance matrix with dummy/reference-cell parameterization.

• LRDOR: Diagnostic odds ratios and likelihood ratios.

• RutterGatsonis_recovered: Recovered parameters in the Rutter-Gatsonis (HSROC) parameterization.

• subgroups: The subgroup levels used in the model fit.

• constrain: Random effects parameters fixed at zero.

• variances: Variance structure used in the fitted model.

References

Reitsma, J. B., et al. (2005). Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. Journal of Clinical Epidemiology, 58(10), 982–990. doi:10.1016/j.jclinepi.2005.02.022

Rutter, C. M., & Gatsonis, C. A. (2001). A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations. Statistics in Medicine, 20(19), 2865–2884. doi:10.1002/sim.942

Harbord, R. M., Deeks, J. J., Egger, M., Whiting, P., & Sterne, J. A. C. (2007). A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics, 8(2), 239–251. doi:10.1093/biostatistics/kxl004

Examples

data("anticcp")
fit <- fitReitsmaSubgroup(
  data = anticcp,
  TP = TP,
  FP = FP,
  FN = FN,
  TN = TN,
  study = study,
  subgroup = generation
)
fit
summary(fit)

Fit the Rutter and Gatsonis (HSROC) model

Description

Fits the hierarchical summary receiver operating characteristic (HSROC) model as proposed by Rutter and Gatsonis for meta-analysis of diagnostic test accuracy (DTA) studies using Template Model Builder (TMB).

Usage

fitRutterGatsonis(
  data,
  TP,
  FP,
  FN,
  TN,
  study,
  conflevel = 0.95,
  constrain = NULL,
  spec = NULL,
  verbose = FALSE
)

Arguments

Details

The function internally transforms the data into long format and fits the model via maximum likelihood using TMB. Random effects are included for study-specific accuracy and threshold parameters.

Reitsma parameterization is recovered from the fitted HSROC parameters.

The constrain argument allows simplified HSROC models to be fitted by fixing selected parameters at zero. These constrained models may improve numerical stability in sparse datasets and can be used to reproduce several simplified models presented in the Cochrane Handbook for Diagnostic Test Accuracy Reviews.

Constraints are imposed using parameter mapping within Template Model Builder (TMB), so constrained parameters are excluded from numerical optimization and treated as fixed constants.

Value

An object of class "RutterGatsonis" containing:

data

Processed input data with derived quantities.

fit

Optimization result from nlminb.

sdreport

TMB standard report.

sdreport2

Summary of reported parameters.

sensspec

Estimated sensitivity at given specificity with confidence intervals.

Reitsma_recovered

Recovered parameters in the Reitsma parameterization.

constrain

Parameters fixed at zero.

Note

Requires a compiled TMB model named "RutterGatsonis".

References

Reitsma, J. B., et al. (2005). Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. Journal of Clinical Epidemiology, 58(10), 982–990. doi:10.1016/j.jclinepi.2005.02.022

Rutter, C. M., & Gatsonis, C. A. (2001). A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations. Statistics in Medicine, 20(19), 2865–2884. doi:10.1002/sim.942

Harbord, R. M., Deeks, J. J., Egger, M., Whiting, P., & Sterne, J. A. C. (2007). A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics, 8(2), 239–251. doi:10.1093/biostatistics/kxl004

Examples

data("RF")
fit <- fitRutterGatsonis(
  data = RF,
  TP = TP,
  FP = FP,
  FN = FN,
  TN = TN,
  study = study
)
summary(fit)

Fit the Rutter and Gatsonis Regression Model

Description

Fits a general HSROC meta-regression model using user-supplied design matrices for estimation and prediction.

Usage

fitRutterGatsonisReg(
  data,
  TP,
  FP,
  FN,
  TN,
  study,
  Z,
  Z_pred = NULL,
  map = NULL,
  init = NULL,
  spec = NULL,
  conflevel = 0.95,
  verbose = FALSE
)

Arguments

Details

This function is intended for advanced users who wish to specify design matrices directly. The user is responsible for constructing appropriate design matrices, choosing prediction covariate patterns through Z_pred, and interpreting or visualizing the resulting regression model.

By default, all fixed and random effects are initialized at zero. For difficult optimization problems, user-supplied starting values may be provided through the init argument.

The fitted model estimates covariate effects on the HSROC accuracy, threshold, and optionally shape parameters. Predicted sensitivities are obtained by evaluating the resulting SROC curve(s) at the specificity value(s) supplied through spec and the covariate patterns defined by Z_pred.

Value

An object of class "RutterGatsonisReg" containing:

data

Processed input data with derived quantities.

fit

Optimization result returned by nlminb.

sdreport

TMB standard report object.

sdreport2

Summary of reported model parameters and derived quantities.

sensspec

Estimated sensitivities at the specified specificity value(s), including confidence intervals.

constrain

Constraints on parameters applied during model fitting.

Note

Requires a compiled TMB model named "RutterGatsonisReg".

References

Reitsma, J. B., Glas, A. S., Rutjes, A. W. S., Scholten, R. J. P. M., Bossuyt, P. M., & Zwinderman, A. H. (2005). Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. Journal of Clinical Epidemiology, 58(10), 982–990. doi:10.1016/j.jclinepi.2005.02.022

Rutter, C. M., & Gatsonis, C. A. (2001). A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations. Statistics in Medicine, 20(19), 2865–2884. doi:10.1002/sim.942

Harbord, R. M., Deeks, J. J., Egger, M., Whiting, P., & Sterne, J. A. C. (2007). A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics, 8(2), 239–251. doi:10.1093/biostatistics/kxl004

Examples

data("RF")
RF2        <- RF[RF$method %in% c("LA","ELISA","Nephelometry"),]
RF2$method <- factor(RF2$method,levels=c("LA","ELISA","Nephelometry"))
Z <- model.matrix(~ method, data = RF2)
Z <- Z[rep(seq_len(nrow(Z)), each = 2), , drop = FALSE]
Z_pred <- matrix(c(1,0,0,1,1,0,1,0,1),ncol=3,nrow=3,byrow=TRUE)

fit <- fitRutterGatsonisReg(
  data = RF2,
  TP = TP,
  FP = FP,
  FN = FN,
  TN = TN,
  study = study,
  Z = Z,
  Z_pred = Z_pred
)

summary(fit)

Fit the Rutter and Gatsonis Subgroup Model

Description

The function fits an HSROC model with a single categorical study-level covariate (subgroup).

Usage

fitRutterGatsonisSubgroup(
  data,
  TP,
  FP,
  FN,
  TN,
  study,
  subgroup,
  constrain = NULL,
  spec = NULL,
  conflevel = 0.95,
  verbose = FALSE
)

Arguments

Details

The function fits an HSROC model with a single categorical study-level covariate (subgroup). Separate subgroup effects are estimated for the accuracy and threshold parameters. Optionally, subgroup-specific effects can also be estimated for the shape parameter.

The fitted model returns subgroup-specific summary sensitivity estimates evaluated at user-specified specificity values. If spec = NULL, the median observed specificity is used as a proxy.

This function is intended as a convenient wrapper for subgroup analyses with a single categorical covariate and provides output suitable for dedicated summary(), plot(), and forest() methods.

Value

An object of class "RutterGatsonisSubgroup" containing:

data

Processed input data with derived quantities.

fit

Optimization result from nlminb.

sdreport

TMB standard report.

sdreport2

Summary of reported subgroup-specific parameters.

sensspec

Estimated subgroup-specific sensitivities at the given specificity value(s), with confidence intervals.

subgroups

The subgroup levels used in the model fit.

constrain

Constraints on parameters applied during model fitting.

Note

Requires a compiled TMB model named "RutterGatsonisReg".

References

Reitsma, J. B., et al. (2005). Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. Journal of Clinical Epidemiology, 58(10), 982–990. doi:10.1016/j.jclinepi.2005.02.022

Rutter, C. M., & Gatsonis, C. A. (2001). A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations. Statistics in Medicine, 20(19), 2865–2884. doi:10.1002/sim.942

Harbord, R. M., Deeks, J. J., Egger, M., Whiting, P., & Sterne, J. A. C. (2007). A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics, 8(2), 239–251. doi:10.1093/biostatistics/kxl004

Examples

data("RF")
fit <- fitRutterGatsonisSubgroup(
  data = RF,
  TP = TP,
  FP = FP,
  FN = FN,
  TN = TN,
  study = study,
  subgroup = method
)
summary(fit)

Forest plot generic

Description

Produces coupled forest plots.

Usage

forest(x, ...)

Arguments

Value

No return value. Called for its side effect of producing a plot.

Coupled Forest plot for diagnostic test accuracy meta-analysis

Description

Provides coupled forest plots of sensitivities and specificities with Clopper-Pearson confidence limits.

Usage

## S3 method for class 'Cochrane'
forest(x, conflevel = 0.95, ...)

Arguments

Value

No return value. Called for its side effect of producing a plot.

Coupled Forest plot for diagnostic test accuracy meta-analysis

Description

Provides coupled forest plots of sensitivities and specificities with Clopper-Pearson confidence limits.

Usage

## S3 method for class 'CochraneSubgroup'
forest(x, conflevel = 0.95, subgroup_label = "Subgroup", ...)

Arguments

Value

No return value. Called for its side effect of producing a plot.

Compute Initial Parameter Values for Hoyer AFT Models

Description

Computes initial values for the threshold-based bivariate time-to-event model of Hoyer et al. (2018).

Usage

initHoyerAFT(restructured, dist = "loglogistic")

Arguments

Details

The function fits separate intercept-only parametric survival models for diseased and non-diseased groups using weighted interval-censored likelihoods. It further derives initial estimates of between-study variability based on study-specific weighted averages of log-thresholds.

To ensure compatibility with survival::survreg, interval bounds are modified as follows:

• Left-censored intervals (ctype = 1) are assigned a small positive lower bound.

• Right-censored intervals (ctype = 3) are assigned an infinite upper bound.

Value

A single-row data frame containing initial parameter values:

beta0_init

Intercept for non-diseased group

lambda0_init

Scale parameter for non-diseased group

beta1_init

Intercept for diseased group

lambda1_init

Scale parameter for diseased group

su0_init

Standard deviation of random effects (non-diseased)

su1_init

Standard deviation of random effects (diseased)

coru0u1_init

Correlation between random effects

distcode

Numeric code for the distribution (1 = Weibull, 2 = lognormal, 3 = loglogistic)

References

Hoyer, A., Hirt, S., Kuss, O. (2018). Meta-analysis of full ROC curves using bivariate time-to-event models for interval-censored data. Research Synthesis Methods, 9(1), 62-72. doi:10.1002/jrsm.1273

Examples

data("diabetes")
res <- restructure_data(
  data = diabetes,
  TP = TP,
  FP = FP,
  FN = FN,
  TN = TN,
  threshold = threshold,
  study = study,
  smallest = 2,
  largest = 10
)
init <- initHoyerAFT(res$restructured)

Extract Log-Likelihood from Diagnostic Test Accuracy Models

Description

Returns the maximized log-likelihood for a fitted diagnostic test accuracy meta-analysis model. The returned value is an object of class "logLik" and includes the number of estimated parameters (df) and the number of observations used in model fitting (nobs).

Usage

## S3 method for class 'RutterGatsonis'
logLik(object, ...)

## S3 method for class 'RutterGatsonisSubgroup'
logLik(object, ...)

## S3 method for class 'RutterGatsonisReg'
logLik(object, ...)

## S3 method for class 'HoyerAFT'
logLik(object, ...)

## S3 method for class 'Reitsma'
logLik(object, ...)

## S3 method for class 'ReitsmaSubgroup'
logLik(object, ...)

Arguments

Value

An object of class "logLik".

See Also

anova.dtametaTMB()

Plot Results from a Hoyer Model

Description

Produces a hierarchical summary receiver operating characteristic (HSROC) plot from a fitted Hoyer AFT model. The plot shows study-level sensitivity and specificity estimates together with the meta-analytic HSROC curve derived from the fitted model.

Usage

## S3 method for class 'HoyerAFT'
plot(
  x,
  scale = 0.02,
  size = c("equal", "sampsize", "se"),
  thresholdrange = NULL,
  main = "Diagnostic Test Accuracy Meta-Analysis",
  ...
)

Arguments

Details

The plot includes:

• Study-specific sensitivity and false positive rate estimates

• Rectangular markers representing study observations

• Lines connecting thresholds within studies

• A meta-analytic HSROC curve based on the fitted AFT model

The HSROC curve is constructed using the estimated model parameters and depends on the specified distribution:

• Weibull

• Lognormal

• Loglogistic

The plot is constructed on the ROC scale with sensitivity on the y-axis and specificity on the x-axis (displayed as 1 - false positive rate on a reversed axis).

Value

No return value. Called for its side effect of producing a plot.

See Also

fitHoyerAFT fitHoyer

Plot Results from a Reitsma Model

Description

Produces a summary ROC plot for objects of class "Reitsma" obtained from fitReitsma. The plot displays study-level estimates of sensitivity and specificity, the summary operating point, and corresponding confidence and prediction regions. Optionally, the HSROC (hierarchical summary ROC) curve can be overlaid.

Usage

## S3 method for class 'Reitsma'
plot(
  x,
  scale = 0.02,
  size = c("fisher", "equal", "sampsize", "se"),
  main = "Diagnostic Test Accuracy Meta-Analysis",
  HSROC = FALSE,
  specrange = c(0.7, 0.995),
  conflevel = 0.95,
  predlevel = 0.95,
  ...
)

Arguments

Details

The plot is constructed on the ROC scale with sensitivity on the y-axis and specificity on the x-axis (displayed as 1 - false positive rate on a reversed axis).

Study-specific estimates are shown as rectangles, where the size reflects approximate study weights derived from the Fisher information matrix.

The following elements are displayed:

• Study-level sensitivity and specificity estimates

• Summary (pooled) estimate

• confidence region around the summary point

• prediction region reflecting between-study variability

• Optional HSROC curve (if HSROC = TRUE)

Confidence and prediction regions are derived using the delta method based on the estimated variance-covariance structure of the model.

Value

No return value. Called for its side effect of producing a plot.

References

Freeman, S. C., Kerby, C. R., Patel, A., Cooper, N. J., Quinn, T., & Sutton, A. J. (2019). Development of an interactive web-based tool to conduct and interrogate meta-analysis of diagnostic test accuracy studies: MetaDTA. BMC Medical Research Methodology, 19, 81. doi:10.1186/s12874-019-0724-x

Harbord, R. M., Deeks, J. J., Egger, M., Whiting, P., & Sterne, J. A. C. (2007). A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics, 8(2), 239–251. doi:10.1093/biostatistics/kxl004

Riley, R. D., Ensor, J., Jackson, D., & Burke, D. L. (2018). Deriving percentage study weights in multi-parameter meta-analysis models: with application to meta-regression, network meta-analysis and one-stage individual participant data models. Statistical Methods in Medical Research, 27(10), 2885–2905. doi:10.1177/0962280216688033

See Also

fitReitsma

Plot Results from a Reitsma Subgroup Model

Description

Produces a summary ROC plot for objects of class "ReitsmaSubgroup" obtained from fitReitsmaSubgroup. The plot displays study-level estimates of sensitivity and specificity, the summary operating point, and corresponding confidence and prediction regions. Optionally, the HSROC (hierarchical summary ROC) curve can be overlaid.

Usage

## S3 method for class 'ReitsmaSubgroup'
plot(
  x,
  scale = 0.02,
  size = c("equal", "sampsize", "se"),
  main = "Diagnostic Test Accuracy Meta-Analysis",
  col = NULL,
  nudge_legend = -0.4,
  HSROC = FALSE,
  specrange = c(0.7, 0.995),
  conflevel = 0.95,
  predlevel = 0.95,
  connectstudies = FALSE,
  ...
)

Arguments

Details

The plot is constructed on the ROC scale with sensitivity on the y-axis and specificity on the x-axis (displayed as 1 - false positive rate on a reversed axis).

Study-specific estimates are shown as rectangles, where the size reflects approximate study weights derived from the Fisher information matrix.

The following elements are displayed:

• Study-level sensitivity and specificity estimates

• Summary (pooled) estimate

• confidence region around the summary point

• prediction region reflecting between-study variability

• Optional HSROC curve (if HSROC = TRUE)

Confidence and prediction regions are derived using the delta method based on the estimated variance-covariance structure of the model.

Value

No return value. Called for its side effect of producing a plot.

References

Harbord, R. M., Deeks, J. J., Egger, M., Whiting, P., & Sterne, J. A. C. (2007). A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics, 8(2), 239–251. doi:10.1093/biostatistics/kxl004

See Also

fitReitsmaSubgroup

Plot Results from a Rutter and Gatsonis Model

Description

Produces a summary ROC plot for objects of class "RutterGatsonis" obtained from fitRutterGatsonis. The plot displays study-level estimates of sensitivity and specificity and the HSROC (hierarchical summary ROC).

Usage

## S3 method for class 'RutterGatsonis'
plot(
  x,
  scale = 0.02,
  size = c("equal", "sampsize", "se"),
  specrange = c(0.7, 0.995),
  main = "Diagnostic Test Accuracy Meta-Analysis",
  ...
)

Arguments

Details

The plot is constructed on the ROC scale with sensitivity on the y-axis and specificity on the x-axis (displayed as 1 - false positive rate on a reversed axis).

Study-specific estimates are shown as rectangles.

The following elements are displayed:

• Study-level sensitivity and specificity estimates

• HSROC curve

Value

No return value. Called for its side effect of producing a plot.

References

Freeman, S. C., Kerby, C. R., Patel, A., Cooper, N. J., Quinn, T., & Sutton, A. J. (2019). Development of an interactive web-based tool to conduct and interrogate meta-analysis of diagnostic test accuracy studies: MetaDTA. BMC Medical Research Methodology, 19, 81. doi:10.1186/s12874-019-0724-x

See Also

fitRutterGatsonis

Plot Results from a Rutter and Gatsonis Subgroup Model

Description

Produces summary ROC plots for objects of class "RutterGatsonisSubgroup" obtained from fitRutterGatsonisSubgroup. The plot displays study-level estimates of sensitivity and specificity, stratified by subgroup, together with subgroup-specific HSROC (hierarchical summary ROC) curves.

Usage

## S3 method for class 'RutterGatsonisSubgroup'
plot(
  x,
  scale = 0.02,
  size = c("equal", "sampsize", "se"),
  nudge_legend = -0.4,
  specrange = c(0.7, 0.995),
  col = NULL,
  main = "Diagnostic Test Accuracy Meta-Analysis",
  connectstudies = FALSE,
  ...
)

Arguments

Details

The plot is constructed on the ROC scale with sensitivity on the y-axis and specificity on the x-axis (displayed as 1 - false positive rate on a reversed axis).

Study-specific estimates are shown as rectangles, with subgroup-specific colours.

The following elements are displayed:

• Study-level sensitivity and specificity estimates by subgroup

• Subgroup-specific HSROC curves

• A legend identifying the subgroups

Value

No return value. Called for its side effect of producing a plot.

References

Freeman, S. C., Kerby, C. R., Patel, A., Cooper, N. J., Quinn, T., & Sutton, A. J. (2019). Development of an interactive web-based tool to conduct and interrogate meta-analysis of diagnostic test accuracy studies: MetaDTA. BMC Medical Research Methodology, 19, 81. doi:10.1186/s12874-019-0724-x

See Also

fitRutterGatsonisSubgroup

Print Hoyer AFT Model Object

Description

Displays a concise summary of a fitted Hoyer AFT model, including distribution, number of studies, convergence status, and likelihood-based fit statistics.

Usage

## S3 method for class 'HoyerAFT'
print(x, ...)

Arguments

Value

Invisibly returns the input object.

See Also

summary.HoyerAFT

Print Method for Reitsma Objects

Description

Displays a concise summary of a fitted Reitsma diagnostic test accuracy model, including number of studies, convergence status and likelihood-based fit statistics.

Usage

## S3 method for class 'Reitsma'
print(x, ...)

Arguments

Value

Invisibly returns the input object.

See Also

summary.Reitsma

Print Method for ReitsmaSubgroup Objects

Description

Displays a concise summary of a fitted Reitsma Subgroup diagnostic test accuracy model, including number of studies, convergence status, and likelihood-based fit statistics.

Usage

## S3 method for class 'ReitsmaSubgroup'
print(x, ...)

Arguments

Value

Invisibly returns the input object.

See Also

summary.ReitsmaSubgroup

Print Method for RutterGatsonis Objects

Description

Displays a concise summary of a fitted HSROC model, including number of studies, convergence status, and likelihood-based fit statistics.

Usage

## S3 method for class 'RutterGatsonis'
print(x, ...)

Arguments

Value

Invisibly returns the input object.

See Also

summary.RutterGatsonis

Print Method for RutterGatsonisReg Objects

Description

Displays a concise summary of a fitted HSROC model, including number of studies, convergence status, and likelihood-based fit statistics.

Usage

## S3 method for class 'RutterGatsonisReg'
print(x, ...)

Arguments

Value

Invisibly returns the input object.

See Also

summary.RutterGatsonisReg

Print Method for RutterGatsonisSubgroup Objects

Description

Displays a concise summary of a fitted HSROC model, including number of studies, convergence status, and likelihood-based fit statistics.

Usage

## S3 method for class 'RutterGatsonisSubgroup'
print(x, ...)

Arguments

Value

Invisibly returns the input object.

See Also

summary.RutterGatsonisSubgroup

Construct Interval Data for Threshold-Based Bivariate Time-to-Event Models

Description

Transforms study-level diagnostic test accuracy (DTA) data with multiple thresholds into interval-censored format suitable for likelihood-based modelling (Hoyer et al., 2018).

Usage

restructure_data(
  data,
  TP,
  FP,
  FN,
  TN,
  threshold,
  study,
  smallest,
  largest,
  testdirection = c("greater", "less")
)

Arguments

Details

The function constructs:

• A left-censored interval (below the first threshold)

• Intermediate intervals between adjacent thresholds

• A right-censored interval (above the last threshold)

Event counts are derived from cumulative counts to represent the number of observations falling within each interval for diseased and non-diseased groups. Therefore, input counts must be cumulative over increasing thresholds within each study.

The function first validates that counts are numeric, non-negative integers and that threshold values are positive.

Within each study, total numbers of diseased (n1) and non-diseased (n0) individuals are required to be constant across thresholds. Intermediate interval counts are computed as differences between cumulative counts.

The log-scale midpoint (lcutmean) is provided to support initialization of random effects in subsequent Hoyer AFT models.

For testdirection = "greater", the function assumes that sensitivity decreases and specificity increases with increasing thresholds. For testdirection = "less", the reverse monotonicity is required. Internally, the function standardizes the definition of a positive test result so that it always corresponds to values above the threshold. For testdirection = "less", this is achieved by relabeling the observed counts. This does not affect the resulting sensitivity, specificity, or ROC curve, but ensures compatibility with the model formulation.

Value

A list with two components:

restructured

A data frame with one row per constructed interval containing:

study

Study identifier

TP, TN, n1, n0

Original counts carried forward

threshold

Threshold associated with the interval

lowerB

Lower interval bound (NA for left-censored)

upperB

Upper interval bound (NA for right-censored)

events1

Number of diseased observations in the interval

events0

Number of non-diseased observations in the interval

ctype

Censoring type (1 = left, 2 = interval, 3 = right)

lcutmean

Midpoint of log-thresholds defining the interval

original

The processed original data including (derived) quantities:

n1

Total number of diseased individuals (TP + FN)

n0

Total number of non-diseased individuals (TN + FP)

sens

Sensitivity (TP / n1)

spec

Specificity (TN / n0)

fpr

False positive rate (FP / n0)

testdirection

As specified by testdirection

References

Hoyer, A., Hirt, S., Kuss, O. (2018). Meta-analysis of full ROC curves using bivariate time-to-event models for interval-censored data. Research Synthesis Methods, 9(1), 62-72. doi:10.1002/jrsm.1273

Examples

data("diabetes")
res <- restructure_data(
  data = diabetes,
  TP = TP,
  FP = FP,
  FN = FN,
  TN = TN,
  threshold = threshold,
  study = study,
  smallest = 2,
  largest = 10
)

Schuetz dataset

Description

This is the schuetz data set from Schuetz (2010) from a meta-analyis of non-invasive coronary angiography using computer tomography (CT) versus magnetic resonance imaging (MRI)

Usage

schuetz

Format

A data frame with 108 rows and 7 variables:

test

Which test was used, CT or MRI

study

Study identifier

TP

Number of true positives

FP

Number of false positives

FN

Number of false negatives

TN

Number of true negatives

indirect

whether the comparison is indirect (=1) or direct (=0)

Source

Schuetz, K., et al. (2010). Meta‐analysis: noninvasive coronary angiography using computed tomography versus magnetic resonance imaging. Annals of Internal Medicine, 152(3), 167-177. doi:10.7326/0003-4819-152-3-201002020-00008

Summary Method for HoyerAFT Objects

Description

Extracts and returns the summary information stored in a fitted HoyerAFT model object.

Usage

## S3 method for class 'HoyerAFT'
summary(object, ...)

Arguments

Details

This method is part of the standard S3 summary() generic and provides access to summary statistics computed from the fitted model, as stored in the sdreport2 and sensspec component of the object.

Value

A list with two data frames containing summary statistics derived from the fitted model.

• sdreport2: Parameter estimates with standard errors as returned from TMB reported parameters.

• sensspec: Estimated sensitivity and specificity with confidence intervals at the specified thresholds.

See Also

fitHoyer fitHoyerAFT

Summary Method for Reitsma Objects

Description

Extracts key results from an object of class "Reitsma", including parameter estimates, sensitivity and specificity summaries, and recovered HSROC parameters from the Rutter–Gatsonis parameterization.

Usage

## S3 method for class 'Reitsma'
summary(object, ...)

Arguments

Value

A list with the following components:

• estimates: Parameter estimates with standard errors.

• sensspec: Estimated sensitivity and specificity with confidence intervals.

• RutterGatsonis_recovered: Recovered parameters in the Rutter-Gatsonis (HSROC) parameterization.

See Also

fitReitsma

Summary Method for ReitsmaSubgroup Objects

Description

Extracts key results from an object of class "ReitsmaSubgroup", including parameter estimates, sensitivity and specificity summaries, and recovered HSROC parameters from the Rutter–Gatsonis parameterization.

Usage

## S3 method for class 'ReitsmaSubgroup'
summary(object, ...)

Arguments

Value

A list with the following components:

• estimates: Parameter estimates with standard errors.

• sensspec: Estimated sensitivity and specificity with confidence intervals.

• RutterGatsonis_recovered: Recovered parameters in the Rutter-Gatsonis (HSROC) parameterization.

• subgroups Subgroup names.

See Also

fitReitsmaSubgroup

Summary Method for RutterGatsonis Objects

Description

This method extracts key components from a fitted HSROC model object returned by fitRutterGatsonis. It returns parameter estimates, sensitivity/specificity summaries, and the recovered Reitsma parametrization.

Usage

## S3 method for class 'RutterGatsonis'
summary(object, ...)

Arguments

Details

Provides a concise summary of a fitted "RutterGatsonis" model.

Value

A list containing the following components:

• estimates Parameter estimates with standard errors as returned from TMB reported parameters.

• sensspec Estimated sensitivity at the specified specificity, including confidence intervals.

• Reitsma_recovered Recovered parameters in the Reitsma parameterization.

See Also

fitRutterGatsonis

Summary Method for RutterGatsonisReg Objects

Description

This method extracts key components from a fitted HSROC model object returned by fitRutterGatsonisReg. It returns parameter estimates, sensitivity/specificity summaries.

Usage

## S3 method for class 'RutterGatsonisReg'
summary(object, ...)

Arguments

Details

Provides a concise summary of a fitted "RutterGatsonisReg" model.

Value

A list containing the following components:

• estimates Parameter estimates with standard errors as returned from TMB reported parameters.

• sensspec Estimated sensitivity at the specified specificity, including confidence intervals.

See Also

fitRutterGatsonisReg

Summary Method for RutterGatsonisSubgroup Objects

Description

This method extracts key components from a fitted HSROC model object returned by fitRutterGatsonisSubgroup. It returns parameter estimates and sensitivity/specificity summaries.

Usage

## S3 method for class 'RutterGatsonisSubgroup'
summary(object, ...)

Arguments

Details

Provides a concise summary of a fitted "RutterGatsonisSubgroup" model.

Value

A list containing the following components:

• estimates Parameter estimates with standard errors as returned from TMB reported parameters.

• sensspec Estimated sensitivity at the specified specificity, including confidence intervals.

• Reitsma_recovered Recovered parameters in the Reitsma parameterization.

• subgroups Subgroup names.

See Also

fitRutterGatsonisSubgroup