fit.bivar: Fit the Bivariate Model of Reitsma et al. (2005)

In Metatron: Meta-analysis for Classification Data and Correction to Imperfect Reference

Description

The function fits the bivariate model of Reitsma et al. (2005) by directly modeling the binomial error and normally distributed random effect structure. We specify the model as a generalized linear mixed model using the glmer function in package lme4, similar to the computational approach by Macaskill (2004) and Harbord et al. (2007). Thus the normal-normal approximation and the MCMC approach can be avoided. A single covariate can be incorporated into the model, users should choose if it affects both the sensitivity and specificity, only sensitivity or only specificity. Results are nearly identical to those by using the Proc NLMIXED in SAS.

Usage

fit.bivar(TP,FN,TN,FP,study,data,mods=NULL,covarying="both",...)

## S3 method for class 'fit.bivar'
print(x,...)
## S3 method for class 'fit.bivar'
summary(object,level=0.95,...)

Arguments

TP	the true positive counts reported in primary studies. Vector of integers, need to be speficied either directly or by referring to a variable in data frame.
FN	the false negative counts reported in primary studies. Vector of integers, need to be speficied either directly or by referring to a variable in data frame.
TN	the true negative counts reported in primary studies. Vector of integers, need to be speficied either directly or by referring to a variable in data frame.
FP	the false positive counts reported in primary studies. Vector of integers, need to be speficied either directly or by referring to a variable in data frame.
study	study names or identities. Vector of characters, need to be speficied either directly or by referring to a variable in data frame.
data	optional data frame that contains the above-mentioned variables and possibly other information such as the covariate.
mods	optional argument to include a single study-level covariate in the model.Vector specifying the values of the covariate. Default is NULL.
covarying	options to specify the influence of the covariate when it's present, one of the character strings "both", "only sensitivity", "only specificity" can be selected. Default is "both".
x	an object of class "fit.bivar" (for print).
object	an object of class "fit.bivar" (for summary).
level	confidence interval level (for summary). Default is 0.95
...	further arguments to be passed to or from other functions

Details

To specify the data, either directly input the TP, FN, FP, TN and study as vectors, or referring the corresponding variable names in a data frame. The argument study gives the study names, which means if there are several classification procedures within a study, they must have the same value at this argument, but different values in covariate to distiguish them. To specify the model, one should assign proper values to the mods and covarying arguments.

Value

An object of class fit.bivar,basically a list with the model speficication and conventional model fit results, such as goodness of fit statistics and parameter estimates, etc.

The print functions displays the basic model fit outcomes, including the estimates of the combined logit-transformed sensitivity and specificity, as well as those at different levels of the covariate if there is any; the random effects coefficients shown as variance-covariance matrix of the combined logit-transformed sensitivity and specificity; and the goodness of fit statistics are also given. The print function returns no object.

The summary function shows additional information such as standard errors and covariance matrix of the parameters which can be useful later in drawing the SROC curve.

Author(s)

Huiling Huang <[e-mail]>

References

Macaskill, P. (2004). Empirical Bayes estimates generated in a hierarchical summary ROC analysis agreed closely with those of a full Bayesian analysis. Journal of Clinical Epidemiology, 57, 925-32.

Harbord, R., Deeks, J., Egger, M., Whiting, P., & Sterne, J. (2007). A unification of models for meta-analysis of diagnostic accuracy studies. Biostatistics, 8, 239-251

Reitsma, J., Glas, A., Rutjes, A., Scholten, R., Bossuyt, P., & Zwinderman, A. (2005). Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. Journal of Clinical Epidemiology, 58, 982-990.

See Also

lmer.

Examples

## fit bivariate model without covariate to data from a review(Nishimura 2007) 
 data(ccp)
(ccp.without<-fit.bivar(TP=TP,FN=FN,TN=TN,FP=FP,study=study_id,data=ccp))
summary(ccp.without)
## fit bivariate model with covariate "generation" to the same data set.
(ccp.generation<-fit.bivar(TP=TP,FN=FN,TN=TN,FP=FP,study=study_id,data=ccp,mods=generation,
                           covarying="both"))
summary(ccp.generation)
##fit bivariate model with covariate "Test" to the data from Schuetz(2010) 
##comparing the accuracy of CI and MRI
data(Schuetz)
(CTvsMRI<-fit.bivar(TP=tp,FN=fn,TN=tn,FP=fp,study=Study_ID,data=Schuetz,mods=Test))
 summary(CTvsMRI)

Example output

Loading required package: lme4
Loading required package: Matrix
Loading required package: mpt
Fit bivariate model of Reitsma et al.(2005) without covariate.

Fixed-effects coefficients:
logit_sensitivity  logit_specificity  
           0.6534             3.1084  


Random-effects coefficients which model the between-study variability,shown as variance-covariance matrix:
                  logit_sensitivity logit_specificity
logit_sensitivity         0.5426024        -0.2702605
logit_specificity        -0.2702605         0.5712106


37 studies 37 classifications 2 fixed and 3 random-effects parameters
   logLik        AIC        BIC  
-272.7808   555.5616   567.0819  

Fit bivariate model of Reitsma et al.(2005) without covariate.
Fixed-effects coefficients:
                  coefficient standard error df      tval            p alpha
logit_sensitivity   0.6533936      0.1274434 35  5.126931 1.092908e-05  0.05
logit_specificity   3.1084075      0.1451168 35 21.420042 0.000000e+00  0.05
                      lower     upper
logit_sensitivity 0.3946697 0.9121174
logit_specificity 2.8138048 3.4030102


Covariance Matrix of Fixed Effect Parameter Estimates: 
2 x 2 Matrix of class "dpoMatrix"
                  logit_sensitivity logit_specificity
logit_sensitivity       0.016241824      -0.007404198
logit_specificity      -0.007404198       0.021058878

Fit bivariate model of Reitsma et al.(2005) with covariate generation that affects both sensitivity and specificity.

Fixed-effects coefficients:
logit_sensitivity_CCP1  logit_sensitivity_CCP2  logit_specificity_CCP1  
               -0.0965                  0.8660                  3.4462  
logit_specificity_CCP2  
                3.0159  


Random-effects coefficients which model the between-study variability,shown as variance-covariance matrix:
                  logit_sensitivity logit_specificity
logit_sensitivity         0.3598267        -0.1966862
logit_specificity        -0.1966862         0.5394822


37 studies 37 classifications 4 fixed and 3 random-effects parameters
   logLik        AIC        BIC  
-266.6856   547.3713   563.4997  

Fit bivariate model of Reitsma et al.(2005) with covariate generation that affects both sensitivity and specificity.
Fixed-effects coefficients:
                       coefficient standard error df       tval            p
logit_sensitivity_CCP1 -0.09654114      0.2203169 35 -0.4381921 6.639398e-01
logit_sensitivity_CCP2  0.86603985      0.1208330 35  7.1672452 2.327272e-08
logit_specificity_CCP1  3.44619692      0.2968664 35 11.6085771 1.489919e-13
logit_specificity_CCP2  3.01588430      0.1613690 35 18.6893604 0.000000e+00
                       alpha      lower    upper
logit_sensitivity_CCP1  0.05 -0.5438083 0.350726
logit_sensitivity_CCP2  0.05  0.6207358 1.111344
logit_specificity_CCP1  0.05  2.8435260 4.048868
logit_specificity_CCP2  0.05  2.6882877 3.343481


Covariance Matrix of Fixed Effect Parameter Estimates: 
4 x 4 Matrix of class "dpoMatrix"
                       logit_sensitivity_CCP1 logit_sensitivity_CCP2
logit_sensitivity_CCP1           4.853956e-02          -9.776551e-06
logit_sensitivity_CCP2          -9.776551e-06           1.460062e-02
logit_specificity_CCP1          -2.461559e-02          -7.155984e-06
logit_specificity_CCP2           8.898482e-06          -6.952524e-03
                       logit_specificity_CCP1 logit_specificity_CCP2
logit_sensitivity_CCP1          -2.461559e-02           8.898482e-06
logit_sensitivity_CCP2          -7.155984e-06          -6.952524e-03
logit_specificity_CCP1           8.812968e-02           5.604273e-04
logit_specificity_CCP2           5.604273e-04           2.603997e-02

Fit bivariate model of Reitsma et al.(2005) with covariate Test that affects both sensitivity and specificity.

Fixed-effects coefficients:
 logit_sensitivity_CT  logit_sensitivity_MRI   logit_specificity_CT  
               3.4804                 2.1771                 1.9169  
logit_specificity_MRI  
               0.8754  


Random-effects coefficients which model the between-study variability,shown as variance-covariance matrix:
                  logit_sensitivity logit_specificity
logit_sensitivity         0.8748607         0.1803049
logit_specificity         0.1803049         0.8446928


103 studies 108 classifications 4 fixed and 3 random-effects parameters
   logLik        AIC        BIC  
-476.5047   967.0095   990.6364  

Fit bivariate model of Reitsma et al.(2005) with covariate Test that affects both sensitivity and specificity.
Fixed-effects coefficients:
                      coefficient standard error  df      tval            p
logit_sensitivity_CT    3.4804035      0.1550089 101 22.452930 0.000000e+00
logit_sensitivity_MRI   2.1770678      0.2457187 101  8.860000 2.886580e-14
logit_specificity_CT    1.9168802      0.1171949 101 16.356351 0.000000e+00
logit_specificity_MRI   0.8754023      0.2111183 101  4.146501 7.040015e-05
                      alpha     lower    upper
logit_sensitivity_CT   0.05 3.1729076 3.787899
logit_sensitivity_MRI  0.05 1.6896280 2.664508
logit_specificity_CT   0.05 1.6843971 2.149363
logit_specificity_MRI  0.05 0.4566004 1.294204


Covariance Matrix of Fixed Effect Parameter Estimates: 
4 x 4 Matrix of class "dpoMatrix"
                      logit_sensitivity_CT logit_sensitivity_MRI
logit_sensitivity_CT           0.024027753           0.007757793
logit_sensitivity_MRI          0.007757793           0.060377688
logit_specificity_CT           0.001916311           0.001196564
logit_specificity_MRI          0.001482075           0.005241366
                      logit_specificity_CT logit_specificity_MRI
logit_sensitivity_CT           0.001916311           0.001482075
logit_sensitivity_MRI          0.001196564           0.005241366
logit_specificity_CT           0.013734634           0.005964241
logit_specificity_MRI          0.005964241           0.044570938

Metatron documentation built on May 1, 2019, 10:20 p.m.