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midas9(Ben Adarkwa Dwamena)-------------------------------------------------------------------------------

midas9 -- Meta-analytical Integration of Diagnostic Accuracy Studies

Syntax

midas9varlist[ifexp] [inrange] [,id(varname)year(varname)modeling_optionsquality_assessment_optionsreporting_optionsexploratory_graphics_optionspublication_bias_Optionsforest_plot_optionsheterogeneity_optionsroc_optionsprobability_revision_optionsgeneral_graphing_options*]

modeling_optionsmay benip(integer 15)estimator()

quality_assessment_optionsmay bequalitabqualibarqlab

reporting_optionsmay beresults()table()

exploratory_graphics_optionsmay bechiplotbivboxplotcuminf

publication_bias_optionsmay bepubbiasfunnelmaxbias

forest_plot_optionsmay beforest()fordata

heterogeneity_optionsmay begalb()hetforcovars

roc_curve_optionsmay besroc1sroc2rocplane

probability_revision_optionsmay bepddam()faganprior()lrmatrixand

general_graphing_optionsmay beplottype(string)testlab(string)csize(real 36)hsize(integer 6)vsize(integer 8)level(integer 95)mscale(real 0.50)textscale(real 0.85)zcf(real0.5)

by...:may be used with midas9; see help by.

Descriptionmidas9 is a comprehensive program of statistical and graphical routines for undertaking meta-analysis of diagnostic test performance in Stata.

Primary data synthesis is performed within the bivariate mixed-efects binary regression modeling framework. Model specification, estimation and prediction are carried out with gllamm(Rabe-Hesketh et.al) in release 9, by adaptive quadrature.

Using the model estimated coefficients and variance-covariance matrices, midas9 calculates summary operating sensitivity and specificity (with confidence and prediction contours in SROC space), summary likelihood and odds ratios. Global and relevant test performance metric-specific heterogeneity statistics are provided. midas9 facilitates extensive statistical and graphical data synthesis and exploratory analyses of heterogeneity, covariate effects, publication bias and influence.

Bayes' nomograms and likelihood ratio matrices may be obtained and used to guide clinical decision-making.

The minimum required varlist is the data from contingency tables of test results. The user provides the data in a rectangular array containing variables for the 2x2 elements a, b, c, and d:

2x2 +---------------------+ table | Test | +---------+----------+----------+ where: | Truth | Positive | Negative | a = true positives, +---------+----------+----------+ b = false positives, | Case | a | c | c = false negatives, +---------+----------+----------+ d = true negatives. | Noncase | b | d | +---------+----------+----------+

Each data file row contains the 2x2 data for one observation (i.e., study).

id(varname)year(varname), if provided , is concatenated to create a study identification variable. Default uses observation number for id.The varlist MUST contain variables for a, b, c, and d in that order.

Note: midas9 requires release 10 to implement modeling with xtmelogit or Stata version 9 for estimation with gllamm (mainly because of use of paired coordinate arrow graphics not available before release 9);

User should install (if not installed) metan and mylabels for either estimator and also gllamm if using release 9.

+----------+ ----+ Modeling +---------------------------------------------------------

nipspecifies the number of integration points used for maximum likelihood estimation based on adaptive gaussian quadrature. Default is set at 15 formidas9even though the default in xtmelogit is 7. Higher values improve accuracy at the expense of execution times. The only values currently supported by gllamm are 5, 7, 9, 11 and 15 (Rabe-Hesketh & Skrondal 2005}, appendix B.)Using xtmelogit with

nip(1), model will be estimated by Laplacian approximation. This decreases substantially computational time and yet provides reasonably valid fixed effects estimates. It may, however, produce biased estimates of the variance components.

estimator(g|x)provides a choice between estimation with xtmelogit in release 10 versus gllamm in version 9 or earlier.The following options MUST have an estimator inorder to work!

pddam(),fagan,forest(),rocplane,sroc1,sroc2,hetfor,results(),table()andlrmatrix. if estimator is missing, midas9 will issue an error message.+--------------------+ ----+ Quality_Assessment +-----------------------------------------------

qualitabcreates, using optional varlist of study quality items (presence=1, other=0) a table showing frequency of methodologic quality items.

qualibarcreates, combined with optional varlist of study quality items (presence=1, other=0) calculates study-specific quality scores and plots a bargraph of methodologic quality.

qlabmay be combined withqualitaborqualibarto use variable labels for table and bargraph of methodologic items.+-----------+ ----+ Reporting +--------------------------------------------------------

results(all)provides summary statistics for all performance indices, group-specific between-study variances, likelihood rato test statistics and other global homogeneity tests.

results(het)provides group-specific between-study variances, likelihood rato test statistics and other global homogeneity tests.

results(sum)provides summary statistics for all performance indices

table(dss|dlr|dlor)will create a table of study specific performance estimates with measure-specific summary estimates and results of homogeneity (chi_squared) and inconsistency(I_squared) tests.dss,dlrordlorrepresent the paired performance measures sensitivity/specificity, positive/negative likelihood ratios and diagnostic score/odds ratios.+----------------------+ ----+ Exploratory Graphics +---------------------------------------------

bivboximplements a two-dimensional analogue of the boxplot for univariate data similar to the bivariate boxplot (Goldberg and Iglewicz,1992). It is used to assess distributional properties of sensitivity versus specificity and for indentifying possible outliers.

chiplotcreates a chiplot (Fisher & Switzer, 1985, 2001) for judging whether or nor the paired performance indices are independent by augmenting the scatterplot with an auxiliary display. In the case of independence, the points will be concentrated in the central region, in the horizontal band indicated on the plot.

plot(dss|dlor|dlr)plots a normal quantile plot to (a) check the normality assumption (b) investigate whether all studies come from a single population (c) search for publication bias (Wang and Bushman, 1998).

cumproduces a cumulative meta-analysis plot showing how evidence has accumulated over time using metan (most current version must be installed and may be obtained my typing {ssc install metan, replace}). midas9 uses year of publication as measure for temporal evolution of evidence.Results are displayed graphically using

serrbar. The ith line on the plot is the summary produced by a meta-analysis of the first ith trials.

infinvestigates the influence of each individual study on the overall meta-analysis summary estimate. This option presents a serrbar of the results of an influence analysis in which the meta-analysis is reestimated omitting each study in turn, using metan (most current version must be installed).+------------------+ ----+ Publication Bias +-------------------------------------------------

pubbiasWhen this option is invoked, midas9 performs linear regression of log odds ratios on inverse root of effective sample sizes as a test for funnel plot asymmetry in diagnostic metanalyses. A non-zero slope coefficient is suggestive of significant small study bias(pvalue < 0.10).

maxbiasperforms Copas' worst-case sensitivity analysis for publication bias. It calculates the upper bound number of missing studies that will overturn statistical significance and estimates the minimun likely publication probability (Copas and Jackson, 2004).

funnelplots a funnel plot, a two-dimensional graph with sample size on one axis and effect-size estimate on the other axis. The funnel plot capitalizes on the well-known statistical principle that sampling error decreases as sample size increases.In a meta-analysis, the funnel plot can be used to investigate whether all studies come from a single population and to search for publication bias.

+--------------+ ----+ Forest Plots +-----------------------------------------------------

forest(dss|dlr|dlor)creates summary graphs with study-specific(box) and overall(diamond) point estimates and confidence intervals for each performance index pair using graph combine. Confidence intervals lines are allowed to extend between 0 and 1000 beyond which they are truncated and marked by a leading arrow.

fordataadds study-specific performance estimates and 95% CIs to right y-axis.+---------------+ ----+ Heterogeneity +----------------------------------------------------

galb(dss|dlr|dlor)The standardized effect measure (e.g. for lnDOR, lnDOR/precision) is plotted (y-axis) against the inverse of the precision(x-axis). A regression line that goes through the origin is calculated, together with 95% boundaries (starting at +2 and -2 on the y-axis). Studies outside these 95% boundaries may be considered as outliers.

hetforcreates composite forest plot of all performance indices to provide a general view of variability.Confidence intervals lines are allowed to extend between 0 and 1000 beyond which they are truncated and marked by a leading arrow.

covarscombined with an optional varlist permits univariable metaregression analysis of one or multiple covariables.+------------+ ----+ ROC Curves +-------------------------------------------------------

sroc1plots observed datapoints, summary operating sensitivity and specificity in SROC space.

sroc2adds confidence and prediction contours.

rocplaneplots observed data in receiver operating characteristic space (ROC Plane) for visual assessment of threshold effect.+-------------------------------+ ----+ Probability Revision Options +------------------------------------

fagancreates a plot showing the relationship between the prior probability, the likelihood ratio(combination of sensitivity and specificity), and posterior test probability.

prior()combined withfaganallows user to specify a pretest probability overriding the default of using disease prevalence calculated from data whenfaganis invoked alone.

pddam(p|r)produces a line graph of post-test probalities versus prior probabilities between 0 and 1 using summary likelihood ratios

lrmatrixcreates a scatter plot of positive and negative likelihood ratios with combined summary point. Plot is divided into quadrants based on strength-of-evidence thresholds to determine informativeness of measured test.

+------------------+ ----+ Graphing Options +-------------------------------------------------

plottype(string)will add type of plot to title of plot

testlab(string)will add any descriptive string to title of plot

csize()allows user to modify relative sizes of combined forest plots along the x axis.

hsize()allows user to modify size of other plots along the x axis.

vsize()allows user to modify relative sizes of combined forest plots along the y axis.

level()specifies the significance level for statistical tests, confidence contours, prediction contours and confidnce intervals.

mscale()affects size of markers for point estimates on forest plots.

scheme(string)permits choice of scheme for graphs. The default is s2color.

textscale()allows choice of text size for graphs especially regarding labels for forest plots.

zcf()defines a fixed continuity correction to add in the case where a study contains a zero cell. By default, midas9 adds 0.5 to each cell of a study where a zero is encountered for logit and log transformations, only to calculate study-specific likelihood ratios and odds ratios. However, thezcf()option allows the use of other constants between 0 and 1.

Remarks on test performance metrics:Sensitivity and specificity , diagnostic odds ratio and likelihood ratios with 95% confidence intervals, are recalculated for each primary study from the contingency tables of true-positive [a], false-positive [b], false-negative results [c], and true-negative [d].

A four-fold (two by two contingency) table comparing test results for a diagnostic/screening test is identical to a four-fold table comparing outcomes of an experimental application of an intervention (Skupski, Rosenberg and Eglinton, 2002).

For an interventional trial, the true positives are the experimental group with the monitored outcome present [a].The false positives are the control group with the outcome present [b]. The false negatives are the experimental group with the outcome absent [c]. The true negatives are the control group with the outcome absent [d]. The expression for the relative risk in the experimental group {[a/ (a + c)]/ [b/ (b + d)]} is identical to the expression for the likelihood ratio for a positive test in an evaluation of a diagnostic or a screening methodology. Similarly, the expression for the relative risk in the control group in an interventional trial is identical to the expression for the likelihood ratio for a negative test(Skupski, Rosenberg and Eglinton, 2002). The LRs indicate by how much a given test would raise or lower the probability of having disease. In order for diagnostic informativeness to be high, an LR of > 10 or < 0.1 would be required for a positive and negative test result, respectively. Moderate informational value can be achieved with LR values of 5-10 and 0.1-0.2; LRs of 2-5 and 0.2-0.5 have very small informational value.

The diagnostic odds ratio of a test is the ratio of the odds of positivity in disease relative to the odds of positivity in the nondiseased (Glas, Lijmer, Prins, Bonsel and Bossuyt, 2003). The expression for the odds ratio (DOR) is (a × d)/(b × c). The value of a DOR ranges from 0 to infinity, with higher values indicating better discriminatory test performance. A value of 1 means that a test does not discriminate between patients with the disorder and those without it. Values lower than 1 point to improper test interpretation (more negative tests among the diseased). The diagnostic odds ratio (DOR) may be used as a single summary measure with the caveat that the same odds ratio may be obtained with different combinations of sensitivity and specificity (Glas, Lijmer, Prins, Bonsel and Bossuyt, 2003)

The area under the curve (AUROC), obtained by trapezoidal integration, serves as a global measure of test performance. The AUROC is the average TPR over the entire range of FPR values. The following guidelines have been suggested for interpretation of intermediate AUROC values: low (0.5>= AUC <= 0.7), moderate (0.7 >= AUC <= 0.9), or high (0.9 >= AUC <= 1) accuracy (Swets, 1988).

Remarks on Meta-analytic Model:Primarily, midas9 uses an exact binomial rendition (Chu & Cole, 2006) of the bivariate mixed-effects regression model developed by von Houwelingen(von Houwelingen, 1993, 2001) for treatment trial meta-analysis and modified for synthesis of diagnostic test data (Reitsma, 2005; Riley, 2006).

It fits a two-level model, with independent binomial distributions for the true positives and true negatives conditional on the sensitivity and specificity in each study and a bivariate normal model for the logit transforms of sensitivity and specificity between studies.

The standard output of the bivariate model includes: mean logit sensitivity and specificity with their standard errors and 95% confidence intervals; and estimates of the between-study variability in logit sensitivity and specificity and the covariance between them.

Based on these parameters, we can calculate other measures of interest such as the likelihood ratio for positive and negative test results, the diagnostic odds ratio, the correlation between logit sensitivity and specificity, several summary ROC linear regression lines based on either the regression of logit sensitivity on specificity, the regression of logit specificity on sensitivity, or an orthogonal regression line by minimizing the perpendicular distances. These lines can be transformed back to the originalROC scale to obtain a summary ROC curve. Summary sensitivity, specificity, and the corresponding positive likelihood, negative likelihood and diagnostic odds ratios are drived as functions of the estimated model parameters; The derived logit estimates of sensitivity, specificity and respective variances are used to construct a hierarchical summary ROC curve.

Remarks on assessment and exploration of heterogeneity:Heterogeneity means that there is between study variation. Galbraith(radial) plot is used to visually identify outliers. To construct this plot, the standardized lnDOR = lnDOR/se is plotted (y-axis) against the inverse of the se (1/se) (x-axis). A regression line that goes through the origin is calculated, together with 95% boundaries (starting at +2 and -2 on the y-axis). Studies outside these 95% boundaries may be considered as outliers.

Many sources of heterogeneity can occur: characteristics of the study population, variations in the study design (type of design, selection prodedures, sources of information, how the information is collected), different statistical methods, and different covariates adjusted for (if relevant) (Dinnes, 2005). Heterogeneity (or absence of homogeneity) of the results between the studies is assessed graphically by forest plots and statistically using the quantity I2 that describes the percentage of total variation across studies that is attributable to heterogeneity rather than chance (Higgins, 2003).

I2 can be calculated from basic results as I2 = 100% x (Q - df)/Q, where Q is Cochran's heterogeneity statistic and df the degrees of freedom. (Higgins, 2003). Negative values of I2 are made equal to 0 so that I2 lies between 0% and 100%. A value of 0% indicates no observed heterogeneity, and values greater than 50% may be considered substantial heterogeneity. The main advantage of I2 is that it does not inherently depend on the number of the studies in the meta-analysis.

Formal investigation of heterogeneity is performed by multiple univariable bivariate meta-regression models. Covariates are manipulated as mean-centered continuous or as dichotomous (yes=1, no= 0) fixed effects. The effect of each covariate on sensitivity is estimated separately from that on specificity. Metaregression is a collection of statistical procedures (weighted/unweighted linear, logistic regression) to assess heterogeneity, in which the effect size of study is regressed on one or several covariates, with a value defined for each study.

Remarks on Publication bias:Publication bias is produced when the published studies do not represent adequately all the studies carried out on a specific topic (Begg and Berlin). This bias may be caused by factors such as the trend to publish statistically significant (p < 0.05) or clinically relevant (high magnitude albeit non-significant) results. Other variables influencing publication bias (Song, 2002) are sample size (more in small studies), type of design, funding, conflict of interest, prejudice against an observed association, sponsorship.

Publication bias is assessed visually by using a scatter plot (Light and Pillemer, 1984) of the inverse of the square root of the effective sample size (1/ESS1/2) versus the diagnostic log odds ratio(lnDOR) which should have a symmetrical funnel shape when publication bias is absent (Deeks, 2005).

Separate funnel plots for sensitivity and specificity (after logit transformation) are unlikely to be helpful for detecting sample size effects, because sensitivities and specificities will vary due to both variability of threshold between the studies and random variability. Simultaneous interpretation of two related funnel plots and two tests for funnel plot asymmetry also presents challenges. Formal testing for publication bias may be conducted by a regression of lnDOR against 1/ESS1/2, weighting by ESS (Deeks, 2005), with P < .05 for the slope coefficient indicating significant asymmetry.

An alternative graphical test of publication bias may be derived by assessing the linearity of the Normal quantile plot (Wang and Bushman, 1998). This plot compares the quantiles of an observed distribution against the quantiles of the standard Normal distribution. In a meta-analysis, such a plot can be used to check the Normality assumption, investigate whether all studies come from a single population, and search for publication bias (Wang and Bushman, 1998).

Remarks on Cumulative meta-analysis:Cumulative meta-analysis is a type of meta-analysis in which studies are sequentially pooled by adding each time one new study according to an ordered variable. For instance, if the ordered variable is the year of publication, studies will be ordered by it; then, a pooling analysis will be done every time a new article appears. It shows the evolution of the pooled estimate according to the ordered variable. Other common variables used in cumulative meta-analysis are the study quality, the risk of the outcome in the control group, the size of the difference between the groups, and other covariates.

Remarks on Clinical Application:The clinical or patient-relevant utility of diagnostic test is evaluated using the likelihood ratios to calculate post-test probability based on Bayes' theorem as follows (Jaeschke, 1994): Pretest Probability=Prevalence of target condition

Post-test probability= likelihood ratio x pretest probability/[(1-pretest probability) x (1-likelihood ratio)]

Assuming that the study samples are representative of the entire population, an estimate of the pretest probability of target condition is calculated from the global prevalence of this disorder across the studies.

In this way, likelihood ratios are more clinically meaningful than sensitivities or specificities. This approach would be useful for the clinicians who might use the likelihood ratios generated from here to calculate the post-test probabilities of nodal disease based on the prevalence rates of their own practice population.

Thus, this approach permits individualization of diagnostic evidence. This concept is depicted visually with Fagan's nomograms. When Bayes theorem is expressed in terms of log-odds, the posterior log-odds are linear functions of the prior log-odds and the log likelihood ratios.

faganplots an axis on the left with the prior log-odds, an axis in the middle representing the log likelihood ratio and an axis on the right representing the posterior log-odds. Lines are then drawn from the prior probability on the left through the likelihood ratios in the center and extended to the posterior probabilities on the right.The likelihood ratio matrix defines quadrants of informativeness based on established evidence-based thresholds:

Left Upper Quadrant, Likelihood Ratio Positive > 10, Likelihood Ratio Negative <0.1:Exclusion & Confirmation

Right Upper Quadrant, Likelihood Ratio Positive >10, Likelihood Ratio Negative >0.1:Confirmation Only

Left Lower Quadrant, Likelihood Ratio Positive <10, Likelihood Ratio Negative <0.1:Exclusion Only

Right Lower Quadrant, Likelihood Ratio Positive <10, Likelihood Ratio Negative >0.1:No Exclusion or Confirmation

Examples. use http://repec.org/nasug2007/midas9_example_data.dta

Summary Statistics

. midas9 tp fp fn tn, es(g) res(all)(click to run)Table of index-specific results

. midas9 tp fp fn tn, es(g) table(dlr)(click to run)

Summary ROC Curve with prediction and confidence Contours

. midas9 tp fp fn tn, es(g) plot sroc2(click to run)Linear regression test of funnel plot asymmetry

. midas9 tp fp fn tn, pubbias(click to run)Funnel plot assessment of publication and other small study biases

. midas9 tp fp fn tn, fun(click to run)Forest plot to demonstrate variability

. midas9 tp fp fn tn,id(author) year(year) ms(0.75)for(dss) es(g) texts(0.80)(click to run)Forest plot to demonstrate study-specific on right y-axis

.midas9 tp fp fn tn, id(author) year(year)es(g) ms(0.75) ford for(dss) texts(0.80)(click to run)Fagan's plot

.midas9 tp fp fn tn, es(g) fagan prior(0.20)(click to run)Likelihood Matrix

.midas9 tp fp fn tn, es(g) lrmat(click to run)Bivariate Boxplot

.midas9 tp fp fn tn, bivbox scheme(s2color)(click to run)

Quality Assessment

.midas9 tp fp fn tn prodesign ssize30 fulverif testdescrrefdescr subjdescr report brdspect blinded, qualib(click to run)Meta-regression

.midas9 tp fp fn tn prodesign ssize30 fulverif testdescrrefdescr subjdescr report brdspect blinded, es(g) covars(click to run)

Saved results

midas9saves the following inr():

Scalars

r(fsens)fixed effects estimate of summary sensitivityr(fspec)fixed effects estimate of summary specificityr(flrn)fixed effects estimate of summary likelihood ratio of a negative testr(flrp)fixed effects estimate of summary likelihood ratio of a positive testr(fdor)fixed effects estimate of summary diagnostic odds ratior(fldor)fixed effects estimate of summary diagnostic score

r(mtpr)mixed effects estimate of summary sensitivityr(mtprse)standard error of mixed effects estimate of summary sensitivityr(mtprlo)lower bound of mixed effects estimate of summary sensitivityr(mtprhi)upper bound of mixed effects estimate of summary sensitivity

r(mtnr)mixed effects estimate of summary specificityr(mtnrse)standard error of mixed effects estimate of summary specificityr(mtnrlo)lower bound of mixed effects estimate of summary specificityr(mtnrhi)upper bound of mixed effects estimate of summary specificity

r(mlrp)mixed effects estimate of summary likelihood ratio of a positive test resultr(mlrpse)standard error of mixed effects estimate of summary likelihood ratio of a positive test resultr(mlrplo)lower bound of mixed effects estimate of summary likelihood ratio of a positive test resultr(mlrphi)upper bound of mixed effects estimate of summary likelihood ratio of a positive test result

r(mlrn)mixed effects estimate of summary likelihood ratio of a negative test resultr(mlrnse)standard error of summary likelihood ratio of a negative test resultr(mlrnlo)lower bound of summary likelihood ratio of a negative test resultr(mlrnhi)mixed effects estimate of summary likelihood ratio of a negative test result

r(mdor)mixed effects estimate of summary diagnostic odds ratior(mdorse)standard error of summary diagnostic odds ratior(mdorlo)lower bound of summary diagnostic odds ratior(mdorhi)upper bound of summary diagnostic odds ratio

r(mldor)mixed effects estimate of summary diagnostic scorer(mldorse)standard error of summary diagnostic scorer(mldorlo)lower bound of summary diagnostic scorer(mldorhi)upper bound of summary diagnostic score

r(AUC)Area under summary ROC curver(AUClo)lower bound of area under summary ROC curver(AUChi)upper bound of area under summary ROC curve

r(covar)covariance of logits of sensitivity and specificity

r(rho)correlation between logits of sensitivity and specificityr(rholo)lower bound of correlationr(rhohi)upper bound of correlationr(reffs1)variance of logit of sensitivityr(reffs1se)standard error of variance of logit of sensitivityr(reffs1lo)lower bound variance of logit of sensitivityr(reffs1hi)upper bound variance of logit of sensitivityr(reffs2)variance of logit of specificityr(reffs2se)standard error of variance of logit of specificityr(reffs2lo)lower bound variance of logit of specificityr(reffs2hi)upper bound variance of logit of specificity

r(Islrt)global inconsistency index from likelihood ratio restr(Islrtlo)lower bound global inconsistency indexr(Islrthi)upper bound global inconsistency index

ReferencesBegg C.B. and Berlin J.A. Publication bias: a problem in interpreting medical data. J R Stat Soc A 151 (1988), pp. 419-463.

Chu H, Cole SR (2006). Bivariate meta-analysis of sensitivity and specificity with sparse data: a generalized linear mixed model approach. Journal of Clinical Epidemiology 59:1331-1332.

Copas J, Jackson D.(2004) A bound for publication bias based on the fraction of unpublished studies. Biometrics 60:146-153

Deeks JJ. Macaskill P and Irwig Les. The performance of tests of publication bias and other sample size effects in systematic reviews of diagnostic test accuracy was assessed. Journal of Clinical Epidemiology, Volume 58, Issue 9, September 2005, Pages 882-893.

Dinnes J, Deeks J, Kirby J, Roderick P. A methodological review of how heterogeneity has been examined in systematic reviews of diagnostic test accuracy. Health Technol Assess 2005;9(12)

Fisher NI, Switzer P (1985) Chi-plots for assessing dependence. Biometrika 72, 253-265.

Fisher NI, Switzer P (2001) Graphical assessment of dependence: Is a picture worth 100 tests? American Statistician 55, 233-239.

Glas AS, Lijmer JG, Prins MH, Bonsel GJ, Bossuyt PMM (2003) The diagnostic odds ratio: a single indicator of test performance. Journal of Clinical Epidemiology, Volume 56, Issue 11, November, Pages 1129-1135.

Harbord RM, Deeks JJ, Egger M, Whiting P, Sterne JA (2006). A unification of models for meta-analysis of diagnostic accuracy studies.

Biostatistics(online advance access).Higgins JP, Thompson SG, Deeks JJ, Altman DG. Measuring inconsistency in meta-analyses [review]. BMJ 2003;327:557-60).

Jaeschke R, Guyatt GH, Sackett DL. Users' guides to the medical literature. III. How to use an article about a diagnostic test. B. What are the results and will they help me in caring for my patients? The Evidence-Based Medicine Working Group. JAMA 1994;271:703-7.

Lau J, Schmid CH and Chalmers TC. Cumulative meta-analysis of clinical trials builds evidence for exemplary medical care. Journal of Clinical Epidemiology, Volume 48, Issue 1, January 1995, Pages 45-57 )

Light R.J.and Pillemer D.B.. Summing up: the science of reviewing research. Harvard University Press, Cambridge, MA (1984)

Rabe-Hesketh S, Skrondal A (2005).

Multilevel and LongitudinalModeling Using Stata.College Station, TX: Stata Press.Rabe-Hesketh S, Skrondal A, Pickles A (2004). GLLAMM Manual.

U.C.Berkeley Division of Biostatistics Working Paper Series.Working Paper 160.Reitsma JB, Glas AS, Rutjes AWS, Scholten RJPM, Bossuyt PM, Zwinderman AH . Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews.

Journalof Clinical Epidemiology(2005) 58:982-990.Riley RD, Abrams KR, Sutton AJ, Lambert P, Thompson JR (2005). The benefits and limitations of multivariate meta-analysis, with application to diagnostic and prognostic studies. University of Leicester Medical Statistics Group Technical Report Series. Technical Report 05-04.

Rutter CM, Gatsonis CA (2001). A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations.

Statistics inMedicine20:2865-2884.Skupski DW, Rosenberg CR, Eglinton GS (2002) Intrapartum Fetal Stimulation Tests: A Meta-Analysis. Obstet. Gynecol. 99: 129 - 134.

Song F, Khan K, Dinnes J. and Sutton A.J. Asymmetric funnel plots and publication bias in meta-analyses of diagnostic accuracy. Int J Epidemiol 31 (2002), pp. 88-95

StataCorp. 2007. Stata Statistical Software: Release 10 College station, TX: StataCorp LP.

Swets JA. Measuring the accuracy of diagnostic systems. Science. 1988;240:1285-1293.

van Houwelingen H.C. , Arends L.R. and Stijnen T. Advanced methods in meta-analysis: multivariate approach and meta-regression, Stat Med 21 (2002) (4), pp. 589-624.

van Houwelingen H.C., Zwinderman K.H. and Stijnen T. A bivariate approach to meta-analysis, Stat Med 12 (1993) (24), pp. 2273-2284

Wang, MC Bushman BJ using the normal quantile plot to explore meta-analytic data sets. Psychological methods (1998) 3;46-54

AuthorBen A. Dwamena, Division of Nuclear Medicine, Department of Radiology, University of Michigan, USA Email bdwamena@umich.edu for problems, comments and suggestions

CitationUsers should please reference program in any published work as: Dwamena, Ben A.(2007)

midas9: Computational and Graphical Routinesfor Meta-analytical Integration of Diagnostic Accuracy Studies inStata.Division of Nuclear Medicine, Department of Radiology, University of Michigan Medical School, Ann Arbor, Michigan.

AcknowledgementThanks to

-Roberto Gutierrez and the Stata Development team for xtmelogit and all that Stata offers....

-Richard Sylvester and Ruth Carlos for encouragement, suggestions and testing of midas9

-Richard Riley for trusting me with pre-prints of his work on bivariate meta-analysis.

-Joseph Coveney for posting syntax for the bivariate model using gllamm on Statalist.

-Sophia-Rabe-Hesketh and other authors of gllamm for their work.

-Derek Wenger for assistance with coding Fagan's plot.

-Nick Cox for his polarsm which was adapted for

bivboxoption in midas9 and for mylabels.-Roger Harbord for his metareg, metafunnel and metamodbias programs which provided very useful ideas for midas9.

-Mike Bradburn ( and R Harris) for metan which was used to implement cumulative and influence meta-analyses in midas9.

Also seeOn-line: help for metan (if installed), gllamm (if installed), mylabels (if installed)