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From |
Roger Harbord <[email protected]> |

To |
[email protected] |

Subject |
Re: st: Hierarchical ordinal logistic regression model for diagnosticmeta-analysis using gllamm |

Date |
Sun, 05 Dec 2004 16:52:08 -0000 |

Hi Ben,

Unfortunately this "HSROC" model can't be fitted in -gllamm- due to the nonlinear nature of the "exp(betai*disij)" term. We checked this with one of the authors of -gllamm-. WinBUGS and the NLMIXED procedure in SAS appear to be the only ways to fit this model at present.

Best wishes,

Roger.

--On 02 December 2004 12:26 -0500 Ben Dwamena <[email protected]> wrote:

Described below is a multilevel model basd on ordinal regression for diagnostic meta-analysis (SROC) for which codes are available for SAS and WinBUGS and wanted to now how this may be modeled using gllamm? I know how to model the expression logit n=thetai+alphai*disij However, I am not sure how to include the scale parameter so that the above is multiplied by exp(betai*disij ) . HSROC MODEL LEVEL 1 For each study (i), the number testing positive is assumed to follow a binomial distribution yij ~B(nij,, alphaij) where j=1 represents diseased group; j=2 represents non-diseased group; nij represents the number in group; nij represents the probability of a positive test result in group j The model is based on the ordinal logistic regression proposed by McCullagh and takes the form: logit (nij) =(thetai+alphai*disij)* exp(-beta*disij) where disij represents the "true" disease status (coded as -0.5 for the non-diseased and 0.5 for the diseased). thetai (threshold parameter) and alphaI (accuracy measure) are modeled as random effects while beta(modeling dependence of accuracy on threshold) is a fixed effect. When beta= 0, the model reduces to a logistic regression model and thetai is estimated by (logit(tpri) + logit(fpri))/2 ( = Si/2) alphai is estimated by logit (tpri) -logit (fpri) ( = Di) Study level covariates may be added to explore associations with threshold and/or accuracy and/or SROC shape LEVEL 2 The random effects are assumed to be independent and normally distributed: thetai ~ N(omega, tau-squared ); alphai ~ N(lamda, tau-squared ) The SROC curve is computed using E (tpr) = invlogit [logit (fpr) exp (- beta+ lamda* exp (-0.5 lamda] for chosen values of fpr When beta= 0, theta provides a global estimate of the expected test accuracy (lnDOR) and the resulting SROC is symmetric. The expected tpr is given by 1/[1+exp(-(omega+0.5*lamda)*exp(- 0.5*beta))] The expected fpr is given by 1/[1+exp(-(omega-0.5*lamda)*exp(- 0.5*beta))] How may this be modeled using gllamm? I know how to model the expression logit n=thetai+alphai*disij However, I am not sure how to include the scale parameter so thatthe above is multiplied by exp(betai*disij ) . Thanks Ben Dwamena

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