an application to HRQoL

Transcription

1 AlmaMate Studoum Unvesty of Bologna A flexle IRT Model fo health questonnae: an applcaton to HRQoL Seena Boccol Gula Cavn Depatment of Statstcal Scence, Unvesty of Bologna 9 th Intenatonal Confeence on Computatonal Statstcs Pas August 22 27, 200

2 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Statement of the polem

3 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn What you NEED What you NEED

4 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn What you HAVE

5 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn A flexle IRT Model s c s + + c = q contnuous tems dchotomous tems odeed polytomous tems total nume of tems Lettng w wth =... e the answe of suect to the contnuous tem v wth = s e the answe of suect to the dchotomous tem t wth = + s s + c e the answe of suect to the odeed polytomous tem

6 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Assumptons and constans Items ae ndependent condtonally on SN α, β, δ =... n Azzaln, 985 E=0 and Va= SKEWNORMAL CENTERED PARAMETERIZED SN cp Gven Z ~ SN0,,δ / 2 2 Z δ π = ~ SNcp0,, δ 2 2 δ π Z theta[] sample: δ = 0,

7 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn A flexle IRT model The condtonal ont densty functon gy of the oseved vaales s q y w v = t = = + s + s + c g y = g y = h w k v l t whee = + = + s+ h. s the Nomal densty functon of mean and vaance σ 2 k. s the Benoull poalty functon of paamete μ = and.=logt lnk l. s the Multnomal poalty functon of paametes PCM and

8 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Patal Cedt Model Mastes, 982 The poalty of suect scong x to tem tem wth k + levels of answe, gven the latent vaale s exp x t t = p x =, fo x =... k k + exp k = t = t k p x =, fo x = k k + exp t k = t= 0

9 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn A flexle IRT model The log lkelhood fo a andom sample of n ndvduals can e expessed as log L = n n + = log f y = log g y = h d whee h s now the Skew Nomal dstuton t functon of mean 0 and vaance.

10 Bayesan estmaton of the paametes A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Jont Posteo dstuton of the paametes of the Bayesan estmaton of the paametes p model, δ δ σ q c s s h h g v g h w g p t y,,, δ δ σ = + + = + = = s h h g v g h w g t whee ~ SN cp 0,,δ p ~ N0,00 σ ~ nvgamma0,0 = δ ~U,

11 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Bayesan estmaton of the paametes Bayesan paamete estmates wee otaned usng Gs samplng algothms as mplemented n the compute pogam WnBUGS.4 Spegelhalte, Thomas, Best, & Lunn, The value taken as the MCMC estmate s the mean ove teatons sampled statng wth the fst teaton followng un n. The R Package CODA Best, Cowles, & Vnes, 995 was used to compute convegence Geweke s dagnostc.

12 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Results Model : Patal Cedt Model 0,000 teatons wth the fst 3,000 as un n Model 2: IRT model fo mxed esponses 25,000 teatons t wth the fst 0, as un n Model 3: IRT fo mxed esponses and skew latent vaale 5,000 teatons wth the fst 5,000 as un n

13 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Results Model Model 2 Model 3 Posteo mean SD MC eo Medan Posteo mean SD MC eo Medan Posteo mean SD MC eo Medan HRQol [43] VAS= [] VAS= [6] VAS= [29] 322 VAS= Model DIC PCM 8. 2 PCM + VAS PCM + VAS + skewed nomal latent vaale a po 29.8

14 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Results eta[2] eta[2] lag vas a teaton teaton vas The pocedue had a un length of 5,000 teatons wth a un n peod of 8,000 teatons. Evey thee states of the chan wee ncluded n the posteo estmates, to avod autocoelaton. a lag lag

15 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Results theta[] teaton theta[6] teaton theta[29] teaton theta[43] teaton theta[] theta[6] lag theta[29] lag theta[43] lag lag

16 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Results The HRQoL mean value s 6 s.d The maxmum value s.065 and the mnmum s 4.25 The ght skewed shape of the hstogam s expected, as well as the mean centeed on 0.

17 A flexle IRT Model fo health questonnae: an applcaton to HRQoL S. Boccol & G. Cavn Some lmts Long computatonal tmes Not use fendly softwae Futhe developments Genealzed Patal Cedt model Covaates

18 Refeences Azzaln, A A class of dstutons whch ncludes the nomal ones. Scand. J. Statst., 2:7 78. Azzaln, A Futhe esults on a class of dstutons whch ncludes the nomal ones. Statstca, 46: Bazan, J., Banco, M., & Bolfane, H A Skew Item Response Model. Bayesan Analyss, 4: Emetson, S., & Rese, S Item esponse theoy fo psychologsts. Mahwah, NJ: Elaum. Gelman, A., Caln, J. B., Stem, H. S., & Run, D. B Bayesan data analyss. New Yok: Chapman and Hall. Maste, G A Rasch model fo patal cedt scong. Psychometka, 47: Moustak, I A latent tat and a latent class model fo mxed oseved vaales. l Bh Btsh ounal of mathematcal and statstcal psychology, 49 2, Moustak, I., & Knott, M Genealzed latent tat model. Psychometka, 653, 39 4.