基于分段函數(shù)的劑量—反應模型的參數(shù)估計和模型選擇.pdf

1、東北師范大學碩士學位論文基于分段函數(shù)的劑量—反應模型的參數(shù)估計和模型選擇姓名：朱小巖申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：陶劍20050501AbstractHormesisisthatdecreasedriskofadverseeffectswouldOccurwithinereaseddoselevelswhensubjectsareexposedtotoxinatlowlevelsThisimpliestheexist

2、enceofathresholdlevel，ashormesis，ifexists，wouldexistbelowthislevelBelowthethresholddoselevel，noadverseeventsabovetheresponseatthecontrollevelwhichiscalledthebackgroundresponseoccur，thenbackgroundresponsealsooccursattheth

3、resholdlevelInordertodescribethisphenomenonwecharacterizetheoveratldose—responserelationshipwithapiecewisefunctionthatconsistsofaquadraticcurvewhichisassumedtobeU—shapecurveandanotherquadraticcurveathighdoselevelsHereweu

4、sefinitemixturenormalmodelsbecausetheexperimentalsubjectsmayhavedifferentresponseslike“moresusceptible1esssusceptible”afteratoxicantexperimentwefirstusetheEMalgorithmtoobtaintheestimatesoftheparametersinthemixturenormalm

5、odels，andthendiscussthemodelselectionproblemsusingBayesfactm‘methodandBootstrapconfidenceintervalmethod，weadopttheroughbutsimplepercentilemethodforBootstrapconfidenceintervalwestudythefollowingthreemodelselectionproblems

6、：first，themodelwechooseisthemixturemodelsorthesingle—componentmodel；secondtheoveralldose—responsefunctionwechooseisapiecewisefunctionornot；1astifwechoosethepiecewisedoseresponsefunction；howtodeterminethecutpointwhichisal

7、socalledthethresholdlevelTheresultsofthesimulationswillindicatethatthemixturemodelsaresignificantlybetterthanthesingle—componentpopulationforthedevelopmentaltoxicitystudies，thepiecewisedose—responsefunctionissignificantl

8、ybetterthanthecurrentdose—responsefunctionwhichisnaivelyassumedstrictlyincreasingovertherangeoftoxicdosesforthehormesis，thesuitablethresholdlevelcanimprovethedose—responsemodel’sabilitytofitthehormeticdataKeywords：hormes