A Survival-Adjusted Quantal-Response Test for Analysis of Tumor Incidence Rates in Animal Carcinogenicity Studies

Transcription

1 Reearch Survval-duted Quantal-Repone Tet for naly of Tumor Incdence Rate n nmal Carcnogencty Stude Shyamal D. Peddada and Grace E. lng otattc ranch Natonal Inttute of Envronmental Health Scence Natonal Inttute of Health Department of Health and Human Servce Reearch Trangle Park North Carolna US In rodent cancer boaay group of anmal are expoed to dfferent doe of a chemcal of nteret and followed for tumor occurrence. The reultng tumor rate are commonly analyzed ung a urvval-aduted Cochran-rmtage (C) trend tet. The C trend tet ha reaonable power when the tumor-repone curve lnear n doe but t may be underpowered for a nonlnear repone. n alternatve urvval-aduted tet procedure baed on otonc regreon methodology ha prevouly been propoed. lthough th alternatve procedure perform well when the tumor repone nonlnear n doe t ha le power than the C trend tet when the repone lnear n doe. Here we ntroduce a new urvval-aduted tet procedure that make ue of both the C trend tet and the otonc regreon-baed trend tet. Ung a broad range of expermental condton typcal of Natonal Toxcology Program (NTP) boaay we conducted extenve computer mulaton to compare the fale-potve error rate and power of the propoed procedure wth the urvval-aduted C trend tet. The new procedure compete well wth the urvval-aduted C trend tet when oberved tumor rate are lnear n doe and perform ubtantally better when oberved tumor rate are nonlnear n doe. Further the propoed trend tet almot alway ha a maller fale-potve rate than doe the urvval-aduted C trend tet. We alo developed an order-retrcted nference-baed procedure for performng multple parwe comparon between each of the doe group and the control group. The trend tet and the multple parwe comparon tet are demontrated ung an example from a tudy conducted by the NTP. ey word: cancer boaay Cochran-rmtage trend tet multple parwe comparon Natonal Toxcology Program order-retrcted nference poly-3 trend tet. Envron Health Perpect 4: (006). do:0.89/ehp.8590 avalable va [Onlne 0 November 005] maor reponblty of the Natonal Toxcology Program (NTP) to nvetgate the potental toxc and carcnogenc effect of varou chemcal. Stude conducted by the NTP are ued by the U.S. Envronmental Protecton gency the Food and Drug dmntraton and other federal and tate agence n ther conderaton of regulaton and polce for protectng publc health. The -year rodent cancer boaay an mportant component of the NTP nvetgaton; thee boaay typcally nvolve group of male and female mce and rat randomly agned to ether a control group or one of three doe group (low medum and hgh). t death each anmal extenvely examned for mcrocopc and macrocopc tumor a well a for abnormal change n tue. Of partcular nteret whether the rate of occurrence of a pecfc tumor related to doe. ecaue ome anmal do not urvve to the end of the -year tudy the NTP tattcal analye of te-pecfc tumor rate employ a urvval-aduted contnuty-corrected Cochran-rmtage (C) trend tet the poly-3 trend tet (rmtage 955; aler and Porter 988; Cochran 954; Porter and aler 989). For mplcty n th artcle we refer to th tet a the. Typcally th trend tet followed by parwe comparon of each doe group wth the control group. It mportant to dtnguh between two type of parameter related to the problem of current nteret namely age-pecfc tumor ncdence rate and lfetme tumor rate. The former the hazard rate aocated wth the age at tumor onet and the latter the expected proporton of anmal that ever develop a tumor (at any age) whch a functon of both the tumor ncdence rate and the mortalty rate. Thu dependng on mortalty pattern lfetme rate generally wll not correpond exactly wth age-pecfc ncdence rate. The age-pecfc ncdence rate a more meanngful but le acceble end pont than the lfetme rate. For mplcty of notaton we have dropped age-pecfc from the phrae age-pecfc tumor ncdence rate. ll pont etmator dcued n th artcle and n other report uch a aler and Porter (988) and Peddada et al. (005) etmate lfetme tumor rate. Further trend tet uch a the the trend tet developed by Peddada et al. (005) and the trend tet propoed n th artcle ue urvval-aduted lfetme tumor rate to tet for trend n tumor ncdence rate. Smulaton tude performed by Dne (99) and Peddada et al. (005) and n th artcle ugget that although thee tet employ lfetme tumor rate rather than tumor ncdence rate they alo provde vald nference about tumor ncdence rate. lthough tumor ncdence rate may trctly ncreae wth doe lfetme tumor rate may have an umbrella-haped or a plateau-haped doe repone curve becaue of hgher mortalty n the upper doe group. n umbrella or plateau-haped repone curve for lfetme tumor rate alo lkely to occur f the tumor ncdence rate ha a plateau-haped doe repone curve. In uch tuaton the may not be entve enough to detect th doe-related repone becaue t baed on lnear regreon of the etmated lfetme tumor rate on doe. For example n a tudy of the chemcal oprene female rat were expoed to or 7000 ppm oprene by nhalaton for year (NTP 999). Mammary gland fbroadenoma occurred n and 3 of 50 anmal repectvely. Survval dd not dffer among doe group and the urvval-aduted lfetme tumor rate were 44% 74% 74% and 73% repectvely. The yelded a p-value of 0.. However each of the parwe comparon wth the control group wa gnfcant at p < 0 (NTP 999). Data uch a thee are not uncommon n NTP tude and n thee tuaton the may fal to detect a gnfcant chemcal effect. Motvated by uch example Peddada et al. (005) developed an order-retrcted nferencebaed procedure that well uted for nonlnear repone. Smulaton tude ugget that th otonc regreon-baed tet perform better than doe the when the tumor rate ncreae nonlnearly n doe (Peddada et al. 005). However th tet may have le power than the when the tumor repone ncreae lnearly wth doe. Therefore n th artcle we propoe a new tet that modfe ther otonc regreon-baed ddre correpondence to S.D. Peddada otattc ranch MD 3-03 Natonal Inttute of Envronmental Health Scence Reearch Trangle Park NC 7709 US. Telephone: (99) 54-. Fax: (99) E-mal: peddada@neh.nh.gov We thank G. Dne and. Gladen for ther helpful comment. We alo thank the revewer and the edtor for everal ueful comment that have mproved the artcle. Th reearch wa upported by the Intramural Reearch Program of the Natonal Inttute of Envronmental Health Scence Natonal Inttute of Health. The author declare they have no competng fnancal nteret. Receved 6 ugut 005; accepted 9 November 005. Envronmental Health Perpectve VOLUME 4 NUMER 4 prl

2 Peddada and lng tet. aed on our extenve mulaton the reultng tet compete well wth the NTP trend tet for trctly lnear doe repone pattern and perform better than the NTP trend tet for nonlnear doe repone pattern. In addton to tetng for doe-related trend NTP perform parwe comparon between each of the doe group and the control group wth partcular attenton pad to the medum- and hgh-doe group. Currently no adutment made for multple comparon. Conequently the NTP parwe comparon tet are ubect to fale-potve rate that exceed the nomnal 5 level. Ung the order-retrcted nference methodology developed n Hwang and Peddada (994) and Peddada et al. (00) we ntroduce a new parwe comparon procedure that control the overall fale-potve rate. Materal and Method Suppoe there are doe group wth doe 0d < d <... < d wth n anmal agned to the th doe group.... We denote the tumor tatu at necropy of the th anmal n the th doe group by y where y f the anmal ha a pecfc tumor and 0 otherwe. To compute the poly-3 urvval-aduted ample ze for the th group (aler and Porter 988; Porter and aler 989) we defne anmal-pecfc weght w f the th anmal had a tumor at necropy otherwe w t 3 where t the fracton of duraton of the tudy for whch the anmal urvved. For the th doe group the poly-3 urvval-aduted ample ze and the poly-3 urvval-aduted etmator for the lfetme tumor rate π Tet for an ncreang trend n doe. The poly-3 urvval-aduted C trend tet tattc d π d π T0 S d d [] where for... n π y n r y π w n r r n n w a n n. n y n. π n and Furthermore Note that S a ackknfe varance etmator ntroduced n eler and Wllam (993). Performance of the above trend tattc wa evaluated by Peddada et al. (005). The NTP ue a contnuty-corrected poly-3 trend tet tattc defned a where CF S r r n. [] [3] The null hypothe of no chemcal effect on tumor ncdence reected n favor of the alternatve that there a potve trend n doe f > 0 and T exceed the ( α)th percentle of a tandard normal dtrbuton. an alternatve to the poly-3 urvvaladuted C trend tet tattc Peddada et al. (005) ntroduced the followng trend tet tattc: π% k TISO [4] n n S n n where n ( ) ( ) n n d d n max d d n ( ) ( ) d and d. %π CF T n π max mn t t n [5] are the otonzed value of π under the order retrcton that π value are nondecreang wth doe. Th tattc perform well n term of power when π value are monotoncally but nonlnearly ncreang wth doe wherea the poly-3 urvval-aduted C trend tet perform well when π value are lnearly ncreang wth doe (Peddada et al. 005). Motvated by thee obervaton we propoe a hybrd tattc that draw on both of thee procedure o that the reultng tet tattc ha mproved power n all tuaton; that the propoed tattc more lkely to detect a doe-related trend f t ext than the poly-3 urvval-aduted C trend tet. Frt we note that n ome ntance t poble for mortalty rate n one or more doe t group to be ubtantally hgher than n the control group. In uch cae n n ( ) ( n n ) n the denomnator of the above tet tattc may nflate the fale-potve or type I error rate. For th reaon we modfy the trend tattc T ISO of Peddada et al. (005) a T π% S max n n n n [6] and propoe the maxmum of the NTP trend tet tattc and the modfed otonc regreon-baed trend tattc T max T T ( ) [7] a the tet tattc for tetng a doe-related nondecreang trend n tumor ncdence rate. Note that T the larger of T a tet tattc for the lnear trend n urvval-aduted proporton and larger than T a tet tattc for the larget dfference n urvval-aduted proporton after tandardzaton to a nondecreang pattern. We approxmate the dtrbuton of T under the null hypothe that there no dfference n tumor ncdence rate among the doe group a follow. We generate ndependent tandard normal random devate X X... X and compute ( d d ) X V ( d d ) ( ) X X max mn and t t X X V. t [8] In the above expreon X^... are the otonzed value of X We approxmate the null dtrbuton of T by mulatng the dtrbuton of max(v V ) from whch p-value or crtcal value for the trend tet can be obtaned. lthough all our computaton were performed n FORTRN language we are n the proce of developng a JV-baed oftware for mplementng the methodology ntroduced n th artcle. For addtonal detal regardng the oftware pleae contact the author. Multple parwe comparon wth the control group. In addton to performng a trend tet centt at the NTP are often ntereted n performng parwe comparon between each of the doe group and the control group. In th tuaton the null 538 VOLUME 4 NUMER 4 prl 006 Envronmental Health Perpectve

3 Survval-aduted quantal-repone tet hypothe that the tumor ncdence rate n the doe group are no larger than the rate n the control group; the alternatve hypothe that the tumor ncdence rate n at leat one doe group trctly larger than n the control group. In order-retrcted nference termnology th alternatve hypothe known a mple tree order. Currently the NTP perform parwe comparon of each doe group wth the control group by applyng tet tattc T on two group the control group and the partcular doe group of nteret. lthough comparon are generated between the control group and each of the doe group NTP reearcher are partcularly ntereted n whether the tumor ncdence rate n ether of the top two doe group exceed the rate n the control group. Th approach doe not account for multple comparon between each of the doe group and the control group. In the followng we propoe a mple tet tattc derved from the order-retrcted nference methodology ntroduced by Hwang and Peddada (994) and ued by Peddada et al. (00). Ung the procedure decrbed by Hwang and Peddada (994) lfetme tumor rate for the doe group are etmated by π π for the control group and π max(π π ). To llutrate the above formula uppoe the poly-3 tumor rate for the four tet group are π 0.3 π 0. π π wth correpondng poly-3 aduted ample ze of n 44. n 45.6 n 3 40 n 4 4 repectvely. Then ung the formula (Equaton 5) for π we have π mn [9] ccordngly π max( ) 0.49 π 3 max( ) 0.4 π max( ) To derve the tet tattc and t dtrbuton under the null hypothe that all doe group have the ame tumor rate we frt generate ndependent tandard normal random devate X X X. Let X X% mn X% max ( X% X ) X% X% V3 max. [0] The propoed tet tattc for comparng the th doe group wth the control group π% R. [] S max n n n n ( ) pproxmate crtcal value for R R 3... R can be obtaned from the mulated dtrbuton of V 3. The propoed parwe procedure reect the null hypothe f R max(r R 3... R ) exceed the crtcal value derved from the dtrbuton of V 3. Th a nonparametrc analogue of Tukey honetly gnfcant dfference pot hoc multple comparon procedure commonly appled n analy of varance ettng. Reult Smulaton tudy. We conducted an extenve mulaton tudy to compare the performance of the propoed trend tet T wth the NTP trend tet. total of 750 nonnull confguraton and 50 null confguraton mlar to thoe commonly encountered n the NTP rodent boaay were mulated. ll mulaton reult reported n th artcle are baed on 0000 mulaton run and the nomnal level of gnfcance α 5. Smulaton parameter were patterned after the NTP rodent cancer boaay. We condered a total of three doe group (low medum and hgh) and a control group wth 50 anmal agned to each group. decrbed by other author (e.g. Dne 99; Peddada et al ) for each anmal n the th doe group 3 4 we generated realzaton of two ndependent Webull random varable Y and Y where Y repreented the tme to tumor onet and Y repreented the tme to death from natural caue. The urvval functon of Y 3 4 and gven by P(Y > t d ) exp( ψ φ d t γ ). We mulated thee random varable uch that the duraton of the tudy wa 4 month whch typcal of the NTP rodent boaay. We mulated two doe pattern -fold doe pacng and 5-fold doe pacng namely (d d d 3 d 4 ) (0 0.5 ) and ( ). prevouly decrbed (Peddada et al. 005) we condered contant doe effect on mortalty; that φ φ wth pattern of φ (no effect).5.5 and 3 (evere effect). We et the mortalty hape parameter at γ 5 and baelne mortalty cale parameter at ψ o that 70% of the anmal n the control group urvved to the end of the -year tudy a rate often oberved. The three tumor onet hape parameter (γ ) value condered n th tudy were.5 3 and 6. Poly-3 urvval adutment are baed on the aumpton that the true tumor onet Webull wth hape parameter γ 3 (Porter and aler 989). Thu the deal tuaton for the poly-3 urvval correcton γ 3. We condered fve dfferent background tumor rate π rangng from rare (0 5) to common ( ). Value of the baelne tumor onet cale parameter ψ correpondng to each π are gven n Table. Fnally we choe x dfferent et of the effect of doe on tumor onet φ for each of the fve background tumor rate; value of φ are gven n Table. In each cae the null hypothe correpond to the cae when the ncdence rate are all equal; that the rato are (:::). Thu a total of 375 nonnull and 75 null confguraton were condered for each of the two doe pacng. Reult of the mulaton tudy are repreented by catter plot of fale-potve error rate (or power) wth the NTP procedure on the horzontal ax and the propoed procedure on the vertcal ax. For the trend tet falepotve error rate are ummarzed n Fgure Table. Pattern of tumor onet hape parameter (γ ) and tumor onet cale parameter (ψ ) by background tumor rate (π ). ackground tumor rate (π ) Varable γ.5 ψ γ 3 ψ γ 6 ψ Table. Pattern of tumor ncdence rato (φ :φ :φ 3 :φ 4 ) for the four doe group by background tumor rate (π ). Tumor ncdence rato (φ :φ :φ 3 :φ 4 ) Very rare tumor Somewhat rare tumor Common tumor Doe effect et (π 0 ) (π 5) (π ) ::: ::: ::: :::0 :::4 ::: 3 ::0:0 ::4:4 ::: 4 :0:0:0 :4:4:4 ::: 5 :5:5:0 :.5:.5:4 :.5:.5: 6 :5:0:5 ::3:4 :.5:.75: Envronmental Health Perpectve VOLUME 4 NUMER 4 prl

4 Peddada and lng and power n Fgure. For the parwe comparon procedure fale-potve error rate are ummarzed n Fgure 3. In each cae the dagonal lne repreent the lne of equalty between the two tet. The horzontal and vertcal lne Propoed tet a hgher fale potve rate n th trangle Propoed tet n Fgure and 3 are drawn at a dtance of (5 0.95)/0000 from the orgn. In Fgure and 3 pont fallng to the rght of the vertcal lne ndcate ntance n whch the NTP procedure exceed the nomnal Fgure. Comparon of fale-potve error rate for -fold doe pacng () and 5-fold doe pacng (). The fale-potve error rate of the propoed trend tet wa plotted agant the fale-potve error rate of the. We plotted only the cae where the two procedure dffered gnfcantly n term of fale-potve error rate; reult are baed on 0000 mulaton run per confguraton. The plot ugget that the fale-potve rate of the propoed tet alway le than that of the when both tet exceed the nomnal level. Propoed trend tet Propoed tet ha hgher power n th trangle hgher power n th trangle a hgher fale potve rate n th trangle Fgure. Comparon of power for -fold doe pacng () and 5-fold doe pacng (). In each panel the power of the propoed trend tet wa plotted agant the power of the. Plu ymbol () ndcate cae n whch the fale-potve error rate of the exceed both the fale-potve error rate of the propoed trend tet and 5. We plotted only the cae where the two procedure dffered gnfcantly n term of power; reult are baed on 0000 mulaton run per confguraton. In both () and () the bow -haped pattern pontng n the northwet drecton wth very few pont below the dagonal lne ugget that the propoed tet ha generally hgher entvty to detect real trend than the. The gan are ubtantal a the doe pacng ncreae from - to 5-fold. Propoed parwe tet Propoed trend tet Propoed tet ha hgher power n th trangle hgher power n th trangle 5 NTP tet lberal n th rectangle; the propoed tet not NTP tet lberal n th rectangle; the propoed tet not NTP parwe tet NTP parwe tet Fgure 3. Comparon of fale-potve error rate for parwe tet for -fold doe pacng () and 5-fold doe pacng (). The fale-potve error rate of the propoed parwe comparon procedure wa plotted agant the fale-potve error rate of the NTP parwe comparon procedure for comparng the two hghet doe group agant the control. We plotted only the cae where the two procedure dffered gnfcantly n term of fale-potve error rate; reult are baed on 0000 mulaton run per confguraton. In both () and () all pont are below the horzontal lne at 54. Th ugget that the fale-potve rate of the propoed procedure almot alway le than that of NTP parwe procedure and never exceed the nomnal 5 gnfcance level. Propoed parwe tet 0.5 level of 5 and pont fallng above the horzontal lne correpond to ntance n whch the propoed tet exceed the nomnal level of 5. In Fgure pont fallng below and to the rght of the dagonal lne correpond to ntance n whch the ha more power than the propoed trend tet wherea pont fallng above and to the left of the dagonal lne correpond to ntance n whch the propoed trend tet ha more power than the. To reduce clutter n the plot we teted equalty of the fale-potve error rate (or power) of the NTP procedure and the propoed procedure ung a two-ample z-tet for proporton and we plotted only thoe pont for whch there wa a gnfcant dfference between the NTP tet and the propoed tet at the 5% level of gnfcance. For the 75 null pattern condered n th mulaton tudy there were 3 pattern where the two tet had gnfcantly dfferent fale-potve error rate (Fgure ). Th reult wa oberved for -fold pacng a well a 5-fold pacng. The propoed tet wa rarely more lberal than the when both tet exceeded the nomnal level; that the fale-potve rate of the propoed tet never exceeded that of the. Furthermore the wa more lberal than the propoed tet for common tumor (π 0.5) condered n th tudy. lthough we only plotted the cae for whch the fale-potve error rate of the two tet dffered gnfcantly the fale-potve error rate of the propoed trend tet never exceeded 87 and that of the never exceeded 99. The power of the two tet dffered gnfcantly n 70 of the 375 nonnull doe pattern for -fold pacng (Fgure ). In approxmately 70% of thee 70 pattern the propoed trend tet had hgher power than dd the. Thu a large number of pont n Fgure are above the dagonal lne. Further n 5 of the 70 pattern (about 6%) the fale-potve error rate of the NTP trend tet exceeded the nomnal 5 gnfcance level and wa gnfcantly hgher than that of the propoed tet. Thee cae are denoted by a n Fgure. The gan n power for the propoed tet wa a hgh a 0.75 (0.69 for the propoed tet v for the the NTP trend tet) a relatve gan of 66%. In contrat the bet gan oberved for the the NTP trend tet wa 48 (0.50 for the the NTP trend tet v for the propoed tet) a modet relatve gan of < 0%. The power gan made by the propoed tet were even more ubtantal for 5-fold doe pacng (Fgure ). Power of the two tet dffered gnfcantly n 64 of the 375 nonnull pattern and the propoed tet had hgher power n almot 85% of thee pattern. Thu mot pont n Fgure are above the dagonal. 540 VOLUME 4 NUMER 4 prl 006 Envronmental Health Perpectve

5 Survval-aduted quantal-repone tet Further a we oberved wth the -fold doe pacng n 3 of the 64 pattern (about 5%) the fale-potve error rate of the the NTP trend tet exceeded the nomnal 5 gnfcance level and wa gnfcantly hgher than that of the propoed tet. n Fgure thee cae are denoted by a. The gan n power for the propoed tet wa a hgh a (0.67 for the propoed tet v. 0. for the ) > 300%. In contrat the bet gan oberved for the wa 38 (0.33 for the v for the propoed tet) a modet relatve gan of < %. In cae for whch tumor ncdence rate ncreaed monotoncally but not lnearly wth doe the propoed trend tet performed better than the n term of both power and fale-potve error rate. expected the performed better than the propoed tet n cae for whch tumor ncdence rate ncreaed lnearly wth doe. ut even n uch cae the gan made by the NTP trend tet were modet. Furthermore the fale-potve error rate of the often exceeded the nomnal 5 gnfcance level. For the null confguraton decrbed above we alo compared fale-potve error rate of the propoed parwe comparon procedure wth the NTP procedure for parwe comparon between the medum- and hgh-doe group wth the control group. Fgure 3 how that the propoed method mantaned fale-potve error rate at or below the nomnal 5 level wherea the NTP procedure wa often lberal exceedng the nomnal level of 5. lthough we plotted only the cae n whch the fale-potve error rate of the two tet dffered gnfcantly the propoed parwe tet never exceeded 5 wherea the NTP parwe tet had fale-potve error rate a hgh a 0.. n NTP example. part of an NTP boaay on oprene female F344/N rat were expoed to oprene for year through nhalaton (NTP 999). Ioprene a naturally occurrng compound n plant a well a a byproduct of ethylene producton. It mlar n tructure to 3-butadene a potent rodent carcnogen. Ffty female rat were expoed to or 7000 ppm oprene; and 3 repectvely developed mammary gland fbroadenoma. Survval-aduted tumor proporton howed a plateau-haped repone wth 44% 74% 74% and 73% repectvely of the anmal developng fbroadenoma. The gave a p-value of 5 wherea each doed group dffered from the control group at p < 0. ecaue of the wde doe pacng and the plateau-haped repone begnnng at the low doe of 0 ppm the wa not entve enough to detect the doe-related repone. The propoed trend tet provded a gnfcant doe-related trend n mammary gland fbroadenoma wth a p-value of 04. ndcated n our mulaton tudy dcued above th tattc capable of detectng monotonc nonlnear trend wth doe and not affected by wde doe pacng. Furthermore ung the propoed method for parwe comparon each doe group dffer from the control group at p < 05. From our mulaton we can be confdent that among all of the parwe comparon wth the control group the overall fale-potve rate of 5 not exceeded. Dcuon We have preented a trend tet for tumor ncdence data that take advantage of the trength of the C trend tet when the doe repone relatonhp lnear and alo take advantage of trength of nonparametrc order-retrcted method when the doe repone relatonhp monotonc but nonlnear. Mot mportant the fale-potve rate of the propoed tet rarely exceed that of the when both tet exceed the nomnal level yet n many ntance the propoed tet outperform the n term of power. Further we have alo provded a mple procedure for performng parwe comparon between each of the doe group and the control group; th procedure control the overall fale-potve error rate when conductng multple tet. ecaue NTP rodent boaay data are ued by federal and tate agence to at n formulatng regulatory polce t crucal for the tattcal method to be powerful enough to detect doe-related trend when they ext. Equally mportant thee method hould not produce exceve fale-potve fndng. The trend tet and the multple comparon procedure that we have propoed here make mportant tep n both drecton. When doe repone relatonhp are monotonc but nonlnear the propoed trend tet more powerful than the. lthough both trend tet can exceed the nomnal 5 level under ome crcumtance the fale-potve error rate of the propoed trend tet almot alway le than that of the when both tet exceed the nomnal level. Therefore the occurrence of fale potve wll be reduced wth ue of the propoed trend tet. Furthermore the NTP parwe comparon method doe not correct for multple comparon and often exceed the nomnal 5 level n parwe comparon of each of the doe group to the control group partcularly for common tumor. The propoed parwe comparon method control the fale-potve rate o that t tay near (or le than) 5 under a wde range of tuaton that we commonly encounter n NTP tude. Thu thee propoed method hould provde more accurate decon about the potental carcnogenc effect of chemcal. REFERENCES rmtage P Tet for lnear trend n proporton and frequence. ometrc : aler Porter C Effect of treatment-nduced mortalty and tumor-nduced mortalty on tet for carcnogencty n mall ample. ometrc 44: eler G Wllam R Rato etmate the delta method and quantal repone tet for ncreaed carcnogencty. ometrc 49: Cochran W Some method for trengthenng the common χ tet. ometrc 0: Dne G. 99. Contant rk dfference n the analy of anmal tumorgencty data. ometrc 47: Hwang J Peddada S Confdence nterval etmaton ubect to order retrcton. nn Stat : NTP Toxcology and Carcnogene Stude of Ioprene (CS No ) n F344/N Rat (Inhalaton Stude). Techncal Report No Reearch Trangle Park NC:Natonal Toxcology Program. Peddada S Dne G Haeman J urvval-aduted quantal repone tet for comparng tumor ncdence rate. ppl Stat 54:5 6. Peddada S Precott Conaway M. 00. Tet for order retrcton n bnary data. ometrc 57:9 7. Porter CJ aler J Tetng for ncreaed carcnogencty ung a urvval-aduted quantal repone tet. Fundam ppl Toxcol : Envronmental Health Perpectve VOLUME 4 NUMER 4 prl