Document 5bE4v3D6r6wYV4B1wMrYE4R60

UNIVERSITY OF CINCINNATI DEPARTMENT OF PREVENTIVE MEDICINE AND INDUSTRIAL HEALTH COLLEGE OF MEDICINE CINCINNATI 19, OHIO Au gu st 25, 1959 M E M OR AN D UM : TO: D r . Ro b e r t A . Ke h o e FROM: Bio m e tr ics S U B JE CT : D e s ig n o f L e a d Study- Purpose 1. Th e p u r p o se of th e e xp e r im e n t w ill be to ob tain r e a s o n a b le e s t im a t e s of tij e ffe ct s th a t w ou ld r e s u lt fr o m s u b je ct in g h u m a n s to le a d -in -a ir fo r p r o lo n ge d p e r io d s of t im e . 2. Th e r e s e a r c h d e sign sh o u ld e n a b le th e in v e s t ig a t o r to p r e d ict : a . An e s t im a t e d va lu e of le a d in u r in e , fe c e s , b lo o d , t is s u e , e t c. a ft e r the s u b je ct b r e a t h e s d iffe r e n t co n ce n t r a t io n s of le a d o r b r e a t h e s th e m fo r p r o lo n ge d p e r io d s of t im e , and; b . Th e e r r o r w ith w h ich su ch p r e d ict io n s ca n be m a d e . ' 3. It is n ot p o s s ib le to fu lfill the a im s of th e e xp e r im e n t w ith ou t co m m it m e n t to a lon g t e r m stu d y in vo lvin g a n u m b e r o f s u b je ct s u n d e r s p e cifie d co n d itio n s of t e s t in g . Un fo r tu n a te ly the a n a ly s e s an d d e sign s of lon g t e r m e xp e r im e n ts a r e n ot ye t in a d va n ce d s t a g e s . So m e su ch e xp e r im e n t s h ave b een p e r fo r m e d in a gr o n o m y w ith m ixe d s u c c e s s e s . Th e s p e c ific d e s ign s u g g e s t e d h e r e w ill in co r p o r a t e d e sign fe a t u r e s th a t h a ve p r o ve n s u cce s s fu l in the p a s t . H o w e ve r , the p r o b le m of e s tim a tin g e ffe ct s to p r o je ct e d e xp e r im e n ta l co n d itio n s d em an d s so m e n ew a p p r o a ch e s . Th e so lu tio n a d vo ca te d h e r e is to u se a p r io r i p r e d ict io n s a s gu id e s to ge n e r a tin g e s tim a tin g fu n ct io n s . Th e a p r io r i p r e d ict io n w ill co n s is t of r e a so n a b le h yp o th e se s co n ce r n in g th e ge n e r a l sh a p e s of e xp e r im e n ta l e ffe c t s . On ly p a r t of the d ata w ill be u se d to ch o o se the b e s t p r e d ict io n eq u a tion w h ich w ill be b a s e d e q u a lly on the h yp o th e s ize d fo r m o f th a t e q u a tio n an d the b e st fit to o b ser ved d ata. The r e s t of the o b se r va tio n s w ill be u se d to s e le ct am on g a lte r n a tive h yp o th eses an d to d e r ive e s tim a te s of p r e d ictio n e r r o r s . R 0018977 N15304 2- - De sign 1. Th e d e sign o f the e xp e r im e n t sh o u ld co n s is t o f a co u n te r b a la n ce d s e r ie s of s u b je ct e xp o s u r e s to d iffe r e n t , co n ce n t r a t io n s o f le a d in a ir , o r , fo r d iffe r e n t p e r io d s o f t im e to fixe d co n ce n t r a t io n s , o r , to a s e r ie s of e xp o su r e s in w h ich both co n ce n tr a tio n an d d u r a tio n a r e v a r ie d . Th e ch o ice of fixin g e ith e r co n ce n tr a tio n o r d u r atio n m a y be d e te r m in e d by e xp e r im e n ta l p r a c t ic a lit ie s . H o w e ve r , it sh o u ld b e p o in te d out th at if both d u r a tio n an d co n ce n tr a tio n can be v a r ie d co n cu r r e n t ly , the u ltim a te n u m b er of su b je cts n eed ed w ill be s m a lle r th an if e a ch v a r ia b le is v a r ie d in s e p a r a t io n , in t e r a ct io n s b etw een d u r a tio n a n d co n ce n t r a tio n ca n be e va lu a te d w ith ou t th e u s u a l p e n u m b r a o f u n ce r t a in t y , a n d e s t im a t io n of p r e d ictio n e r r o r w ill be im p r o ve d . 2. Aft e r d is cu s s in g p r a ct ica l p r o ce d u r e s an d fe a s ib le e xp e r im e n t a l co n d itio n s w ith M r . Sc h a fe r , fr o m th e e va lu a t io n o f d ata c o lle ct e d in p r e v io u s e x p e r i m e n t s , a n d w ith th e e xp e ct a t io n of u t iliz in g th a t d a ta a s p a r t o f the fin a l a n a ly s is it a p p e a r s th a t th e fo llo w in g co m b in a tio n s o f co n d itio n s an d t r e a t m e n ts w ill m a ke fo r th e m o st e fficie n t d e sign : a . Ea ch s u b je ct can be u s e d a s a co m p le te e xp e r im e n t . Op tim u m e fficie n cy is ob tain ed if the fin a l n u m b er of s u b je cts is so m e m u ltip le o f 4 . ( i. e . 4 , 8 , 1 6 , e t c .) b . Tw o s e ts o f e xp e r im e n ta l co n d itio n s sh o u ld be v a r ie d co n co m ita n tly: i. Co n ce n t r a t io n o f le a d in a ir : Va lu e s to be u s e d to v a r y fr o m 7 5 ^ / m ^ t o 125 ^ -/ m ^ , lSOj'/ m ^ , a n d 17 5 ^ / m ^ . M r . Sc h a fe r e s t im a t e s th e tim e n e e d e d to m o d ify the eq u ip m e n t (to p e r m it d a ily v a r ia t io n s o f co n ce n tr a tio n s) n ot to e xce e d one m on th . ii. Du r a tio n s of e xp e r im e n ta l s e s s io n js : Len gth of s e s s io n s to be d ivid e d in to tw o gr o u p s : Sh o r t - te r m s e s s io n s : 2, 4 , 6 , an d 8 h o u r s , Lon g - t e r m s e s s io n s : 9 , 10, 11, an d 12 h o u r s . T h e r a t io o f s h o r t t o lo n g t e r m e x p o s u r e s c o u ld b e 3:1. Th e s u b je c t w ou ld a v e r a g e s lig h t ly le s s th an 7 d a ily e xp o s u r e h o u r s . O v e r t im e , r a n gin g fr o m on e to fo u r h o u r s w ou ld o ccu r e it h e r o n ce o r tw ice e a ch w e e k . ( If t h is s ch e d u le s h o u ld p r o v e t o fto n e r o u s fo r th e s u b je c t th e r a t io o f s h o r t t o lo n g t e r m s e s s io n s c o u ld b e c h a n g e d t o 4:1 w it h o u t a p p r e cia b ly ch an gin g the to ta l d e s ign . ) H 00i 23?u 3- - c . Co u n te r b a la n cin g sh o u ld b e su ch th a t s e r ia l e ffe ct s of e xp e r im e n t a l s e s s io n s can be se p a r a te d fr o m s p e cific tr e a tm e n t e ffe ct s . The m o s t e fficie n t d e sign fo r th at is a va r ia t io n of or th o go n a l Gr a e c o -La t in Sq u a r e s . Th e s p e cific b lo ck d e sign w ill be su ch th at e a ch tr e a tm e n t le v e l p r e ce d e s an d fo llo w s a ll o th e r t r e a t m e n t le v e ls . Su cce s s iv e b lo ck s m a y be t r e a t e d a s w ith in s u b je ct r e p lica t io n s an d a d va n ta ge can be ta ken of the con ve n ien t a n a lo gy b etw een La t in Sq u a r e d e sign an d co n fo u n d in g in fa c t o r ia l e x p e r im e n t s . d. The n u m b er of e xp e r im e n ta l s e s s io n s is give n by the m in im u m n u m b er of lon g t e r m e xp o su r e s e s s io n s n e ed ed fo r m a xim u m e ffic ie n cy . Th is n u m b e r i s 32 a n d s in c e t h e r a t io o f s h o r t t o lo n g t e r m e x p o s u r e s is 3:1, th e t o t a l e xp e r im e n t sh o u ld co n s is t o f 128 e xp e r im e n t a l d a y s . ( F o r a 4:1 r a t io o f s h o r t t o lo n g t e r m s e s s i o n s , t h e t o t a l n u m b e r o f e xp e r im e n t a l d a ys w ou ld be 160. ) e . Th e fir s t b lo ck of 16 s h o r t t e r m an d 4 lo n g t e r m s e s s io n s in the p la n n e d q u a s i o r th o go n a l Gr a e c o -La t in Sq u a r e a r e give n b e lo w Week 1 2 Du r ation in Ho u r s 2 4 6 12 8 4 2 11 8 6 / m 75 125 150 75 175 173" 150 125 125 75 Week 3 4 5 Du r ation in Ho u r s 6 10 8 2 4 9 8 6 4 11 2 etc. ^ /m^ 125 150 75 175 150 175 150 175 75 175 125 f. P r o ce d u r e : A ir in take w ill be p r e s ca le d so th at a d e s ir e d co n ce n tr a tio n can be "d ia le d " fo r each e xp e r im e n ta l d ay. Th e r oom w ill be m ad e r ea d y a t 8 A . M . an d th e su b je ct w ill s t a r t e a ch day a t 9 A . M . A ll e xp e r im e n t a l s e s s io n s w ill be co n tin u o u s e xce p t fo r a 10 to 20 m in u te b r e a k e a ch fo u r h ou r s to p e r m it the s u b je ct tim e to^and to r e fr e s h h im s e lf. ( All n o u r ish m e n t is to be taken ou tsid e th e r o o m a ft e r a th or ou gh m o u th w a s h in g. ) U r in e , fe c e s , b lo o d , a n d s a m p le s o f fo o d w ill b e c o lle ct e d a s w as done p r e v io u s ly w ith one e xce p t io n . Th e s u b je ct w ill be a s k e d to k'E' 00129?; 4- - em p ty h is b la d d e r a t the end of so m e e xp e r im e n t a l s e s s io n s an d co lle ct h is u r in e fo r the n e xt 48 h o u r s in in d ivid u a l co n ta in e r s - on ea ch of w h ich h e is to m a r k the tim e of u r in a tio n . T h is p r o ce d u r e is to be fo llo w e d fo r a t le a s t 8 to 12 w e e k e n d s. Estim a tio n 1 . Co m p o n e n t v a r ia b le s w ill b e e v a lu a t e d fo r e ffe c t s a n d p o s s ib le in t e r a c t io n s . Be ca u s e of the p a r t icu la r co u n te r b a la n cin g of the Gr a e c o -La t in Sq u a r e d e sign th is can be done v e r y e fficie n t ly . Aft e r the fir s t p a r t of the a n a ly s is se le cts the v a r ia b le s that a p p e a r to a ffe ct , e ith e r sin gly or in co m b in a tio n , the va lu e s o f le a d e x c r e t e d in u r in e o r fe c e s o r th e a m o u n t s fo u n d in the b lo o d , t h e s e v a r ia b le s w ill th en be u s e d a s e s t im a t o r s o r p r e d ict o r s fo r the se co n d p a r t of th e a n a ly s is . 2. Es t im a t io n of e ffe ct s to p r o je ct e d e xp e r im e n ta l co n d itio n s w ill be b a s e d on the b e s t fit t in g fu n ct io n th a t ca n be d e r iv e d fr o m th e d ata u n d e r th e fo llo w in g s p e cific con d itio n s: a . No m o r e th an 2/ 3 of the d ata w ill be u s e d to d e r ive a p r e d ict io n e q u a tion ; b . Th e ge n e r a l fo r m of the p r e d ictio n e q u a tio n w ill be s p e cifie d by an a p r io r i h yp o th e sis; c . F it t in g the e q u a tio n it s e lf w ill be lim it e d to p o in ts d e r ive d fr o m sh o r t tim e e xp e r im e n ta l e xp o s u r e s . No m o r e th an 2/ 3 of the d ata w ill be u s e d in d e r ivin g e q u a tion s so th at the r e m a in in g 1/ 3 ca n s e r v e a s ch e ck on th e v a lid it y o f the fin a l fu n ctio n . Th e s p e c ific an d ge n e r a l fo r m of th e p r e d ict io n e q u a tio n sh o u ld be d e te r m in e d m o r e b y p h y s io lo g ica l co n s id e r a t io n s th an cu r v e fit t in g . In t h is w ay th e fin a l p r e d ict io n w ill n ot o n ly s u it the co lle ct e d d ata but w ill a ls o c a r r y the co n victio n o f b ein g p h y s io lo g ica lly r e a s o n a b le . Cu r ve fittin g p r o ce d u r e s w ill be lim it e d , t h e r e fo r e , to th e d e t e r m in a t io n s o f co n s t a n ts fo r an o t h e r w is e in d ep e n d e n t q u an tita tive h yp o th e s is . Th e in te r a ctio n b etw een fittin g the fin a l cu r ve an d u se of a p r io r i h yp o th e se s n e e d s fu r t h e r e la b o r a t io n . Th e a p r io r i s ta te m e n t sh o u ld d e s cr ib e a r e a s o n a b le p h ys io lo gica l e xp e cta tio n . F o r e xa m p le , one co u ld p o stu la te th at e xcr e t io n of le a d in u r in e a p p r o a ch e s som e p h y s io lo gica l lim it w h ich r e m a in s fixe d , or th at e xcr e tio n of le a d in u r in e a p p r o a ch e s a p h y s io lo gica l lim it th at is it s e lf d e te r m in e d b y oth e r co n d itio n s, or th at e xcr e t io n of le a d in u r in e a p p r o a ch e s a p h y s io lo g ica l lim it th a t in c r e a s e s co n s t a n t ly w ith a d a p ta tio n to h igh e r le v e ls , an d so on . E a ch o f th e s e s ta te m e n ts can be d e s cr ib e d in g e n e r a l q u a n tita tive K o U I 6 J J u 5- - fo r m s . A sim p le q u an tita tive tr a n s la tio n of the sta te m e n t th at the p h y s io lo gica l lim it o f le a d e xcr e t io n r e m a in s fixe d w ou ld be E (lu ) = U (1 - e -3 ^ ) * p e ; w h e r e E (lu ) = e x p e c t e d u r in e le a d ; U = the p h ys io lo gica l lim it , A = a p h ys io lo gica l co n sta n t, d = d u r ation o f e xp o s u r e , an d p e = e r r o r o f p r e d ict io n . Sim ila r q u an titative sta te m e n ts can be m ad e to e xp r e s s the o th e r a lt e r n a t iv e s . W ith in th e s e q u a n tita tive e xp r e s s io n s a r e s t ill oth e r a lt e r n a t iv e s an d th e p r o ce s s of a n a ly s is w ill co n s is t of a ste p w ise e lim in a tio n of n o n -p r e d ictive fo r m s o f e q u a tio n s . W ith p r e s e n t co m p u te r fa c ilit ie s su ch a p r o je ct d oes not a p p e a r to be e xce s s iv e ly d ifficu lt . F it t in g the fir s t a p p r o xim a tio n e q u a tio n s on ly to the e ffe ct s o f s h o r t d u r a tio n e xp e r im e n ts is the fir s t step in the e lim in a tio n of p oo r a p p r o xim a tio n . Sin ce the p r o b le m e s s e n t ia lly co n s is t s o f d e r ivin g e s t im a t e s of th e e ffe ct s o f lon g d u r atio n e xp o su r e s fr o m o b s e r ve d s h o r te r d u r atio n e xp o s u r e s , the m eth o d of a n a ly s is w ill a tte m p t to p r e d ict the o b s e r ve d e ffe ct s of lo n ge r d u r a tio n s fr o m th e o b s e r ve d e ffe ct s of s h o r t e r d u r a tio n s . In t h is fa s h io n it w ill be p o s s ib le to s e le ct am on g the p o s s ib le q u an tita tive sta te m e n ts th ose th a t, w hen fit t e d to s h o r t d u r a tio n e xp e r im e n t s , w ill a ls o p r e d ict lon g d u r a tio n e xp e r im e n ts. If th e d iffe r e n t e xp e r im e n t a l e xp o s u r e s r a n ge fr o m 2 to 12 h o u r s th en on ly the data fo r d u r ation s of no m o r e th an 6 h o u r s w ill be u se d to d e te r m in e th e co n sta n ts in the e q u a tio n . Alt e r n a t iv e eq u a tio n s w ill be r e je ct e d o r s e le ct e d a cco r d in g to the s iz e o f the e r r o r w ith w h ich th e y p r e d ict th e e ffe ct s o f e xp e r im e n ta l d u r a tio n s of lo n ge r than 6 h o u r s . 3. Tw o s a fe gu a r d s a r e in tr o d u ce d b y th is m e th o d of a n a ly s is . F ir s t th e fo r m of the eq u ation th at g iv e s the b e s t fit is o r ig in a lly d e te r m in e d by p h y s io lo g ica l co n s id e r a t io n s . Th u s th e e xp e cta tio n s a r e , fr o m th e b e gin n in g, th a t w ith the c o r r e c t ly p h r a s e d eq u a tion one m a y e xp e ct to fit a ll p o s s ib le p oin ts on the cu r v e . Se co n d ly, the d a t a ^ ^ u s e d in p a r t a s if e ffe ct s of lo n ge r d u r atio n e x p o s u r e s , ( fr o m 8 to 12 h o u r s ) a lt h o u gh o b s e r v e d d u r in g t h e e x p e r im e n t , a r e to be p r e d icte d - a s w e ll a s the e ffe ct s to e xp o su r e d u r a tio n s w h ich h ave n o t b e e n o b s e r v e d ( e .g . fr o m 13 to 24 h o u r s ) . It is r e a s o n a b le to a s s u m e that if the m eth od y ie ld s s a tis fa cto r y e s tim a te s of o b se r ve d p hen om en a ( i. e . fo r 8 to 12 h o u r s ) it w ill a ls o y ie ld s im ila r ly s a t is fa c t o r y e s t im a t e s o f u n o b ser ved p e r io d s of e xp o su r e . 4 . Th e v a lid it y o f th e fin a l e q u a tion s s e le ct e d a s p r e d ict o r s w ill be e s t a b lis h e d a ga in st th r ee so u r ce s; KE 0032381 6- a . Th e 1/ 3 of the d a ta , not u se d to d e r ive the p r e d ictio n co n s ta n ts , w ill be p r e d icte d . Be s id e s se r vin g a s a ch e ck on the va lid ity of the fin a l m eth od of e s tim a tio n , the e r r o r s of e s tim a te w ill be d e te r m in e d a ga in st that d ata. b . Th e data co lle ct e d d u r in g p r e vio u s stu d ie s in th is la b o r a t o r y w ill be u s e d in a s im ila r fa s h io n . Th e e q u a tio n s d e ve lo p e d to p r e d ict p lu s the e s tim a te s of a cce p ta b le e r r o r d e r ive d fr o m the r e m a in in g 1/ 3 o f the data w ill be u se d to p o std ict r e s u lt s a v a ila b le sin ce the b egin n in g of th e s e r ie s of e xp e r im e n ts. c . It is r e co m m e n d e d th at su b je cts be e xp o se d to two or th r e e p r o lo n ge d e xp e r im e n ta l s e s s io n s (up to 24 h ou r s) an d th at the o b s e r ve d e ffe ct s o f t h e s e fe w s e s s io n s be e v a lu a t e d a g a in s t th e p r e d ict io n s b a s e d on th is m eth od of a n a ly s is . / KE 0012332