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Journal of Biopharmaceutical StatisticsPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t713597263

Statistical comparison of stability study designsEarl Nordbrock a

a Marion Merrell Dow Inc., Kansas City, Missouri

To cite this Article Nordbrock, Earl(1992) 'Statistical comparison of stability study designs', Journal of BiopharmaceuticalStatistics, 2: 1, 91 — 113

To link to this Article: DOI: 10.1080/10543409208835033

URL: http://dx.doi.org/10.1080/10543409208835033

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Ke? ~ v r c i s . iabiii iy study design; Siieif iife; Fractional faciiirial;

Power; Exnerimental des ign

Studies are roii tlneiy conciucteci d u r~ n g evelopm ent of a new drug

to invest igate the effect o!' s t rength, package, batch, s torage con-

di t ion, and s torage t ime on s tabi l i ty of t he dosage fo rm. A typical

cttidj: wi!! h n w f!lrce h:!:~.hes. wveral s t rengths . sevsral packages .an d PC..C-.~ V C I I L I -bo-.)i ~L i ge undi t ions . Thus, it every batch by strength by

package combinat ion is tes ted for every s torage condi t ion, i.e., if

a cv rnp le i e facio r ia l des ign is u z d , a subs tant i a l expensc i s in -

voived. T o reduce expense, a m atrix des ign is comrnonly used; 2 .g . .

only the smal les t and largest bot tles are tes ted. Fract ional factorial --- ....ypL <-L . - - ~ . . .- ; r ,h ig ; i> -tau:i::y ~LII;L;GISx e propiiseci. 2nd ih c sta:isticu:

. .p i w e r s of various de:;:g:::; are compared .

Introduction

Before marketing a drug product, a pharmaceutical .-,\--,,,,par,y ~ u s tonduct astudy to investigate the stability of the drug product over time. In a typical

study, response variables such as potency, dissolution, and degradation prod-

Copyright Q 1992 by Marcel Dekkcr , Inc.

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The first step in designing a stability study is to list slopes that must be com-

pared, or equivalently to list design factors and design factor interactions (for

slopes) that may affect stability. Listed below are factors that are important,

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- - - ~njirj;:a \Ti ip,, :.i

FiDPIr vs. hi1;ii.r

Stri-ngth--I O v s . ?O

Strength-20 v s . <%hers

Im t A vs . ti

is ilope fo r 10 rng the iarnc as dope fo r 30

x . , f i .

is slope fo r lot A the same as s iopc l ~ roi B!

Table 3 . Stress Contrast Definitions

3 Storage by package--1 Is difference between slope of HDPE4 anti slope of

HDPEYI the wm e f i x R T :ind S'WRSS'!

3 Storage hy pcknge-2 I \ difference between slope of blister '~n d he aveldge

h u e oi HDFE th e \ame iur RT m d STRESS'

3 Storage by strength-2 I \ difference between slope o i Z i l mg and tne average

siope of' i O and 3 0 mg ihc same fo r RT aridn-,-r, r . P " , >

.> I K C 3 3 . '

3 Storage by iot i \ differnce bcru~cen ivpe of i o r i'i and slope oi' lot 3the sarnc for KT and STRESS'?

4 KT vs . STRESS Is slope of KT the same as siope at STRESS'!

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Figure 1. P o wer o f package by srrcngth- 1 1 . 12--monthR T analysis

Figure 2 . P o w e r ot packaze by mength-12, 12- tnonth R T d n a l y s ~ s

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Figure 3 . Power of packdgc by strength-2i, 1 2 -m o n th R T anxlys i s

Figure 4. P o w e r o t p a c k a g e b y streng th-22 , 12-month R T a n d l q s ~ \

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Design

Figure 5. Powcr of HDPE v s . blister, 12-mon th K T analysis

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Figure 8. P o w c r of \ t rength 20 vs o t he r s , 12-month RT a n a l y \ ~ \

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The PROC GLM models arc as follows.

Each mode? h2s separate :nterc:epis fo r each i i j t hy strength i i . ~ . . f a each!,. <.+-xi i , f r . , 3 , i 1 has separate slopes for each pac?.age-h~i-ctrr,noth

Ld&lSbl lC IJClLLIIJ . L V I \ I C I b I I- J L ' - - - - - - - - A -

ccrnbinar ion and has separate s!opes f o r each lot Model 2 has separate slopes

for each !ot. for each strength, and for each package. Modei 1 is used to tesr

thc A:':fi:':S tern1 a nd associated contrasts and thus io answer question I in the

General Soliltion secilori above. If the A4'P4 'S term ar,d associated contrastsare not significant, then rnodei 2 is used for further analysis, i .e . , to answer

questions 2-4.

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E'ipre I n . P~ lw e r f storage hy package-1; 6-month RT and stress anaiysis

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& - ; r r . . m. ,,,, 1 1 . P o ~ c : l' s torage by package--2. 6-;non:h R? 2nd ;:ic;s xna!y.;is

Design

Figure 1 2 . P o w e r o f s torage by s t r eng t h - ] , & m ont h R T and stress analysis

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Figure 14. Power o i storage by l o t . 6-irionth K T and stress ana lhh is

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Figure 15. Power of KT vs . stress. 6 -mon th KT and stress arialyarn

Code RT timepoints tested STRESS timepoints tested

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(continued)

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"See Table 4 !'or code d e f i n i t l o n i .

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Stress Statisticia

i n addirion ro ihe notation previousiy defined, notariori is as n'oliows:

Each model h as separate intercepts for each lot by strength. I\/Iodel 3 has

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.----: r ii i

j ! t i 3, ,

11 iiii. -,-,i ,()()

separate slopes for each lot by storage condition, for each strength by storage

condition, for each package by storage condiiion, arid f o r each package by

strength. Mnde! 4 is sirni!ar lo model I but also has a separate siope for each

slorzge condition. The powx!: fcr whether the contrasts listed in Tabk 3 are. .

Zen: caiculatp,d 2s &scribed g!.euloilsivJ .

Ir is possibje ro pai r each of th e i O stress design:, with each of the 10 RT

designs, and then to evaluate each of these lrIjO designs. Owing to spacelimitations, oniy designs whcre th e same design is used for both RT and stress

are considered.

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Two main approaches for reducing the cost of stability studies have been

investigated:

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, . . . .i p<><?c,;(j L > p ~ pL \ ~ ; ~ ~ i ~ ; ) , ~ ~ ; < ~ ~ : : p ., l ( ( p ! ! J ? p ( I T A&pp f , t { ( r ?L7 > ( - , < . j ~ ~ r ! t 7 r ~ ~ ( : ~ l ( ~ ~ l;> r $<> yfg&{!j;\;L

- . . - -,.* LJ !>".,.<>< , , ' > , f t?;/,;,l<31(.<-

< * , 3 : " > 7 :,,,- i I , - I T # ? L . Ipc! 3.kt.>i<zz!<-5. {-jt$z:;e ! ?? ;-$r!-!,<~cq!;k:yg,, :::s,: -.:v.;u :::::. :z ::t ,. :..,: :

.,,:,; .,-,.,; m : . . : t i . x x y . : < n c , 7c!s,. ....,,% % - . % . 7%<!r"p.~.,8tfi'- ? 2 2 , , i - 7 , - :

? :,.L- !:\1:". \'tirr;r,r;,.,,ri !):...,,...:? , , r , ~ : , ~ r ! l l J . . - ; . ,.; L kr!.fl:-;rr.r,,?~,. hl:!:.!r.(jl:r.: NIA\\iy<\r& C>! 1&. j i i i i i i ,. ,,". L , , . , . b . , L * . ". .,- ,.&.. 1 ... ' ,.,... $9 A. . * , . . ...I I..... I.-..I." .I..I... 1 1 - 1 . -... - i

&.-L..~, , r , , , , , , , n c... 0. ;';;~ !)iz.ii,yn wid :,;;uiv.ci.; ;:'i<,~i;;,rki:r;t:.~. ricgc:.. Hu::tir.~:c:n. Nk'. 1973. . .

4, Selr!c SK : I t j . !cor. &f:::jph WI!~.:., New Yo rk , 1Y- i i

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