Shelf life calculation of drugs

Shelf life calculation of drugs- ASEAN GUIDELINES

1. SHELF LIFE CALCULATION
Shelf life is the period of time, from the date of manufacture, that a drug product is expected to remain within its approved
product specification while stored under defined conditions. Shelf life is typically expressed in units of months, i.e. 24
months, 36 months, to a maximum of 60 months.
PURPOSE:
To establish a shelf life defined as that time when one can be 95% confident that a product contains not less than the lower
specification limit e.g. 90% of the drug.
Note; three batches were included in the study. Preliminary evaluation indicated that the batch-to-batch variation was
satisfactory and therefore the data could be combined.

month Assay Average
x x2 x-x̄ (x-x̄)² Y1 Y2 Y3 (Y1)² (Y2)² (Y3)² XY
0 0 -8 64 51 51 53 2601 2601 2809 51.7 0
3 27 -5 25 51 50 52 2601 2500 2704 51.0 459
6 108 -2 4 50 52 48 2500 2704 2304 50.0 900
9 243 1 1 49 51 51 2401 2601 2601 50.3 1359
12 432 4 16 49 48 47 2401 2304 2209 48.0 1728
18 972 10 100 47 45 49 2209 2025 2401 47.0 2538

Ʃx= 144

Ʃ(x-x̄)²= 630 Ʃy= 894

Ʃxy= 6984
N= 18

Ʃy²= 44476


Ʃx²= 1782
x̄= 8

ӯ= 49.67

2. SHELF LIFE CALCULATION

Y1 (y1-ӯ) (y1-ӯ)² Y2 (y2-ӯ) (y2-ӯ)² Y3 (y3-ӯ) (y3-ӯ)²


51 1.33 1.8 51 1.33 1.8 53 3.33 11.1


51 1.33 1.8 50 0.33 0.1 52 2.33 5.4


50 0.33 0.1 52 2.33 5.4 48 -1.67 2.8


49 -0.67 0.4 51 1.33 1.8 51 1.33 1.8


49 -0.67 0.4 48 -1.67 2.8 47 -2.67 7.1


47 -2.67 7.1 45 -4.67 21.8 49 -0.67 0.4


total= 11.7

total= 33.7

total= 28.6



Ʃ(y-ӯ)²= 74


i. examination of the graph indicates that the linear relationship would be a reasonable represntation of the data.

ii. In this case one will assume that the concentration and time are truly linearly related, i.e:


C= Co-K x t


Where: C= Concentration at time t


Co= Concentration at time 0


k = rate constant


t = time (storage time)


iii. Estimation of the slope and intercept of the least squares (regression) line:

equations:


ӯ= a + b x̄



a = y intercept


b = slope


C = Co - kt


Hence k = -b


or k = - slope

3. SHELF LIFE CALCULATION
b= N x ƩXY -ƩX x Ʃy -3024

N x ƩX² - (ƩX)² 11340

b= -0.267 mg/month, k= 0.267
a= ӯ-b x x̄
a= 51.8

iv. The equation for a straight line best fit is therefore:



C = Co - k x t



C=51.8 - 0.267 x t

v. the variance estimate, S²xy represents the variability of tablet potency at a fixed time, assuming it is equivalent across all
time points.



S²xy = [ƩY²-(ƩY)²/N]-[b² x Ʃ(x- x̄)²]/N-2


S²xy = 1.825


Sxy= 1.35
vi. To calculate the time at which the tablet potency is 90% (45 mg) of the labeled amount, solve for t when


C= 45 ,i.e.:


t=
(Co -
C)/k


t= 25.5 months., (X=25.5)


X
mean= 17.5

4. SHELF LIFE CALCULATION
vii. Lower 95% confidence interval of the mean time.


since one is intrested in being 95% confident that at expiry the concentration is not less than 45 mg (90%) confidence limit for
mean time estimate

confidence interval for true X (time) at a given value for Y.


The lower 95% confidence interval is equal to:



[(X-(g x x̄)]-[t x (Sxy)/b x √((1-g)/N+[(x-x̄)²/Ʃ(x-x̄)²])


(1-g)



where g= t² x (Sxy)


(b² x [Ʃ(x-x̄)²]


vii. For example: Y= 45 mg, X= 25.5 months; for one sided confidence interval :


tN-2 = t16,0.975 = 2.12




g= 0.183


(1-g)= 0.817



The lower confidence interval is:



months= 19.8

REFERENCE: Operational Manual for Implementation of GMP (Asean Guidelines)