Shelf-life calculation

Figure 4.26. Shelf-life calculation for active components A and B in a cream see data file CREAM.dat. The horizontals are at the j = 90 (specification limit at t = shelflife) resp. y = 95% (release limit) levels. The linear regression line is extrapolated until the lower 90%-confidence limit for Kfl = a + h x intersects the SLs the integer value of the real intersection point is used. The intercept is at 104.3%.

Preliminary Shelf Life Calculation from Stressed Data... 

The shelf life for a single batch is usually computed based on regression techniques. An appropriate approach to shelf life estimation when using regression analysis is by calculating the earliest time at which the 95% confidence limit for the mean intersects the proposed acceptance criterion [8]. A detailed description of shelf life calculations is provided in Sections 7.2.3 and 7.2.4. 

A numerical example is presented below to illustrate, step by step, the shelf-life calculation procedure. 

Example 5 Multiple-Factor Stability Study A well-known example introduced by Shao and Chow [19] is used to illustrate the application of shelf life calculations for a multifactor case. A stability study was conducted on a 300-mg tablet of a drug product to establish the shelf life for each of the two types of packages used for this product bottle and blister. The results are shown in Table 24. Each type of package includes five batches. The tablets were tested for potency at 0, 3, 6, 9,12, and 18 months. Determine the shelf life based on these stability data. 

Simplified shelf-life calculation. For many applications, the steady-state permeation equation (Eq. 11.10) is an acceptable approximation to correlate a product s shelf life x with package area A, wall thickness (, and environmental conditions of pressure and temperature. This approximation is valid for thin films and when the time to reach steady-state fiow rate, fjj, is very small compared with the package shelf life. Consider a permeation process through a container wall as illustrated in Fig. 11.20. 

Suppose an initial rate of reaction Vq is measured in the first few percentage of a reaction. Calculate the shelf life (tgo) if... 

An algorithm for calculating the symmetrical (two-tailed) /-factors for p = 0.1 is incorporated its use corresponds to the statement that the probability that measurements on a future batch, given the linear trend already established, will inadvertently be found to be below the specification limits of Y% of nominal, at a shelf-life that would lead one to expect a residual content at or above the specification limit, is p = 0.05. ... 

False. Use-by dates have been carefully calculated by manufacturers to indicate how long a product can be stored before it becomes less safe to eat. Poor storage can shorten this shelf life . 

Stability is then considered as known and defined when Rf Uj is not significantly different from one. However the uncertainty calculated for the ratio RT based on the sum of CVs of two measurements carried out at two temperatures is a CV and not a confidence interval. In fact it does not consider the number of measurements carried out at the two temperatures and the use of this combined CV is not correct. In many cases it is an underestimation, as usually only two or three replicates are made. However, stability should be determined on the basis of a trend analysis, which is of importance also for any shelf life quantification see below. 

This section considers the stability analysis of the long-term studies. The purpose of this section is to provide a set of fundamental statistical tools to calculate the shelf life for single and multiple packages and strengths. The statistical methods will be... 

The regression subroutine also provides the following calculations MSE = 2.407, x = 10.8571, and Sxx = 1.754.6. Thus, to determine the shelf life, the following equation can be used ... 

Minimum Approach for Multiple Batches When the hypothesis for equality of slopes is rejected at the 0.25 significance level, the minimum approach should be implemented. This is because the degradation lines of individual batches cannot be considered the same since they have different degradation rates. In this situation the FDA guideline establishes that the overall expiration dating period has to ensure that the product will remain within acceptable limits regardless of the batch from which it comes. Thus, the shelf life for each batch is calculated and the expiration dating period is based on the lowest of all shelf lives. Mathematically, this can be expressed as... 

The reference point for this equation is xref = 41.89 and the initial point to accomplish convergence is xref - 7. The root for this equation is xR(l) = 33.25 and the shelf life for batch 1 is xL(l) = 33 months. Since the sampling times are the same for all batches, the following values remain invariant for all batches n = 12, x = 8, Sxx = 420, and to.o5,io = 1.8125. The values required by the quadratic equation and the associated shelf life for each batch are given in Table 27. The computer program to perform this calculation is given in the Appendix. 

Chemical reaction kinetics can be used to evaluate degradation data at accelerated conditions and predict the drug product assay at normal conditions for periods longer than the proposed shelf life. This is applicable to limited cases because the reaction kinetics is often complex for drug products. The following example illustrates the procedure to follow to calculate the API concentration with time for a drug product stored at normal conditions when such data are not yet available. 

Preliminary shelf life can be calculated based on accelerated results. Regression techniques described in Section 7.2.3 applies to the estimation assays obtained from... 

This Appendix contains four computer programs in MatLab that can be used by the reader to perform typical calculations related to shelf-life estimations. 

Case 2. Linearity demonstrated from 50% of the ICH reporting limit to 150% of the shelf life specification of related substance. No significant y-intcrccpt is observed (Figure 3.7). In this case, a high-low calculation is more suitable, as... 

Using the known Q (e.g. expressed in volume at STP) allows calculation of the amount of CO2 the package will lose, V OSS (also at STP), by the end of its shelf-life time t ... 

A precondition for the optimization of a package having a specified minimum shelf life date for a food with a known oxygen and/or water sensitivity is the calculation of the permeability of laminate structures. The total permeability Qv of a laminate film made from n different plastic layers with thicknesses d, and having permeability coefficients of Pj can be calculated using the following formula ... 

The simplest estimation of migration is to use the mass balance calculation shown in Eq. (14-1) below. This equation assumes that all of the styrene found in the polymer will migrate into the food instantly. This is of course not realistic but the estimation gives an upper limit to the possible migration that could occur at the end of the product s shelf life. 

Example 14-5 Calculate the maximum allowable amount of styrene monomer (Mr = 104.2) that can be allowed in a PS thermoformed portion pack with foil lid (7.5 g product) for condensed milk (see Example 14-1). Assume that based on experience a concentration above 300 pg/kg in the product will produce an off-flavor and lead to consumer complaints. The package surface area to food mass ratio ( ) is jf = 1.5 cm2 g . The product is shelf stable and has an intended shelf life of 6 months. 

Figures 14-1 and 14-2 show estimations of shelf life in a 7.5 g PS containing portion pack before two different taste threshold concentrations (2 and 0.1 mg/kg) of styrene are exceeded in the product. In each graph the diffusion coefficients from Linssen et al. (1992) for a 1 1 PS HIPS polymer blend at room temperature (23 °C) and refrigeration temperature (4 °C) are used. The estimation using Eq. (14-5) at 23 °C and 4 °C and an calculated apparent diffusion coefficient for PS/PE and PS/EVOH/PE structures (see Table 14-3) are used in Eq. (14-4) (see example 14-5) to calculate the days before a styrene taint is detected in the product. The shelf life is decreased by a factor of the square of the increase in the material s residual styrene content. As seen in Figures 14-1 and 14-2 a reduction in the taste threshold by a factor of ten means almost a 100 times decrease in the shelf life.

As shown in Equation (5.14a) and Equation (5.14b), the half-life and the shelf-life are constant and independent of the drug concentration, [A]0. For example, if the half-life of a first-order reaction is 124 days, it takes 124 days for a drug to decompose to 0.5 [A]0. Also it takes another 124 days for 50% of the remaining 50% of the drug to decompose. In Equation (5.13), the time required for 100% degradation cannot be calculated because In ([A] / [A]o) is an indefinite number. 

An initial assay of a solution product indicated a concentration of 5.5 mg/mL. Eighteen months later, however, an assay showed only 4.2 mg/mL. Assuming that both of the above assays were accurate, calculate the rate constant and shelf-life (10% degradation) ... 

A drug is hydrolyzed via a first-order reaction in a solution. The solubility of the drug in water is 3.5 mg/lOOmL. A pharmacist made a suspension formulation of the drug containing 2.7 mg/mL. The shelf-life of the suspension was 15 days. Calculate the half-life of the solution. 

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