EVALUATION OF NON-ACCELERATED STABILITY DATA. Kathleen Karpenter Dietrich and Daniel L. Weiner Merrell Dow Pharmaceuticals Inc. 1. Y ij. 2. Y a. + bx.

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1 VALUATIO OF O-ACCLRATD STABILITY DATA Kathleen Karpenter Dietrich and Daniel L. Weiner Merrell Dow Pharmaceuticals Inc. Abstract A package of SAS macros has been written which allows users to evaluate the data acquired from a stability program. The package first reads the data from an ASCII disk file, prints descriptive reports, and creates graphs using SAS/GRAPH. ext, the packag2 fits several linear models to the data and determines which model fits best. If the chosen model is a straight line and if the slope is significantly different from zero, a shelf life will be estimated. Finally, a report is written which summarizes ~he results corresponding to the appropriate model. Background To quantify shelf life, characteristics indicative of that particular product's deterioration are monitored over time. Collectively, m2asurements of deterioration are referred to as stability measurements. The goal of shelf life estimation is to predict the time when some measure of stability will no longer be within preset specification limits. These limits demarcate a range, and provided the measure of stability is within that range, the identity, strength, purity, and quality of that drug can be assured. Commonly used specification limits are the standards established by the United States Pharmacopeial Convention (USP). The USP is a nonprofit organization that sets standards which are recognized by the Food, Drug, and Cosmetic Act as the minimum standards of strength, quality, and purity. If a drug fails to meet these standards, the Food and Drug Administration can seize it or ask the manufacturer to recall it. Shelf Life stimation A long-term stability study under ambient conditions is required by the Food and Drug Administration (FDA) and is referred to as nonaccelerated testing. Stability measurements are obtained at the initial time of manufacture (sometimes referred to as the time of release) and at time points such 3, 6, 9, 12, 24, 36, 48, and 60 months, thereafter. The FDA will not allow a shelf life in excess of 60 months; therefore. most manufacturers do not collect stability data beyond this time period. Table I is an example of a typical data set resulting from a long-term stability study. The data are expressed as a percentage of the labeled strength of the active ingredient. otice that most of the observations occur at the time paints of 12 months or less. Also, the data are not balanced; this is because the batches are manufactured at different times, and, consequently, are not entered 10to the stability program at the same time. If a linear model 1s found to adequately fit the data, then a shelf life that has been proposed is the time at which the lower (or upper) 95% confidence band about the estimated degradation curve intersects the acceptable lower (or upper) specification limit (Patel, 1980; Dykstra, 1980). In Figure 1, the shelf life is the time denoted by the arrow-. Because stability data consist of measurements from several batches, differences between batches may possibly exist. So, the model that "bestl! describes the degradation with respect to time must be found. The first step of this process is to test for nonlinearity. If the F-test for deviation from linearity is not significant, the degradation will be described best by one of the following models. 1. Y ij a. 1 + bix j 2. Y a. + bx. ij 1 J 3. Y a ij + bx. J For the above models. y.. is the jth stability measurement from f~e ith batch and X. is the time of the jth stability mjasur~ment. Modell indicates that an individual slope and intercept for each batch is the appropriate degradation model. Model 2 indicates that the batches are degrading at the same rate, but a separate intercept is necessary for each batch. Model 3 indicates that a common line 1s adequate to describe the degradation of all the batches. For model I, a shelf life must be estimated for each batch. The shelf life estimate for the ith batch may be written as follows: where M is the acceptable market limit t = t(ni-l, 1-~/2) is the usual t-statistic with n -1 degrees of 1 freedom is the number of observations for the ith batch SXX i is the corrected sum of squares of time points for the ith batch s is the square root of the mean square error associated with the degradation model gi = t2s2/btsxxi 317

2 The II.:!:" above depends on the sign of b i For wodel 2, also, a shelf life must be estimated for each batch. But. since the batches are degrading at the same rate, the data are pooled to obtain the values b, Sxx, and g. When model 3 is appropriate, one shelf life may be estimated using the information from all of the batches. In this case, a 1 a for all batches, b i _= b for all batches. and pooled values of X, Sxx, n, and g are obtained. To the nonstatistician, finding the appropriate model and then obtaining the correct shelf life estimate seems to be a formidable undertaking. In addition, the shelf life estimate is usually required quickly. So, the information system described in the next section was developed to meet the needs of the nonstatistician. The Stability Monitoring Package This package provides statistical support, first, by finding an adequate model for the product's degradation using appropriate statistical tests. Second, the shelf life estimate corresponding to that model is calculated. Since macros are the backbone of th1s package, the actual SAS statements and the statistical testing are unapparent. In order to use this package, the stability data, which are stored in an IQUIR database. are written to an ASCII disk file. The first record of this file must contain the catalog number, product name. stability test name, upper market limit, lower market limit, and the labeled or theoretical amount of active ingredient. The subsequent input records must have the batch label in the first field followed by the stability measurements for each t~e station. If an observation is not available for a particular time station, then that must be indicated with a missing value code. To illustrate the abilities of this package, the data from a typical stability study are used as an example. The first report, shown in Table I is a listing of the raw data expressed as percent of theory. The uppercase "" indicates a stability measurement was not obtained for that time station and batch. The next few pages of output, which are not shown, list the frequency distributions for all the variables in the input data set. These are to be used as an edit check. The minimum, maximum~ and frequency distribution for each variable must be inspected to locate unreasonable values. Further, logic checks should be performed as dictated by the structure of the data. The report shown in Table II gives univariate statistics for each batch. In addition, statistics obtained by pooling all of the data are given and denoted by the label name "POOLD". For this particular data set, model 2 was determined by the program to adequately fit the data. The report shown in Table III lists the results of fitting model 2 to the data and estimating a shelf life. Since model 2 was fit to these data, there is an individual shelf life estimate for each batch. This portion of the paekage relies heavily upon the three macros written by Roger S. Cohen (1981). These macros "capture" the output from. FROC GlM and place the statistics into data sets. To find the rlbest" model, several models are fit to the data, and F-statistics for each are examined. If the best model is not linear, a message will be printed to that effect, and all further processing will be terminated. If the best model has a nonsignificant slope, again, a message will be printed and all processing will be terminated. If a linear model is found to be adequate and if the slope is significantly different from zero, the final report will be printed listing the parameter estimates. If either the slope or intercept is determined to be different for each label, then separate parameter estimates are printed for each label. Once the model has been identified, shelf life estimates are obtained using one of the equations previously described. These estimates are listed in Table III, in addition to the parameter estimates. Figures 2-4 illustrate the graphics that may be obtained using this package. Figure 2 shows the average trend over time. Figure 3 indicates the distribution of the data at each sampling time. Figure 4 shows the degradation of each batch over time. Armed with this package of macros, the nonstatistician should be able to evaluate routine stability data in a t~ely fashion. If the data are peculiar, there are built in messages referring the user to a statistician. and the graphs will give the statistician a starting point to help identify the problems. References Cohen, R.S. "A Triad of SAS Macros to Capture the Output from PROC GLM," Proceedings of the Sixth Annual SAS Users Group International Conference, Orlando, FL, 1981, pp Dykstra, O. "The Acquisition and Analysis of Stability Data," paper presented at the Annual Meeting of the Biostatistics Subsection, Pharmaceutical Manufacturers Association, Tarpon Springs, FL. October 5-8, Patel, R.M. "Stability and the FDA Guidelines." paper presented a't the 13th Annual Industrial Pharmacy Management Conference, Madison, WI, October 13,

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