where t is the average of t, C is the average of C, and b is constant, the confidence interval of the time at which drug content diverges from specifications, determined by regression analysis of n sets of time-content data, is described by tL = t + Ut-T)g±—B
where t' is the one-sided Student's t valuk with degrees of freedom and n -2.
The shelf life (the lower confidence limit of the time at which the drug content diverges from the specification range) can thus be estimated. When the lower limit of content specification is 90%, the shelf life corresponds to tL at C of 90%. If Ve is large or b is small, shelf life cannot be estimated because the value of g must be not less than 1. Because the confidence interval becomes narrowest at fas shown in Fig. 192, a more precise estimate of shelf life can be obtained by extrapolating the regression curve determined from a larger number of time-content data points at larger t.
The Carstensen equation is used to calculate the confidence limit of C at a specific t765:
Figure 192. Time-drug content curve with 95% confidence intervals. A zero-order degradation of 2%/year was assumed. Assay error was assumed to be 2% standard deviation. , 95% significant limit calculated from data represented by open circles;---, 95% significant limit calculated from all the data including data represented by open triangles.
where k is the average annual rate constant. Thus, whereas the Woolfe equation allows one to estimate the confidence limit of t as a function of C, the Carstensen equation permits estimation of the confidence limit of C as a function of t.
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