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Pharmaceutical Technology Europe BIO/PHARMA OUTSOURCING INNOVATION eBOOK 2022 13 to use a calibrator and then add the positive control to a plate, however, as this doubles the analytical error. Figure 1 shows the systems suitability back-calculated from a fixed position on the reference standard. Validity criteria for signal control Before relative potency of a test article to a reference stan- dard can be calculated, it is crucial to verify that there is a clear signal from the dose response for the reference standard. There are two methods for verifying a reliable signal; the dose response test and curve depth. Based upon health authority input, the dose response test is a standard approach to show signal-to-noise control. The dose test measures the effect of analyte concentration, which is used to generate a statistically significant signal (alpha = 0.05, two-sided). A regression model may be linear, square root, log, three parameter exponential model, or four pa- rameter logistic regression (4PL), depending on the method. The curve depth of the reference standard is another method to demonstrate a clear signal. Curve depth is the mean signal for the highest concentration subtracted from the mean signal from the lowest concentration. For assays using 4PL fit, curve depth is calculated by subtracting the lower asymptote of the standard from the upper asymptote of the standard (Figure 2). Normally the limit is set at 50% of the curve depth from qualification or validation assay runs. R 2 of a fitted curve is not recommended for a validity cri- terion, but should be for report-only. Confidence intervals (CIs) of the reportable value are a more reliable indication of the errors in quantitation due to curve fitting. Validity criteria for bioassy parallelism USP <1032> defines parallelism as the following: "A quality in which the concentration–response curves of the Test sample and the Reference Standard are identi- cal in shape and differ only by a horizontal difference that is a constant function of relative potency" (3). Parallelism must be evaluated as a validity criterion be- cause parallelism between the test article and reference stan- dard demonstrates that the two are similar, and, therefore, relative potency may be determined. F-tests for parallelism are not recommended because they are too sensitive and may cause a high degree of invalid results. Demonstrating parallelism in a bioassay is done for a sig- moidal curve and may be evaluated using the upper asymptote ratio (UAR). The UAR is compared to a two-sided limit. If the ratio of the upper asymptote for the reference standard and the UAR for the test article is within defined limits, then the curves can be constrained, and relative potency can be calculated. UAR only checks parallelism at one point on the sigmoidal curve. Slope ratios may be used for a parallel line analysis of the reference and test article. A highly recommended method for determining parallelism is the absolute difference between the relative potency of the unconstrained model and the con- strained model. This measures how the forcing function of constraining the curves changes the reported relative potency. An equivalence test may be used in evaluating the UAR. If the slope ratio is outside of the equivalence bounds, the assay run fails parallelism and is invalid. Figure 3 is a parallelism test example with a resulting slope ratio of 0.993. Linearity ratio calculation for bioassays A bioassay also has a requirement to be linear in the dose response. The Linearity Ratio method of analysis uses a measure of curvature relative to the linear line rather than a measure of probability by comparing the effect size at- tributed to the quadratic term (curve) to the effect size at- tributed to the linear term in the full model. In practical terms, the question of linearity is, what percentage of the linear line is curvature? A scaled estimate for the linear term is half the change in the signal over the range (distance from centre). To deter- mine the full change over the range linear effect of concen- tration, it must be multiplied by two. The quadratic term is curving and ½ the range is the full curvature, which is then divided by full change in the linear signal. 1.8 � - - - - - - - - - - � 1. 6 � U neon ECS0 1 .45 --- --- - --- 0 � 1.2 1.0 0.8 • • 0. 6 �����-��� N Log Dose 0 N !_quivalence between Sample 1 an� Reference 1.75 - 1.5 1.25 - . Q 1.00 0.75 - 0.5 0.25 - 0.00 - a= 0.05 I u C Equivalence Summary Parameter 0 UDL LDL Lower Upper Limit Level Confidence Limit Ratio Confidence Limit Exceeded Intercept 0.92958 0.955834 0.982089 Slope 0.747411 � 1.239282 Figure 1. Systems suitability at a fixed position. 1.8 � - - - - - - - - - - � 1. 6 � U neon ECS0 1 .45 --- --- - --- 0 � 1.2 1.0 0.8 • • 0. 6 �����-��� N Log Dose 0 N !_quivalence between Sample 1 an� Reference 1.75 - 1.5 1.25 - . Q 1.00 0.75 - 0.5 0.25 - 0.00 - a= 0.05 I u C Equivalence Summary Parameter 0 UDL LDL Lower Upper Limit Level Confidence Limit Ratio Confidence Limit Exceeded Intercept 0.92958 0.955834 0.982089 Slope 0.747411 � 1.239282 Figure 2. Curve depth comparison. Systems suitability should be understood to be separate from validity criteria. ALL FIGURES ARE COURTESY OF THE AUTHORS.