In-vitro dissolution testing is a critical component in the quality control of manufactured drug products. The $\mathrm{f}_2$ statistic is the standard for assessing similarity between two dissolution profiles. However, the $\mathrm{f}_2$ statistic has known limitations: it lacks an uncertainty estimate, is a discrete-time metric, and is a biased measure, calculating the differences between profiles at discrete time points. To address these limitations, we propose a Gaussian Process (GP) with a dissolution spline kernel for dissolution profile comparison. The dissolution spline kernel is a new spline kernel using logistic functions as its basis functions, enabling the GP to capture the expected monotonic increase in dissolution curves. This results in better predictions of dissolution curves. This new GP model reduces bias in the $\mathrm{f}_2$ calculation by allowing predictions to be interpolated in time between observed values, and provides uncertainty quantification. We assess the model's performance through simulations and real datasets, demonstrating its improvement over a previous GP-based model introduced for dissolution testing. We also show that the new model can be adapted to include dissolution-specific covariates. Applying the model to real ibuprofen dissolution data under various conditions, we demonstrate its ability to extrapolate curve shapes across different experimental settings.

翻译：体外溶出测试是药品生产质量控制的关键环节。$\mathrm{f}_2$统计量是评估两条溶出曲线相似性的标准指标。然而，$\mathrm{f}_2$统计量存在已知的局限性：缺乏不确定性估计、属于离散时间度量，并且作为一种有偏估计，仅计算离散时间点上的曲线差异。为应对这些局限，我们提出了一种采用溶出样条核的高斯过程（GP）用于溶出曲线比较。溶出样条核是一种以逻辑函数为基函数的新型样条核，使GP能够捕捉溶出曲线预期的单调递增特性，从而获得更好的溶出曲线预测效果。该新型GP模型通过在观测值之间进行时间插值预测，降低了$\mathrm{f}_2$计算中的偏差，并提供了不确定性量化。我们通过模拟和真实数据集评估了模型的性能，证明其相较于先前为溶出测试引入的基于GP的模型有所改进。我们还展示了新模型可扩展至包含溶出特异性协变量。通过将模型应用于不同条件下的真实布洛芬溶出数据，我们证明了其在不同实验设置间外推曲线形态的能力。