Prostate cancer is a common cancer among males in the USA and is often treated by intermittent androgen deprivation therapy. This therapy requires a patient to alternate between periods of androgen suppression treatment and no treatment. Prostate-specific antigen levels are used to track relative changes in tumor volume of prostate cancer patients undergoing intermittent androgen deprivation therapy. During this therapy, there is a pause between treatment cycles. Traditionally, continuous ordinary differential equations are used to estimate prostate-specific antigen levels. In this paper, we use dynamic equations to estimate prostate-specific antigen levels and construct a novel time scale model to account for both continuous and discrete time simultaneously. This allows us to account for breaks between treatment cycles. Using empirical data sets of prostate-specific antigen levels, a known bio-marker of prostate cancer, across multiple patients, we fit our model and use least squares to estimate two parameter values. We then compare our model to the data and find a resemblance on treatment intervals similar to our time scale.

中文翻译：

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一种模拟前列腺癌间歇性激素治疗的时间尺度方法

前列腺癌是美国男性常见的癌症，通常通过间歇性雄激素剥夺疗法进行治疗。这种疗法需要患者在雄激素抑制治疗和不治疗之间交替。前列腺特异性抗原水平用于跟踪接受间歇性雄激素剥夺治疗的前列腺癌患者肿瘤体积的相对变化。在此治疗期间，治疗周期之间存在暂停。传统上，连续常微分方程用于估计前列腺特异性抗原水平。在本文中，我们使用动态方程来估计前列腺特异性抗原水平，并构建一个新的时间尺度模型来同时考虑连续和离散时间。这使我们能够考虑治疗周期之间的中断。使用前列腺特异性抗原水平的经验数据集，前列腺癌的已知生物标志物，在多个患者中，我们拟合我们的模型并使用最小二乘法来估计两个参数值。然后我们将我们的模型与数据进行比较，并找到与我们的时间尺度相似的治疗间隔的相似之处。