Copy of patient data.xlsx from Hyperthyroidism in the personalized medicine era: the rise of mathematical optimization

Thyroid over-activity or hyperthyroidism constitutes a significant morbidity afflicting the world. The current medical practice of dose titration of anti-thyroid drug (ATD) treatment for hyperthyroidism is relatively archaic, being based on arbitrary and time-consuming trending of thyroid function that requires multiple clinic monitoring visits before an optimal dose is found. This prompts a re-examination into more deterministic and efficient treatment approaches in the present personalized medicine era. Our research project seeks to develop a personalized medicine model that facilitates optimal drug dosing via the titration regimen. We analysed 49 patients' data consisting of drug dosage, time period and serum free thyroxine (FT4). Ordinary differential equation modelling was applied to describe the dynamic behaviour of FT4 concentration. With each patient's data, an optimization model was developed to determine parameters of synthesis rate, decay rate and IC₅₀. We derived the closed-form time- and dose-dependent solution which allowed explicit estimates of personalized predicted FT4. Our equation system involving time, drug dosage and FT4 can be solved for any variable provided the values of the other two are known. Compared against actual FT4 data within a tolerance, we demonstrated the feasibility of predicting the FT4 subsequent to any prescribed dose of ATD with favourable accuracy using the initial three to five patient-visits' data respectively. This proposed mathematical model may assist clinicians in rapid determination of optimal ATD doses within allowable prescription limits to achieve any desired FT4 within a specified treatment period to accelerate the attainment of euthyroid targets.

甲状腺功能亢进（hyperthyroidism）是全球范围内造成显著疾病负担的常见病症。目前临床针对甲状腺功能亢进的抗甲状腺药物（anti-thyroid drug, ATD）剂量滴定治疗方案仍相对陈旧：其基于主观性较强且耗时的甲状腺功能趋势监测，患者需多次前往门诊进行指标监测，方可确定最优给药剂量。这促使我们在当前个性化医疗时代，重新审视更具确定性与高效性的治疗方案。本研究旨在开发一款个性化医疗模型，通过剂量滴定方案辅助确定最优给药剂量。我们分析了49例患者的临床数据，涵盖药物剂量、监测周期与血清游离甲状腺素（serum free thyroxine, FT4）三项指标。采用常微分方程（ordinary differential equation, ODE）建模以描述FT4浓度的动态变化特征；针对每例患者的临床数据，构建优化模型以确定合成速率、降解速率与半数抑制浓度（IC₅₀）三项参数。我们推导得到了与时间和给药剂量相关的闭式解析解，可对个性化预测的FT4水平进行明确估算。针对包含时间、药物剂量与FT4的方程组，若已知其中两项变量的数值，即可求解得到第三项变量的结果。将模型预测结果与实际FT4检测值在允许误差范围内进行比对后，我们验证了：仅利用患者前3次或前5次门诊的就诊数据，即可精准预测任意ATD给药剂量后的FT4水平，具备良好的预测精度。本研究提出的数学模型可帮助临床医生在处方允许范围内快速确定最优ATD给药剂量，从而在既定治疗周期内将FT4水平调控至目标值，加速实现甲状腺功能正常（euthyroid）的治疗目标。