Name: a method of trigonometric modelling of seasonal variation demonstrated with multiple sclerosis relapse data
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The authors would like to thank Ivan Hanigan for his support in extracting and interpreting the ultraviolet radiation satellite data. The work was supported by the NHMRC Career Development Award (Clinical) to HB [ID628856], NHMRC Project Grant [1032484], NHMRC Center for Research Excellence [Grant ID 1001216] and the MSBase Foundation. The MSBase Foundation is a not-for-profit organization that receives support from Merck Serono, Biogen Idec, Novartis Pharma, Bayer-Schering, Sanofi-Aventis and BioCSL. RL is supported by a NHMRC Career Development Award [ID 1004898].

注:所述对应的Stata的代码段在提供的代码文件相同数目的每个步骤。 Stata的命令名称已被斜体在以下协议。 1.准备并绘制观察到的复发发病数据<ol><li>通过点击"新建待办事项文件编辑器"按钮，打开一个做文件，并使用生成的命令来计算追溯至每十二个日历月为三个地理层次的复发起始点的号码为蓝本:位置，半球和全球性的。通过点击DO-文件中的"执行（做）"做文件操作按钮的动作命令。 </li><li>使用swilk或sktest命令测试复发计数使用夏皮罗-威尔克或修改Jarque-Bera检验的位置总复发数据的基础分布正常或分别分解患者水平复发的数据。选择的代码，然后单击"执行（做）"。 38,39。 </li><li>使用生成命令创建一个新的变量"north_month"的南半球日历个月+6偏移，允许北部和南半球复发绘制季节沿同一水平轴线。选择的代码，然后单击"执行（做）"。 <ol><li>图的观察每月复发起始点与y轴和日历月份对x轴为使用双向散射命令每个半球复发频率的散点图。重复每个位置。通过查看图查看器中自动打开屏幕的每个情节观察波峰和波谷的复发发生在历年的模式。 </li></ol></li><li>使用雷达命令绘制雷达图复发次数的按日历月的分布，每个雷达捕捉轴单月下令以顺时针方式。选择的代码，然后单击"执行（做）"。 <ol><li>重复的所有网站。通过查看图查看器中自动打开屏幕的每个情节观察波峰和波谷的复发发生在历年的模式。 </li></ol></li><li>运行SEAST命令跨越观测数据复发申请季节性的爱德华的考验。40-42重复所有地理层面。 </li></ol> 2.模型的建立与选择<ol><li>使用生成命令来指定在回归中使用的年周期的正弦和 ​​余弦三角函数。选择的代码，然后单击"执行（做）"。 </li><li>使用回归命令指定与复发数为因变量的结果，并计算正弦和 ​​余弦项基本模型的形式在步骤2.1作为主要解释变量。 <ol><li>添加特定位置的紫外线辐射37的基本模型作为一个额外的调整协变量和使用分析重aweight选择加权模式，为患者贡献的各位置的号码。选择的代码，然后单击"执行（做）"。 注:记录确定（R 2），并在结果窗口自动打开筛选剩余误差的模型系数。紫外线辐射:日均红斑加权环境紫外线辐射的每月1979至2004年包括由美国国家航空和航天局地球探测臭氧总量绘图系统，发布包含在分析中的所有个别位置37。 </li></ol></li><li>存储使用预测命令的模型预测每月日志（复发）。转换日志复发回整复发计数使用根儿 exponentiating日志（复发）项吃了命令。选择的代码，然后单击"执行（做）"。重复的所有网站。 </li><li> 2.3在使用双向散射命令观察到的月度复发的数据叠加的指数化预测月度复发的估计。选择的代码，然后单击"执行（做）"。 <ol><li>重复的所有网站。在图形显示浏览器的每个情节。 </li></ol></li><li>使用回归命令通过添加附加的谐波正弦/余弦对扩大在2.2中指定的模型。选择的代码，然后单击"执行（做）"。 注:记录残差和决心的系数。保存和转换模型的估计按2.3和打印模型估计出的观测数据按2.4。重复的所有网站。 </li><li>使用回归命令通过增加两个额外的谐波正弦/余弦对，以进一步扩大在2.2指定的型号。选择的代码，然后单击"执行（做）"。 注:记录残差和系数决心。直接使用似然比检验的基础模型进行比较这一模式。使用ESTAT IC后估计命令生成赤池和贝叶斯信息准则。保存和转换模型的估计按2.3和打印模型估计出的观测数据按2.4。重复所有地理层面。 </li></ol> 3.估算峰值复发概率<ol><li>使用的估计功能（nlcom）非线性组合来计算点估计和95％置信区间的相移，通过使用2.6确定从步骤2.1最佳拟合模型。选择的代码，然后单击"执行（做）"。 <ol><li>将这些点估计和相关的置信区间为代表的峰值复发次数（T max）和波谷复发次数（T 分），日历日期的编号，其中1 = 1 月1日和365 = 12月31日和T最大=相移+ （四分之三百六十五）和T最小=相移+（（四分之三百六十五）* 3）。重复所有地理层面。比赛T最大和T 分钟，以通过Excel查找文件中的日历日期。 </li></ol></li><li>使用生成命令来计算峰值到低谷的差别（T最大减T 分）的每个位置，标准为每每个站点100例。使用Wilcoxon秩和检验比较规范的纬度范围内的峰值到低谷的差别。选择的代码，然后单击"执行（做）"。 </li></ol> 4.模拟紫外辐射数据<ol><li>运行使用命令加载的紫外线辐射数据。计算平均每月紫外线辐射的使用EGEN命令的每个位置。选择的代码，然后单击"执行（做）"。 </li><li>绘制每月紫外线辐射（Y轴），按日历月（X轴）的散点图使用的双向散射作用的每个位置。在图形显示查看器中自动打开屏幕的每个情节。 </li><li>众议员吃步骤1.2的紫外线辐射数据，并使用该回归命令指定的，其中每月UVR被指定为因结果变量，并且在步骤2.1中指定的正弦和 ​​余弦三角函数位置级年度UVR趋势基础模型被结合到模型中作为解释变量。 </li><li>重复步骤2.4至2.6的紫外线辐射模型并仅限于该特定位置的模型。这涉及到重新运行双向散射命令覆盖预测估计的观测数据，并使用回归命令来运行扩展的谐波模型的替代品。 </li><li>通过4.4使用的步骤4.2确定特定地点的月度紫外线辐射的最佳拟合模型中使用的生成命令再次申请步骤3.1中指定的双角公式来计算相移点估计和相关的95％置信区间紫外线辐射。计算T最小（槽紫外线辐射的日期），使用日每个位置在步骤3.1Ë公式来描述。选择的代码，然后单击"执行（做）"。 </li></ol> 5.模拟紫外线辐射谷底到复发峰值滞后<ol><li>从步骤4.5，并从使用合并命令每个位置步3.1复发高峰日期追加的紫外线辐射的季节性低谷模型估计的日期。使用生成命令来计算失效的紫外线辐射低谷日期和随后的复发高峰日期间个月的时间。选择的代码，然后单击"执行（做）"。 </li><li>使用sktest命令使用夏皮罗-威尔克测试选择的代码，从正态性检验紫外线辐射低谷到复发高峰期滞后变量显著出发，然后单击"执行（做）"。 </li><li>使用合并命令追加位置级别的纬度数据集。相对纬度转换为使用ABS（x）函数绝对纬度。选择的代码，然后单击"执行（做）"。 </li><li>使用回归命令，测试线性Ôf显示运行线性和二次回归和残差比较滞后，绝对的纬度之间的关系。选择的代码，然后单击"执行（做）"。 </li><li>使用倒退 ，指定线性意味着与紫外线辐射谷底到复发峰值滞后作为因变量的结果，绝对的纬度在10度的预测变量单位回归模型。重量的模型的患者贡献的使用aweights倒退选项的每个位置的数目。选择的代码，然后单击"执行（做）"。 </li><li>使用双向散射命令绘制关于对UVR-槽到复发滞后y轴的绝对纬度在月上的x轴。叠加线使用lfit图选择最适合的。 Visualise每个位置的使用aweight分析权重的选择相对患者体重。选择的代码，然后单击"执行（做）"。 </li></ol>患者级复发第6页。敏感性分析ropensities <ol><li>使用mepossion命令来指定一个混合效应泊松回归，其中每月的复发次数是因结果变量，在步骤2.1规定的正弦和 ​​余弦三角函数再次纳入模型作为固定变量，基线EDSS，年龄在MS发病和事先接触到MS特定疾病修饰治疗被包括作为潜在的混杂因素和独特的患者标识符被指定为随机效应。选择的代码，然后单击"执行（做）"。 </li><li>重复步骤2.4至2.6，以确定最佳拟合泊松模型。这涉及到重新运行双向散射命令覆盖预测估计的观测数据，并使用回归命令来运行扩展的谐波模型的替代品。 </li><li>使用的估计量函数（nlcom）的非线性组合来计算点估计和95％置信区间为相移和计算日期高峰复发次数。比较与主要的分析结果。 </li><li>使用生成命令如步骤5.1中所述，使用高峰期复发日期衍生步骤6.3病人级泊松模型估计重新计算紫外线辐射谷底到复发峰值滞后几个月的每个位置。选择的代码，然后单击"执行（做）"。 </li><li>使用回归命令步骤5.5描述和比较的初步分析结果重塑绝对纬度滞后的预测。选择的代码，然后单击"执行（做）"。 </li></ol>

蒂姆·斯佩尔曼收到酬金咨询和从Biogen Idec公司公司差旅资金;奥尔拉灰色收到的差旅补助从Biogen Idec公司，默克雪兰诺和诺华;补偿服务从Biogen Idec公司，Genzyme公司，诺华公司和默克雪兰诺公司的科学顾问委员会;罗宾·卢卡斯并没有透露任何利益争夺和赫尔穆特Butzkueven得到报酬担任科学顾问委员会，并担任顾问的Biogen Idec公司和诺华公司;从Biogen Idec公司澳大利亚，默克雪兰诺澳大利亚和诺华澳大利亚扬声器酬金;旅行从Biogen Idec公司澳大利亚和默克雪兰诺澳大利亚的支持;研究支持中国社会科学院基金会（澳大利亚），默克雪兰诺澳大利亚皇家墨尔本医院友神经科学基金会和墨尔本大学。

这里所描述的协议的细节进行系统回归基础的技术，通过可视化图分析全球MS复发发作的数据，指导。它需要为出发点，从整个两个半球20个国家的复发数据的相对简单的描述性分析，使用户能够探索复发发作时间在MS的时间性，并通过使用三角模型正式测试这些理论理论。通过第一绘制全局复发发作的数据，然后系统地作图和评估观察到的数据的候补几何配合的逐步过程，被观察到的季节槽UVR和随后的峰复发发作概率之间的纬度依赖性的相关性，相关性在迄今前所未有MS流行病学。此外通过结合趋势的可视化与正式的统计模型，这种分析也证实了先前的荟萃分析表明季节性因素是复发发作时间的因素在北半球，也是第一次，延长该观察到南半球。 三角函数回归模型是一个灵活的工具，正式探索循环，时间或季节相关的周期现象，允许符合几何形状趋势数据的统计特性，如在这两个复发发作时间和紫外线辐射数据探索发现每年周期性的正弦曲线在这份报告中。然而给出的形状和结构，复杂的，多因素的流行病学趋势现象的范围如复发发作定时可以潜在地假定，原始数据和这样观察到的数据和由一个特定的模型预测之间的差异都可视化（即，残差）是两个假说产生严重（发病复发时间跨越年度季节性变化）和假设检验本研究的阶段（这个季节是可预测的，并圣描述使用正弦回归）。其结果是一套新颖的，关于季节和纬度在疾病发作模式的MS潜在的全球影响力的经验接地推论。 在协议中的关键步骤是可能的最简单的执行，利用简单的描述性散点图观测复发发作数据的可视化。鉴于可能的时空​​结构的周期性数据可以采取，观测数据的简单图的千头万绪和多样性，同时提供了对周围形成复发发作模式的设定以及为出发点，建立模型的经验基础上，最好捕获这些趋势并能随后用于统计推断和预测。设计到协议的一个重要修改是对可供选择的模式示范基地吸收新的三角调和函数的系统比较。 "最佳"契合是一个相对的状态，外核层ÿ通过测试针对可行的替代品的基本模型的性能是最适合在这种情况下，能够被确定。全球，半球和地点 - 另外一个关键的步骤是在地理的三个不同层面复制每个复发率和紫外线辐射模型。这不仅提供的初步结果（在全球和半球层面观察到的较高功率的趋势被复制在该位置的水平），也允许用来运行图和模型的代码故障排除内部验证。意外的结果或不可信的模型拟合​​，并不总是显而易见的，在全球或半球水平的分析，得出在该位置的水平被用来作为红旗的质量检查中使用过各级地域的代码。这提供了信心，季节周期和全球范围内观察到的纬度格局并没有数据聚合或错误编码的假象。此协议的另一个优点是，它不仅可以上尉茜和描述季节性和半球和纬度与适当的健壮性的影响，它也调整这些关联的潜在混杂从患者水平偏向性复发包括不同残疾的水平和不同疾病修饰药曝光之前复发。这使我们能够更好地隔离季节和纬度造成的，更好地接近真相的效果估计的复发概率为独立预测因子。这是特别重要，因为本研究的潜在的临床后果。 可预测的，纬度依赖性滞后冬槽紫外线辐射水平和随后的复发峰值频率之间的观测可能部分涉及改变在给定的地理位置的维生素D状况的影响，每个都有它自己独特的紫外线辐射轮廓。几个维生素D介导的免疫调节相关与MS复发发作概率以前已观察到，包括希夫廷T辅助淋巴细胞远离促炎Th1型信息到少炎性Th2细胞43-46和抑制树突细胞和IgM / IgG抗体生产43,47-50的。耦合到这个观察的两个季节和纬度中的复发定时的动力学的潜在作用，这表明在临床实践中作用为纬度特异性，位置适当补充维生素D减少未来复发的可能性。当然，尽管这个建议，MSBase研究没有收集病人级维生素D状况也正式紫外线辐射皮肤暴露量化，因此纵向数据这一理论的维生素D状态和随后的复发率呈负相关仍然正是这样，只是一个假设。正式的，适当供电随机临床试验才能建立因果关系。维生素D单药治疗，澳大利亚/新西兰PREVANZ试验（注册ACTRN12612001160820）两个这样的试验和法国的"D-打下MS"的研究（物理研究中心的注册-N / 2012 / ET），目前正在进行中。 也许最值得注意的是，这项研究很能说明问题的可能的协同效应可从正式的统计建模和数据可视化技术的诊断相结合流行病学家。该技术相对于其它形式的时间序列的分析意义在于，其拒绝常规时间序列的假设的分析，任何潜在的时间性主要是一个随机过程。通过比较三角回归明确地要求了结构的环状的，周期现象如MS复发时间变动。这样的三角模型是在两个观测数据和模型估计，以指导，并证实了模型构建和评估过程中，每一步的方式进行系统的可视化精致依赖。无论是可视化或建模就已经足够了在异LATION - 图分析是必要的，用于建立现实的假设关于复发概率的季节性和纬度影响的存在和结构形式，然后测试所得模型的性能，而三角回归是必要的既定量这些关系，调整为重要的混杂因素，并提供确定性的措施，因为这些团体是如何合理的。 本文所描述的技术是一个功能强大的隔离方法，如MS复发的定时季节性或纬度上复杂的，多因素事件的作用或影响。因此，它具有广泛的应用前景研究已知或怀疑与季节和/或纬度不同系统的其他临床或生物学现象的未来潜力。这种技术将是预测疾病的流行病学，无论是在传染病和非传染性疾病方面特别相关的TI关键事件，如感染或疾病进展的明很复杂，往往由众多两个环境因素（季节，温度，纬度）和病人级特征（年龄，合并症，接触处理）的驱动。这样的工具可以帮助风险分层的患者更容易出现不利的健康事件，从而指导早期干预。

多发性硬化的最常见的形式（MS）被复发缓解多发性硬化（RRMS）。 RRMS的特征在于发作恶化神经功能，随后部分或完全恢复。全球范围内，MS的发病率和患病率增加而增加距离赤道两个半球1-3复发事件的发生特别是在RRMS的频率是否也随纬度而变化，以及是否有任何潜在的季节性变化在该等联想，仍不清楚。迄今为止的研究探索季节性复发时间被限制在单一临床中心，限制就季节性趋势复发时机孤立的地理位置，从而无法 ​​开拓更广阔的纬度影响的任何推论4-14这些研究通过小样本被进一步限制大小和稀疏复发的数据。从欧元临床中心2000年的一份荟萃分析10项研究OPE，美国和加拿大，其中每个研究包括至少30例报告复发的的发病季节，说明复发发作的时间明显的季节性趋势，复发高峰在春季和冬季槽4 。类似周期性年度趋势发病在随后的已观察到，虽然小，研究在日本15和西班牙16。然而，可比美国研究未能证实这一图案 17。迄今为止，这些研究和观察被限制在北半球。该MSBase研究小组最近分析了在这两个南半球和北半球MS复发的一个大的全球数据，探讨除了峰复发概率和季节紫外线（紫外线辐射）槽18之间的关系纬度影响，季节性趋势复发发病时间。中央对这些方法是三角回归的应用可视化和复发发作和紫外线辐射分布的时机评价的发展趋势。 这项研究的总体目标是测试复发发作MS的时刻在时间上的变化可预测变化与季节北部和南半球的假设，这是季节性的影响纬度。对于使用三角函数模型来调查这些问题的理由是它的灵活性用于表征已知或怀疑来描述离散的，可预测的和一致的形状或图案，如波峰和波谷通常的年度周期二维或三维现象在生物或流行病学现象具有季节性变化。19-22常规时间序列的缺点的分析，包括傅立叶分析，是假定，时间序列的特点往往是随机过程。21,23,24相比之下，结合三角函数我NTO回归型模型的定期和系统结构的周期性数据既便于开采利用的同时回归模型结构，开拓其他相关因素或调整季节性因素的混杂因素的优势。 三角函数回归以前已广泛应用于医学流行病学文献，探讨时间性的主题多种多样传染病疫情检测，昼夜节律的，一切从植物神经系统功能紊乱早产胎盘早剥通过先天畸形和时间的季节性相关因素的作用急症的演示。25-32这种建模通常要求较大的样本量超过常规的时间序列分析和因此这是第一次已经被施放到MS的复发发作全局数据集。这里所描述的三角回归是合适的工具，研究者探索任何pH值enomena这是众所周知的或可疑的骑自行车的系统随着时间的推移。不仅可这种建模帮助检定和可视化这些模式，进一步允许探索潜在的驱动程序，以及这些趋势相互关联的用户。 至于MS复发发作这里提出，利用散射和剩余地块具体的例子来可视化和评估如何接近一个假设三角模型形式拟合数据构成确定关键步骤:1）是否观察到的数据提供足够的证据支持季节性或其他时间趋势在复发发作的定时的假说;和2）是否正弦和余弦函数限定特定三角函数模型的频率和排列是足够以允许使用该模型用于随后的推理和预测的。回归模型还允许控制任何观察到的季节性或纬度的影响重要的混杂因素如病人级倾向为复发，这在本身随时间变化的诸如预复发暴露于疾病修饰药（DMD）治疗持续时间特别因素。分离独立地理和时间预测以及在MS复发发作定时相关因素有引导生物调查的复发事件而这又可以通知将来的治疗干预，以防止或延缓疾病发作的发展机制的潜力。 该MSBase注册 MS患者造成复发的数据这一分析国际MSBase注册表进行采购。成立于2004年，注册纵向整理人口，疾病活动度，临床检查和调查的特点和使用一个基于互联网的，医生拥有和经营系统同意参加MS患者的临床指标，33个会员中心遵循一个共同的protoc醇，定义所需的最小数据集以商定定期上载以保证结果的数据，如复发事件一致地和前瞻性编译。复发发作的日期是作为一个强制性的最低数据集变量。除了这些复发事件相关联的相关临床数据通常收集包括皮质类固醇治疗和受影响的功能系统。使用通用IMED数据输入系统进一步确保了中心的一个统一的方法来收集数据和报告。该项目包含人类研究伦理委员会每届促进中心批准或豁免。根据来自所有患者的当地法律的知情同意包括在分析中是强制性的。 纳入标准 总共有9811例患者造成32762复发事件被纳入分析。临床MS用最少的20例患者登记中心同意，uploaDED和跟踪在注册表中的1日2013年12月（资料整理的日）有资格列入分析。为了确保包含在分析中所有复发事件进行前瞻性观察，仅复发声母日之后的第一个记录，患者残疾评估（使用Kurtzke扩展残疾状态评分（EDSS））被包括在分析中。这些都有助于复发的数据来分析患者满意正规的诊断标准MS。34,35 结果措施 这项研究考虑了两个主要结果:1）是否有复发发作的地理位置，半球和/或全球水平的概率随时间的变化;和2）是否有在几个月纬度和滞后，之间的关系，季节性UVR波谷的定时和随后的峰复发概率日期之间。该MSBase研究组hypothe大小，作为绝对维生素D水平较低的区域中进一步远离赤道和特定位置的季节性群体水平的维生素D最低点更早有可能达到以下冬至在这种远侧位置，维生素D水平低的则上增加MS的效果复发的概率将同样描述了这样的时间和纬度分布格局。 复发的定义和日期 甲复发被定义为发生的新的症状或现有的症状至少持续24小时，在不存在的并发疾病或发烧的发作，和先前的攻击后发生至少30天。这个定义以前在MSBase复发的表型分析中得到应用。36随访时间为每个符合条件的患者横跨其复发的事件可以被观察到的定义是通过跨越第一EDSS评估日期的最近日期起计EDSS评估记录之前，数据提取和汇编的数据注册表。在情况下复发发作的确切日期是不可用或者不能被特定月份确定的，诊所使用，也可以在1日或者一个月的默认日期的第 15天。在32762复发本报告中分析中，有7913（24.2％）和4594（14.0％）被记录在每月的1日和15日当天分别显著高于比例记录在其范围在每月的任何一天从0.8％至5.6％。为了校正此，记录于复发任一月份的第 15天第 1次被随机分配到一个天15天都这些默认日期的时间间隔任一侧内。这种方法的内部效度是通过敏感性分析证实了这证明，峰值复发日起在默认的日期随机模拟的估计是不显著不同于模无论使用EL原来的报道日期，但不包括默认的日期完全。

<table><tbody><tr><td>Stata SE Version 13</td><td>StataCorp, College Station, Texas</td><td>Version 13</td><td>Statistical analysis software used for analysis</td></tr><tr><td>Microsoft Excel 2010</td><td>Microsoft</td><td>2010</td><td>Spreadsheet program for calendar date look-up</td></tr></tbody></table>

a method of trigonometric modelling of seasonal variation demonstrated with multiple sclerosis relapse data

This report describes a novel Stata-based application of trigonometric regression modelling to 55 years of multiple sclerosis relapse data from 46 clinical centers across 20 countries located in both hemispheres. Central to the success of this method was the strategic use of plot analysis to guide and corroborate the statistical regression modelling. Initial plot analysis was necessary for establishing realistic hypotheses regarding the presence and structural form of seasonal and latitudinal influences on relapse probability and then testing the performance of the resultant models. Trigonometric regression was then necessary to quantify these relationships, adjust for important confounders and provide a measure of certainty as to how plausible these associations were. Synchronization of graphing techniques with regression modelling permitted a systematic refinement of models until best-fit convergence was achieved, enabling novel inferences to be made regarding the independent influence of both season and latitude in predicting relapse onset timing in MS. These methods have the potential for application across other complex disease and epidemiological phenomena suspected or known to vary systematically with season and/or geographic location.

三角函数回归到来自全国各地20个国家的46个临床中心采购的32762复发事件该应用程序的基础是提供观察，复发发作的MS时机周期性和季节性的跨越南北半球和季节之间的持续时间可辩护的统计参数紫外线辐射槽和随后的复发高峰期与相关的自由度。关键这是依赖于情节的分析来指导模型开发，评估和细化的必然反复的过程。 复发次数由一个月散点图观测数据的分析建议以年为周期，世界各地的地理水平春运高峰，秋季低谷。雷达图全球复发的数据证实了北半球的复发高峰月份（图1A）。这春运高峰持续的时候南半球复发发作数据结合北方数据&lt;STRONG&gt;（图1B），与南部地区演示十一月份的峰值。秋季槽也被记录在两个半球与北部和南部分别在十一月，五月观察半球复发的最低频率。一个爱德华的试验进一步证实，复发发作证明，从一个统一的，非季节性分布显著离港。两者合计，这些结果表明，在所有三级地理学，在MS复发发作中观察到的周期性时间变动最好地描述单个年度循环由一个单峰和单个槽由常规6个月的间隔隔开。因此，与一对正弦和 ​​余弦函数指定一个三角函数回归模型被选为跨越两个半球的基础用例模型（ 图2）。相比于竞争的三角模型解决方案扩展到包括两个或三个周期的谐波，整个北半球禄示范基地ations最小残留误差的平方和返回的观测数据的一个优越配合（P &lt;0.0001，调整，R 2 = 0.263）相比，无论是模型结合有额外的谐波（p值= 0.0001，调整，R 2 = 0.198），或附加的两项谐波（P = 0.0014，调整R 2 = 0.181）。类似地，相同的基本模型时，适用于南半球的基础模型（P &lt;0.0001，调整，R 2 = 0.241）再次减小到的型号，包括观察到的和估计的数据相对之间的残余差异外执行的扩展谐波替代两个额外的谐波（P &lt;0.0001，调整，R 2 = 0.167）;一额外的谐波模型所述的相似配合相对于基座（P &lt;0.0001，调整，R 2 = 0.243）。重要的是对特定地点的纬度建模的紫外线辐射，低谷到复发高峰期滞后，基础模型的预测又出执行任意扩展，哈rmonic模型在单个地理位置的水平。 使用单一正弦/余弦对指定的基本模式，相移跨越全球估计为-24.8（95％CI为-45.8，-3.9）所有的复发，翻译成估计北半球复发高峰发病7日期个月（95％CI:2月10日， 日三月二十八日）和9月5日的的南半球峰值的日期（95％CI:10 日八月9月26日）。有由半球中相移的估计没有差别（相互作用的检验:p = 0.254）。平均（SD）标准的峰值到低谷的复发差为7.6（6.6），每100名患者复发。虽然位于40度或绝对纬度中心更多记录，一个较大的峰 - 波谷差（平均8.6，SD 7.6）相对于位于20至39度的绝对纬度范围内的地点（平均5.7，SD 3.3），这种差异并不STatistically显著（p值= 0.135）。 紫外线辐射按日历月的散点图分析表明，如上所述在一个正弦/余弦谐波对定义的基本模式是同样适用于紫外线辐射的季节性，在所有地理层面。作为例证， 图3描述了覆盖在观察到的紫外线辐射数据为四个选定个别位置，两名来自每个半球的回归模型每月紫外线辐射的估计。我们可以从这些图可以理解是多么密切的模型测算的基础上，以年为周期的单峰和低谷正弦回归，赋予的观测数据。基本紫外线辐射模型再次跑赢无论是扩展谐波模型的残差最小化和决心的卓越系数的条款。 通过叠加相当于曲线复发发作周期性紫外线辐射正弦曲线表明，紫外线辐射低谷之前一直复发的高峰发病probability。此外，这种滞后出现收缩进一步南北的特定位置选址是远离赤道。施加均值的线性回归，每隔10度纬度的距离在任一半球用在这种滞后的28.5天的UVR-槽到复发峰值滞后一个统计学显著降低有关（95％CI赤道: 3.29，53.7; P = 0.028）。 如图4所示，绝对纬度增加远离赤道的两个半球，越早复发见顶后的冬季紫外线辐射低谷。有由半球中该协会没有差别（交互作用的P测试= 0.811）。 主要的正弦值回归的患者级混合效应泊松扩展返回非常相似的结果估计在短短两天晚于由主要基础模型（3月9日与7 个月的北半球相比，估计高峰复发日期位置，9月7日与9月5日南部地区）。同样的紫外线辐射低谷到复发的高峰期滞后是在主或敏感性车型相媲美，与患者级泊松推广示范，平均在滞后只有4.1日期与不同的（平均延迟=24.8天，95％CI:2.0，49.2 ）相对于所述主​​地点级模型。再次，有由半球（相互作用的检验，p = 0.671）在此关联没有差别。 <img alt="图1" src="/files/ftp_upload/53169/53169fig1.jpg" /> 图1.雷达图观测到的全球复发次数由一个月。（A）北半球，（B）联合南北半球<a href="https://www-jove-com.bdigitaluss.remotexs.co/files/ftp_upload/53169/53169fig1large.jpg" target="_blank">请点击此处查看该图的放大版本。</a> 图2.基本模型预测VS观察到的复发 。通过半球使用的基本情况三角模型描述了一个峰一谷六个月分离的单个年度周期预测复发观察比较，每月复发地块。 <a href="https://www-jove-com.bdigitaluss.remotexs.co/files/ftp_upload/53169/53169fig2large.jpg" target="_blank">请点击此处查看该图的放大版本。</a> <img alt="图3" src="/files/ftp_upload/53169/53169fig3.jpg" /> 图3.基准模型预测VS观察复发地块进行比较发现平均每月的紫外线辐射与示范基地预测的紫外线辐射的加拿大蒙特利尔。墨尔本，澳大利亚;巴里，意大利和阿根廷的布宜诺斯艾利斯。 <a href="https://www-jove-com.bdigitaluss.remotexs.co/files/ftp_upload/53169/53169fig3large.jpg" target="_blank">请点击此处查看人</a>arger版本这个数字。 <img alt="图4" src="/files/ftp_upload/53169/53169fig4.jpg" /> 图4.绝对纬度和紫外线辐射，波谷到复发峰值滞后之间的最佳匹配的加权行。 <a href="https://www-jove-com.bdigitaluss.remotexs.co/files/ftp_upload/53169/53169fig4large.jpg" target="_blank">请点击此处查看该图的放大版本。</a>

Watch this Scientific Journal Video about A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data at JoVE.com

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Combining plot analysis with trigonometric regression is a robust method for exploring complex, cyclical phenomena such as relapse onset timing in multiple sclerosis (MS). This method enabled unbiased characterisation of seasonal trends in relapse onset permitting novel inferences around the influence of seasonal variation, ultraviolet radiation (UVR) and latitude.

季节变化的三角建模的方法证明与多发性硬化症复发数据

This report describes a novel Stata-based application of trigonometric regression modelling to  55 years of multiple sclerosis relapse data from 46 ...

a-method-trigonometric-modelling-seasonal-variation-demonstrated-with

Universidad San Sebastian

Research

JoVE Journal

Medicine

10.6K 次观看.  Royal Melbourne Hospital. Combining plot analysis with trigonometric regression is a robust method for exploring complex, cyclical phenomena such as relapse onset timing in multiple sclerosis (MS). This method enabled unbiased characterisation of seasonal trends in relapse onset permitting novel inferences around the influence of seasonal variation, ultraviolet radiation (UVR) and latitude. 

视频: A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Modeling Neural Immune Signaling of Episodic and Chronic Migraine Using Spreading Depression In Vitro

Migraine and its transformation to chronic migraine are healthcare burdens in need of improved treatment options. We seek to define how neural immune signaling modulates the susceptibility to migraine, modeled in vitro using spreading depression (SD), as a means to develop novel therapeutic targets for episodic and chronic migraine. SD is the likely cause of migraine aura and migraine pain. It is a paroxysmal loss of neuronal function triggered by initially increased neuronal activity, which slowly propagates within susceptible brain regions. Normal brain function is exquisitely sensitive to, and relies on, coincident low-level immune signaling. Thus, neural immune signaling likely affects electrical activity of SD, and therefore migraine. Pain perception studies of SD in whole animals are fraught with difficulties, but whole animals are well suited to examine systems biology aspects of migraine since SD activates trigeminal nociceptive pathways. However, whole animal studies alone cannot be used to decipher the cellular and neural circuit mechanisms of SD. Instead, in vitro preparations where environmental conditions can be controlled are necessary. Here, it is important to recognize limitations of acute slices and distinct advantages of hippocampal slice cultures. Acute brain slices cannot reveal subtle changes in immune signaling since preparing the slices alone triggers: pro-inflammatory changes that last days, epileptiform behavior due to high levels of oxygen tension needed to vitalize the slices, and irreversible cell injury at anoxic slice centers. 
In contrast, we examine immune signaling in mature hippocampal slice cultures since the cultures closely parallel their in vivo counterpart with mature trisynaptic function; show quiescent astrocytes, microglia, and cytokine levels; and SD is easily induced in an unanesthetized preparation. Furthermore, the slices are long-lived and SD can be induced on consecutive days without injury, making this preparation the sole means to-date capable of modeling the neuroimmune consequences of chronic SD, and thus perhaps chronic migraine. We use electrophysiological techniques and non-invasive imaging to measure neuronal cell and circuit functions coincident with SD. Neural immune gene expression variables are measured with qPCR screening, qPCR arrays, and, importantly, use of cDNA preamplification for detection of ultra-low level targets such as interferon-gamma using whole, regional, or specific cell enhanced (via laser dissection microscopy) sampling. Cytokine cascade signaling is further assessed with multiplexed phosphoprotein related targets with gene expression and phosphoprotein changes confirmed via cell-specific immunostaining. Pharmacological and siRNA strategies are used to mimic and modulate SD immune signaling.

Modeling Neural Immune Signaling of Episodic and Chronic Migraine Using Spreading Depression In Vitro

Migraine and its transformation to chronic migraine are immense healthcare burdens in need of improved treatment options. We seek to define how neural immune signaling modulates the susceptibility to migraine, modeled in vitro using spreading depression in hippocampal slice cultures, as a means to develop novel therapeutic targets.

使用扩频萧条的情节和慢性偏头痛的神经免疫信号建模<em在体外</em

Migraine and its transformation to chronic migraine are healthcare burdens in need of improved treatment options.  We seek to define how neural immune ...

科研

神经科学

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

The scaled subprofile model (SSM)1-4 is a multivariate PCA-based algorithm that identifies major sources of variation in patient and control group brain image data while rejecting lesser components (Figure 1). Applied directly to voxel-by-voxel covariance data of steady-state multimodality images, an entire group image set can be reduced to a few significant linearly independent covariance patterns and corresponding subject scores. Each pattern, termed a group invariant subprofile (GIS), is an orthogonal principal component that represents a spatially distributed network of functionally interrelated brain regions. Large global mean scalar effects that can obscure smaller network-specific contributions are removed by the inherent logarithmic conversion and mean centering of the data2,5,6. Subjects express each of these patterns to a variable degree represented by a simple scalar score that can correlate with independent clinical or psychometric descriptors7,8. Using logistic regression analysis of subject scores (i.e. pattern expression values), linear coefficients can be derived to combine multiple principal components into single disease-related spatial covariance patterns, i.e. composite networks with improved discrimination of patients from healthy control subjects5,6. Cross-validation within the derivation set can be performed using bootstrap resampling techniques9. Forward validation is easily confirmed by direct score evaluation of the derived patterns in prospective datasets10. Once validated, disease-related patterns can be used to score individual patients with respect to a fixed reference sample, often the set of healthy subjects that was used (with the disease group) in the original pattern derivation11. These standardized values can in turn be used to assist in differential diagnosis12,13 and to assess disease progression and treatment effects at the network level7,14-16. We present an example of the application of this methodology to FDG PET data of Parkinson's Disease patients and normal controls using our in-house software to derive a characteristic covariance pattern biomarker of disease.

Multivariate techniques including principal component analysis (PCA) have been used to identify signature patterns of regional change in functional brain images. We have developed an algorithm to identify reproducible network biomarkers for the diagnosis of neurodegenerative disorders, assessment of disease progression, and objective evaluation of treatment effects in patient populations.

鉴定的使用神经影像学数据的与疾病-相关的的空间协方差模式

The scaled subprofile model (SSM)1-4 is a multivariate PCA-based algorithm that identifies major sources of variation in patient and control group brain ...

医学

Lexical Decision Task for Studying Written Word Recognition in Adults with and without Dementia or Mild Cognitive Impairment

Older adults are slower at recognizing visual objects than younger adults. The same is true for recognizing that a letter string is a real word. People with Alzheimer&#39;s disease (AD) or Mild Cognitive Impairment (MCI) demonstrate even longer responses in written word recognition than elderly controls. Despite the general tendency towards slower recognition in aging and neurocognitive disorders, certain characteristics of words influence word recognition speed regardless of age or neuropathology (e.g., a word&#8217;s frequency of use). We present here a protocol for examining the influence of lexical characteristics on word recognition response times in a simple lexical decision experiment administered to younger and older adults and people with MCI or AD. In this experiment, participants are asked to decide as quickly and accurately as possible whether a given letter string is an actual word or not. We also describe mixed-effects models and principal components analysis that can be used to detect the influence of different types of lexical variables or individual characteristics of participants on word recognition speed.

This article describes how to implement a simple lexical decision experiment to assess written word recognition in neurologically healthy participants and in individuals with dementia and cognitive decline. We also provide a detailed description of reaction time analysis using principal components analysis (PCA) and mixed-effects modeling.

研究成人有无痴呆症或轻度认知障碍的文字识别的词汇决策任务

Older adults are slower at recognizing visual objects than younger adults. The same is true for recognizing that a letter string is a real word. People ...

行为学

Dynamic Digital Biomarkers of Motor and Cognitive Function in Parkinson's Disease

As Parkinson&#8217;s disease (PD) is a heterogeneous disorder, personalized medicine is truly required to optimize care. In their current form, standard scores from paper and pencil symptom- measures traditionally used to track disease progression are too coarse (discrete) to capture the granularity of the clinical phenomena under consideration, in the face of tremendous symptom diversity. For this reason, sensors, wearables, and mobile devices are increasingly incorporated into PD research and routine care. These digital measures, while more precise, yield data that are less standardized and interpretable than traditional measures, and consequently, the two types of data remain largely siloed. Both of these issues present barriers to the broad clinical application of the field&#8217;s most precise assessment tools. This protocol addresses both problems. Using traditional tasks to measure cognition and motor control, we test the participant, while co-registering biophysical signals unobtrusively using wearables. We then integrate the scores from traditional paper-and-pencil methods with the digital data that we continuously register. We offer a new standardized data type and unifying statistical platform that enables the dynamic tracking of change in the person&#8217;s stochastic signatures under different conditions that probe different functional levels of neuromotor control, ranging from voluntary to autonomic. The protocol and standardized statistical framework offer dynamic digital biomarkers of physical and cognitive function in PD that correspond to validated clinical scales, while significantly improving their precision.&#160;

This protocol offers a digitization of portions of traditional clinical tasks commonly used to measure cognition and motor control in Parkinson&#8217;s disease. Clinical tasks are digitized while biophysical rhythms are co-registered from different functional levels of the nervous systems, ranging from voluntary, spontaneous, automatic to autonomic.

帕金森病中运动与认知功能的动态数字生物标志物

As Parkinson&#8217;s disease (PD) is a heterogeneous disorder, personalized medicine is truly required to optimize care. In their current form, standard ...

The Multiple Sclerosis Performance Test (MSPT): An iPad-Based Disability Assessment Tool

Precise measurement of neurological and neuropsychological impairment and disability in multiple sclerosis is challenging. We report a new test, the Multiple Sclerosis Performance Test (MSPT), which represents a new approach to quantifying MS related disability. The MSPT takes advantage of advances in computer technology, information technology, biomechanics, and clinical measurement science. The resulting MSPT represents a computer-based platform for precise, valid measurement of MS severity. Based on, but extending the Multiple Sclerosis Functional Composite (MSFC), the MSPT provides precise, quantitative data on walking speed, balance, manual dexterity, visual function, and cognitive processing speed. The MSPT was tested by 51 MS patients and 49 healthy controls (HC). MSPT scores were highly reproducible, correlated strongly with technician-administered test scores, discriminated MS from HC and severe from mild MS, and correlated with patient reported outcomes. Measures of reliability, sensitivity, and clinical meaning for MSPT scores were favorable compared with technician-based testing. The MSPT is a potentially transformative approach for collecting MS disability outcome data for patient care and research. Because the testing is computer-based, test performance can be analyzed in traditional or novel ways and data can be directly entered into research or clinical databases. The MSPT could be widely disseminated to clinicians in practice settings who are not connected to clinical trial performance sites or who are practicing in rural settings, drastically improving access to clinical trials for clinicians and patients. The MSPT could be adapted to out of clinic settings, like the patient&#8217;s home, thereby providing more meaningful real world data. The MSPT represents a new paradigm for neuroperformance testing. This method could have the same transformative effect on clinical care and research in MS as standardized computer-adapted testing has had in the education field, with clear potential to accelerate progress in clinical care and research.

The Multiple Sclerosis Performance Test MSPT: An iPad-Based Disability Assessment Tool

Precise measurement of neurological and neuropsychological impairment and disability in multiple sclerosis is challenging. We report methodologic details on a new test, the Multiple Sclerosis Performance Test (MSPT). This new approach to the objective of quantification of MS related disability provides a computer-based platform for precise, valid measurement of MS severity.

多发性硬化症性能测试（MSPT）：一个iPad为基础的残疾评估工具

Precise measurement of neurological and neuropsychological impairment and disability in multiple sclerosis is challenging. We report a new test, the ...

Modeling Fast-scan Cyclic Voltammetry Data from Electrically Stimulated Dopamine Neurotransmission Data Using QNsim1.0

Central dopaminergic (DAergic) pathways have an important role in a wide range of functions, such as attention, motivation, and movement. Dopamine (DA) is implicated in diseases and disorders including attention deficit hyperactivity disorder, Parkinson's disease, and traumatic brain injury. Thus, DA neurotransmission and the methods to study it are of intense scientific interest. In vivo fast-scan cyclic voltammetry (FSCV) is a method that allows for selectively monitoring DA concentration changes with fine temporal and spatial resolution. This technique is commonly used in conjunction with electrical stimulations of ascending DAergic pathways to control the impulse flow of dopamine neurotransmission. Although the stimulated DA neurotransmission paradigm can produce robust DA responses with clear morphologies, making them amenable for kinetic analysis, there is still much debate on how to interpret the responses in terms of their DA release and clearance components. To address this concern, a quantitative neurobiological (QN) framework of stimulated DA neurotransmission was recently developed to realistically model the dynamics of DA release and reuptake over the course of a stimulated DA response. The foundations of this model are based on experimental data from stimulated DA neurotransmission and on principles of neurotransmission adopted from various lines of research. The QN model implements 12 parameters related to stimulated DA release and reuptake dynamics to model DA responses. This work describes how to simulate DA responses using QNsim1.0 and also details principles that have been implemented to systematically discern alterations in the stimulated dopamine release and reuptake dynamics.

Fast-scan cyclic voltammetry can monitor in vivo dopamine neurotransmission in the context of drugs, disease, and other experimental manipulations. This work describes the implementation of QNsim1.0, a software to model electrically stimulated dopamine responses according to the quantitative neurobiological model to quantify estimates of dopamine release and reuptake dynamics.

使用QNsim1.0从电刺激多巴胺神经传递数据建模快速扫描循环伏安数据

Central dopaminergic (DAergic) pathways have an important role in a wide range of functions, such as attention, motivation, and movement. Dopamine (DA) is ...

脑深部刺激治疗重度抑郁症

Closed-Loop Neurostimulation for Biomarker-Driven, Personalized Treatment of Major Depressive Disorder

Deep brain stimulation involves the administration of electrical stimulation to targeted brain regions for therapeutic benefit. In the context of major depressive disorder (MDD), most studies to date have administered continuous or open-loop stimulation with promising but mixed results. One factor contributing to these mixed results may stem from when the stimulation is applied. Stimulation administration specific to high-symptom states in a personalized and responsive manner may be more effective at reducing symptoms compared to continuous stimulation and may avoid diminished therapeutic effects related to habituation. Additionally, a lower total duration of stimulation per day is advantageous for reducing device energy consumption. This protocol describes an experimental workflow using a chronically implanted neurostimulation device to achieve closed-loop stimulation for individuals with treatment-refractory MDD. This paradigm hinges on determining a patient-specific neural biomarker that is related to states of high symptoms and programming the device detectors, such that stimulation is triggered by this read-out of symptom state. The described procedures include how to obtain neural recordings concurrent with patient symptom reports, how to use these data in a state-space model approach to differentiate low- and high-symptom states and corresponding neural features, and how to subsequently program and tune the device to deliver closed-loop stimulation therapy.

作者聚焦:闭环深部脑刺激在抑郁症治疗中的治疗益处 

Deep brain stimulation triggered by a patient-specific neural biomarker of a high-symptom state may better control symptoms of major depressive disorder compared to continuous, open-loop stimulation. This protocol provides a workflow for identifying a patient-specific neural biomarker and controlling the delivery of therapeutic stimulation based on the identified biomarker.

闭环神经刺激用于重度抑郁症的生物标志物驱动型个性化治疗

Deep brain stimulation involves the administration of electrical stimulation to targeted brain regions for therapeutic benefit. In the context of major ...

小鼠实验性自身免疫性脑脊髓炎的诱导和评价

Modeling Multiple Sclerosis in the Two Sexes: MOG35-55-Induced Experimental Autoimmune Encephalomyelitis

Multiple Sclerosis (MS) is a chronic autoimmune inflammatory disease affecting the central nervous system (CNS). It is characterized by different prevalence in the sexes, affecting more women than men, and different outcomes, showing more aggressive forms in men than in women. Furthermore, MS is highly heterogeneous in terms of clinical aspects, radiological, and pathological features. Thus, it is necessary to take advantage of experimental animal models that allow the investigation of as many aspects of the pathology as possible. Experimental autoimmune encephalomyelitis (EAE) represents one of the most used models of MS in mice, modeling different disease features, from the activation of the immune system to CNS damage. Here we describe a protocol for the induction of EAE in both male and female C57BL/6J mice using myelin oligodendrocyte glycoprotein peptide 35-55 (MOG35-55) immunization, which leads to the development of a chronic form of the disease. We also report the evaluation of the daily clinical score and motor performance of these mice for 28 days post immunization (28 dpi). Lastly, we illustrate some basic histological analysis at the CNS level, focusing on the spinal cord as the primary site of disease-induced damage.

作者聚焦：创建与雄性和雌性小鼠相关的多功能实验性自身免疫性脑脊髓炎模型 

Experimental autoimmune encephalomyelitis is one of the most widely used murine models of multiple sclerosis. In the current protocol, C57BL/6J mice of both sexes are immunized with myelin oligodendrocyte glycoprotein peptide, resulting mainly in ascending paresis of the tail and limbs. Here we discuss the protocol of EAE induction and evaluation.

季节变化的三角建模的方法证明与多发性硬化症复发数据

摘要

探索更多视频

此视频中的章节

使用扩频萧条的情节和慢性偏头痛的神经免疫信号建模

鉴定的使用神经影像学数据的与疾病-相关的的空间协方差模式

研究成人有无痴呆症或轻度认知障碍的文字识别的词汇决策任务

帕金森病中运动与认知功能的动态数字生物标志物

多发性硬化症性能测试（MSPT）：一个iPad为基础的残疾评估工具

使用QNsim1.0从电刺激多巴胺神经传递数据建模快速扫描循环伏安数据

闭环神经刺激用于重度抑郁症的生物标志物驱动型个性化治疗

闭环神经刺激用于重度抑郁症的生物标志物驱动型个性化治疗

闭环神经刺激用于重度抑郁症的生物标志物驱动型个性化治疗

两性多发性硬化症建模：MOG_35-55 诱导的实验性自身免疫性脑脊髓炎

季节变化的三角建模的方法证明与多发性硬化症复发数据

摘要

探索更多视频

此视频中的章节

使用扩频萧条的情节和慢性偏头痛的神经免疫信号建模

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