segmented regression

分段回归
  • 文章类型: Journal Article
    背景:在美洲,疫苗可避免的疾病死亡是儿童死亡率的重要因素。减少这种情况的重要手段是通过广泛的疫苗覆盖率。由于COVID-19大流行对医疗保健系统的影响,它对疫苗覆盖率构成了潜在的破坏。
    目的:本研究旨在评估COVID-19大流行对美洲DTP3疫苗接种率的影响,调查2012年至2022年的趋势,以确定重大变化,地区差异,以及大流行对实现全球免疫目标的总体影响。
    方法:这项研究使用了第三剂白喉的覆盖率数据,破伤风,和百日咳疫苗(DTP3)从联合国儿童基金会数据库中提取了2012年至2022年。我们进行了Joinpoint回归来识别显著趋势变化的点。计算了美国及其地区的年度百分比变化(APC)和95%置信区间(95%CIs)。我们还使用了分段回归分析。使用卡方检验,我们比较了2019年至2022年每个国家的DTP3疫苗接种覆盖率。
    结果:总体而言,在此期间,美国的疫苗覆盖率有所下降,APC为-1.4(95%CI-1.8;-1.0)。这一趋势因地区而异。在北美,减少可以忽略不计(-0.1%APC).南美下降幅度最大,APC为-2.5%。中美洲也下降了,APC为-1.3%。我们的研究结果表明,美洲DTP疫苗接种率下降的趋势令人担忧,在某些地区加剧,在COVID-19大流行之后。2019年至2022年间,美洲疫苗覆盖率的绝对下降为-4%,其中最重要的下降是中美洲(-7%)。然而,六个国家报告说,以巴西为首的COVID-19疫苗接种率增加,增加7%。相反,22个国家的DTP3疫苗覆盖率下降,平均降幅为-7.37%。这种下降对实现世卫组织到2030年第三剂DTP覆盖率90%的目标构成了重要挑战,从2019年到2022年实现这一目标的国家数量减少就证明了这一点。
    结论:COVID-19大流行影响了美国的疫苗覆盖率,导致下降,尤其是在中美洲。
    BACKGROUND: In the Americas, deaths by diseases avoidable with vaccines are a significant contributor to child mortality. An essential means of reducing this is through broad vaccine coverage. The COVID-19 pandemic has posed a potential disruption to vaccine coverage due to its effects on the healthcare system.
    OBJECTIVE: this study aims to evaluate the impact of the COVID-19 pandemic on DTP3 vaccination coverage in the Americas, investigating trends from 2012 to 2022 to identify significant changes, regional disparities, and the overall effect of the pandemic on progress towards global immunization targets.
    METHODS: This study used the coverage data for the third dose of the diphtheria, tetanus, and pertussis vaccine (DTP3) pulled from UNICEF databases spanning 2012 to 2022. We conducted a Joinpoint regression to identify points of significant trend changes. The annual percentage change (APC) and 95% confidence intervals (95% CIs) were calculated for America and its regions. We also used segmented regression analysis. Using the Chi-square test, we compared DTP3 vaccination coverage for each country between 2019 and 2022.
    RESULTS: Overall, America saw a decrease in vaccine coverage during this period, with an APC of -1.4 (95% CI -1.8; -1.0). This trend varied across regions. In North America, the decrease was negligible (-0.1% APC). South America showed the steepest decrease, with an APC of -2.5%. Central America also declined, with an APC of -1.3%. Our findings suggest a concerning trend of declining DTP-vaccination rates in the Americas, exacerbated in certain regions, in the wake of the COVID-19 pandemic. The absolute decrease in vaccine coverage in the Americas was -4% between 2019 and 2022, with the most important drop being in Central America (-7%). However, six countries reported increased vaccination rates post-COVID-19, led by Brazil, with a 7% increase. Conversely, twenty-two countries registered a decline in DTP3 vaccine coverage, with the average decrease being -7.37%. This decline poses an important challenge to achieving the WHO\'s target of 90% coverage for the third dose of DTP by 2030, as evidenced by the reduction in the number of countries meeting this target from 2019 to 2022.
    CONCLUSIONS: The COVID-19 pandemic has impacted vaccine coverage in America, leading to a decrease, especially across Central America.
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  • 文章类型: Preprint
    背景分段回归,中断时间序列(ITS)分析的通用模型,主要利用两个方程参数化。系数的解释在两个分段回归参数之间变化,导致偶尔的用户误解。方法为了说明ITS分析中分段回归的两种常见参数之间的系数解释差异,我们得出了分析结果,并提供了使用可公开访问的数据集评估意大利吸烟法规政策影响的说明.使用两个常用的参数化获得估计系数及其标准误差,用于连续结果的分段回归。我们阐明了系数解释和干预效果计算。结果我们的调查显示,两个参数化代表相同的模型。然而,由于参数化的差异,在这两种方法下,干预措施的直接效果估计不同。关键区别在于对干预实施二元指标相关系数的解释,影响直接效果的计算。结论分段回归的两个常见参数表示相同的模型,但对关键系数的解释不同。采用两种参数化的研究人员在解释系数和计算干预效果时应谨慎行事。
    UNASSIGNED: Segmented regression, a common model for interrupted time series (ITS) analysis, primarily utilizes two equation parametrizations. Interpretations of coefficients vary between the two segmented regression parametrizations, leading to occasional user misinterpretations.
    UNASSIGNED: To illustrate differences in coefficient interpretation between two common parametrizations of segmented regression in ITS analysis, we derived analytical results and present an illustration evaluating the impact of a smoking regulation policy in Italy using a publicly accessible dataset. Estimated coefficients and their standard errors were obtained using two commonly used parametrizations for segmented regression with continuous outcomes. We clarified coefficient interpretations and intervention effect calculations.
    UNASSIGNED: Our investigation revealed that both parametrizations represent the same model. However, due to differences in parametrization, the immediate effect of the intervention is estimated differently under the two approaches. The key difference lies in the interpretation of the coefficient related to the binary indicator for intervention implementation, impacting the calculation of the immediate effect.
    UNASSIGNED: Two common parametrizations of segmented regression represent the same model but have different interpretations of a key coefficient. Researchers employing either parametrization should exercise caution when interpreting coefficients and calculating intervention effects.
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  • 文章类型: Journal Article
    背景:中断时间序列(ITS)设计是评估临床实践或公共卫生中大规模干预措施的常用方法。然而,不正确地使用这种方法会导致有偏差的结果。
    目的:使用ITS设计来研究药物利用研究的设计和统计分析特征,并提出改进建议。
    方法:从2021年1月至2021年12月基于PubMed进行了文献检索。我们纳入了使用ITS设计来调查药物利用的原始文章,而不限制研究人群或结果类型。一个结构化的,开发了经过试点测试的问卷,以提取有关研究特征的信息以及有关设计和统计分析的详细信息。
    结果:我们纳入了153项符合条件的研究。其中,28.1%(43/153)清楚地解释了使用ITS设计的理由,13.7%(21/153)阐明了使用指定的ITS模型结构的理由。一百四十九项研究使用汇总数据进行ITS分析,和20.8%(31/149)澄清了时间点数量的理由。自相关的考虑,这些研究往往缺乏非平稳性和季节性,只有14项研究提到了所有三个方法论问题。在31项研究中提到了缺失的数据。只有39.22%(60/153)报告了回归模型,而15项研究给出了由于时间参数化导致的水平变化的错误解释。在24项研究中考虑了随时间变化的参与者特征。在包含分层数据的97项研究中,23项研究阐明了集群之间的异质性,并使用统计方法来解决这一问题。
    结论:ITS药物利用研究的设计和统计分析质量仍不令人满意。三个新出现的方法问题值得特别关注,包括由于时间参数化导致的水平变化的错误解释,时变参与者特征和层次数据分析。我们提供了有关设计的具体建议,ITS研究的分析和报告。
    BACKGROUND: Interrupted time series (ITS) design is a commonly used method for evaluating large-scale interventions in clinical practice or public health. However, improperly using this method can lead to biased results.
    OBJECTIVE: To investigate design and statistical analysis characteristics of drug utilization studies using ITS design, and give recommendations for improvements.
    METHODS: A literature search was conducted based on PubMed from January 2021 to December 2021. We included original articles that used ITS design to investigate drug utilization without restriction on study population or outcome types. A structured, pilot-tested questionnaire was developed to extract information regarding study characteristics and details about design and statistical analysis.
    RESULTS: We included 153 eligible studies. Among those, 28.1% (43/153) clearly explained the rationale for using the ITS design and 13.7% (21/153) clarified the rationale of using the specified ITS model structure. One hundred and forty-nine studies used aggregated data to do ITS analysis, and 20.8% (31/149) clarified the rationale for the number of time points. The consideration of autocorrelation, non-stationary and seasonality was often lacking among those studies, and only 14 studies mentioned all of three methodological issues. Missing data was mentioned in 31 studies. Only 39.22% (60/153) reported the regression models, while 15 studies gave the incorrect interpretation of level change due to time parameterization. Time-varying participant characteristics were considered in 24 studies. In 97 studies containing hierarchical data, 23 studies clarified the heterogeneity among clusters and used statistical methods to address this issue.
    CONCLUSIONS: The quality of design and statistical analyses in ITS studies for drug utilization remains unsatisfactory. Three emerging methodological issues warranted particular attention, including incorrect interpretation of level change due to time parameterization, time-varying participant characteristics and hierarchical data analysis. We offered specific recommendations about the design, analysis and reporting of the ITS study.
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  • 文章类型: Meta-Analysis
    背景:当随机化可能不可行时,中断时间序列(ITS)是评估公共卫生和政策干预或暴露的强大设计。有几种统计方法可用于ITS研究的分析和荟萃分析。当应用于现实世界的ITS数据时,我们试图从经验上比较可用的方法。
    方法:我们从已发布的元分析中获取ITS数据,以创建在线数据存储库。使用两种ITS估计方法重新分析每个数据集。使用固定效应和四种随机效应荟萃分析方法计算并组合了水平和斜率变化效应估计值(和标准误差)。我们检查了荟萃分析水平和斜率变化估计值的差异,他们95%的置信区间,p值,以及统计方法对异质性的估计。
    结果:在40个合格的荟萃分析中,我们获得了17项荟萃分析的数据,包括282项ITS研究(主要调查公共卫生中断的影响(88%)),并进行了分析.我们发现平均而言,元分析效应估计,他们的标准误差和研究间差异对荟萃分析方法的选择不敏感,与ITS分析方法无关。然而,在整个ITS分析方法中,对于任何给定的荟萃分析,元分析效应估计可能存在小到中等的差异,和荟萃分析标准误差的重要差异。此外,meta分析效应估计值的置信区间宽度和p值根据置信区间方法和ITS分析方法的选择而变化.
    结论:我们的实证研究表明,荟萃分析效应估计,他们的标准误差,置信区间宽度和p值可能受统计方法选择的影响。这些差异可能会影响荟萃分析的解释和结论,并表明统计方法在实践中不可互换。
    BACKGROUND: The Interrupted Time Series (ITS) is a robust design for evaluating public health and policy interventions or exposures when randomisation may be infeasible. Several statistical methods are available for the analysis and meta-analysis of ITS studies. We sought to empirically compare available methods when applied to real-world ITS data.
    METHODS: We sourced ITS data from published meta-analyses to create an online data repository. Each dataset was re-analysed using two ITS estimation methods. The level- and slope-change effect estimates (and standard errors) were calculated and combined using fixed-effect and four random-effects meta-analysis methods. We examined differences in meta-analytic level- and slope-change estimates, their 95% confidence intervals, p-values, and estimates of heterogeneity across the statistical methods.
    RESULTS: Of 40 eligible meta-analyses, data from 17 meta-analyses including 282 ITS studies were obtained (predominantly investigating the effects of public health interruptions (88%)) and analysed. We found that on average, the meta-analytic effect estimates, their standard errors and between-study variances were not sensitive to meta-analysis method choice, irrespective of the ITS analysis method. However, across ITS analysis methods, for any given meta-analysis, there could be small to moderate differences in meta-analytic effect estimates, and important differences in the meta-analytic standard errors. Furthermore, the confidence interval widths and p-values for the meta-analytic effect estimates varied depending on the choice of confidence interval method and ITS analysis method.
    CONCLUSIONS: Our empirical study showed that meta-analysis effect estimates, their standard errors, confidence interval widths and p-values can be affected by statistical method choice. These differences may importantly impact interpretations and conclusions of a meta-analysis and suggest that the statistical methods are not interchangeable in practice.
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  • 文章类型: Journal Article
    在2020年3月的全国封锁期间,选择性手术被暂停,以遏制COVID-19大流行在马来西亚的蔓延。我们试图评估封锁对白内障手术的影响,并为未来的疫情提供教训。
    我们进行了中断的时间序列分析,以检查锁定之前和期间的白内障手术率。
    我们使用了马来西亚白内障手术登记处2015年至2021年的全国白内障手术数据。使用季节性调整的泊松模型进行分段回归分析。进行了分层分析,以确定锁定对白内障手术的影响是否因医院名称而异,白内障服务的类型,性别,和年龄组。
    白内障手术在2020年3月封锁开始时开始下降,在2020年4月达到低谷,随后有所上升,但从未恢复到封锁前的水平。2021年12月白内障手术率仍比预期手术量低43%,相当于2513例白内障手术的损失。没有证据表明COVID-19指定医院和非COVID-19指定医院之间的封锁效果不同。在外展服务和40岁及以上的人群中,白内障手术率的相对下降似乎最大。
    封锁导致白内障手术率立即降低至基线率的近一半。尽管它逐渐复苏,如果没有重新分配或增加资源来支持积压和新案件,预计还会有进一步的延误。
    UNASSIGNED: Elective surgeries were suspended during the national lockdown in March 2020 to curb the spread of the COVID-19 pandemic in Malaysia. We sought to evaluate the impact of the lockdown on cataract surgeries and suggest lessons for future outbreaks.
    UNASSIGNED: We conducted an interrupted time series analysis to examine rates of cataract surgery before and during the lockdown.
    UNASSIGNED: We used national cataract surgical data between 2015 and 2021 from the Malaysian Cataract Surgery Registry. Segmented regression with a seasonally adjusted Poisson model was used for the analysis. Stratified analyses were performed to establish whether the effect of the lockdown on cataract surgeries varied by hospital designation, type of cataract service, sex, and age groups.
    UNASSIGNED: Cataract surgeries began falling in March 2020 at the onset of the lockdown, reached a trough in April 2020, and subsequently increased but never recovered to pre-lockdown levels. Cataract surgical rates in December 2021 were still 43 % below the expected surgical volume, equivalent to 2513 lost cataract surgeries. There was no evidence of a differential effect of the lockdown between COVID-19 designated and non-COVID-19 designated hospitals. The relative decrease in cataract surgical rates appears to have been greatest in outreach services and in people 40 years and older.
    UNASSIGNED: The lockdown caused an immediate reduction in cataract surgical rates to nearly half of its baseline rate. Despite its gradual recovery, further delays remain to be expected should there be no redistribution or increase in resources to support backlogs and incoming new cases.
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  • 文章类型: Journal Article
    自1995年以来,韩国的无烟区已经扩大,相关运动也已经开始实施。因此,在过去的15年中,家庭二手烟(SHS)暴露有所减少。我们评估了队列效果,2008年运动对家庭SHS暴露的影响,以及公共场所全面禁烟和加重处罚的影响,于2011年12月实施。
    使用了具有全国代表性的韩国青少年横断面15波调查数据。810,516名参与者被分为6个年级组,15个周期组,和20个中学录取组。年龄-时期-队列分析,用内在估计方法进行,用于评估家庭SHS暴露的队列效应,并进行了中断时间序列分析,以评估无烟政策和运动的效果。
    对于从2002年至2008年进入中学的同伙,男孩和女孩的家庭SHS暴露风险均降低。在实施无烟政策后,男孩的家庭SHS暴露率明显下降(系数,-8.96;p<0.05),女孩则无显著差异(系数,-6.99;p=0.07)。竞选结束后,男孩的家庭SHS暴露量按队列显着下降,立即和干预后(系数,-4.84;p=0.03;系数,-1.22;p=0.02,分别)。
    发现了青少年家庭SHS暴露的入学队列效应,这与无烟政策和运动有关。反吸烟干预措施应一致和同时实施。
    OBJECTIVE: Smoke-free areas have expanded and related campaigns have been implemented since 1995 in Korea. As a result, household secondhand smoke (SHS) exposure has decreased over the past 15 years. We assessed the cohort effect, the effect of a 2008 campaign on household SHS exposure, and the impact of a complete smoking ban in public places along with increased penalties, as implemented in December 2011.
    METHODS: Nationally representative cross-sectional 15-wave survey data of Korean adolescents were used. The 810,516 participants were classified into 6 grade groups, 15 period groups, and 20 middle school admission cohorts. An age-period-cohort analysis, conducted with the intrinsic estimator method, was used to assess the cohort effect of household SHS exposure, and interrupted-time series analyses were conducted to evaluate the effects of the smoke-free policy and the campaign.
    RESULTS: For cohorts who entered middle school from 2002 to 2008, the risk of household SHS exposure decreased among both boys and girls. Immediately after implementation of the smoke-free policy, the prevalence of household SHS exposure by period decreased significantly for boys (coefficient, -8.96; p<0.05) and non-significantly for girls (coefficient, -6.99; p=0.07). After the campaign, there was a significant decrease in household SHS exposure by cohort among boys, both immediately and post-intervention (coefficient, -4.84; p=0.03; coefficient, -1.22; p=0.02, respectively).
    CONCLUSIONS: A school-admission-cohort effect was found on household SHS exposure among adolescents, which was associated with the smoke-free policy and the campaign. Anti-smoking interventions should be implemented consistently and simultaneously.
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  • 文章类型: Journal Article
    两阶段多项式回归模型(Robison,1964年;富勒,1969年;勇敢和富勒,1973年;詹等人。,1996)广泛应用于生态学中,公共卫生,以及其他建模非线性关系的应用领域。这些模型的特点是存在阈值参数,在这个范围内,均值函数被允许改变。阈值是要从数据估计的模型的参数是两阶段模型的基本特征。它区分了他们,更普遍的是,多相模型,来自样条模型,对模型的计算和推断都有深远的影响。两阶段多项式回归模型的估计是非凸的,非光滑优化问题。网格搜索为估计问题提供了高质量的解决方案,但是用蛮力完成时非常慢。在我们先前关于分段线性两阶段回归模型估计的工作的基础上,我们为两阶段多项式回归模型开发了快速网格搜索算法,并展示了它们的性能。此外,我们为均值函数开发了基于Bootstrap的逐点和同时置信带。进行蒙特卡罗研究以证明所提出方法的计算和统计特性。使用三个真实数据集来帮助说明两阶段模型的应用,特别注意模型的选择。
    Two-phase polynomial regression models (Robison, 1964; Fuller, 1969; Gallant and Fuller, 1973; Zhan et al., 1996) are widely used in ecology, public health, and other applied fields to model nonlinear relationships. These models are characterized by the presence of threshold parameters, across which the mean functions are allowed to change. That the threshold is a parameter of the model to be estimated from the data is an essential feature of two-phase models. It distinguishes them, and more generally, multi-phase models, from the spline models and has profound implications for both computation and inference for the models. Estimation of two-phase polynomial regression models is a non-convex, non-smooth optimization problem. Grid search provides high quality solutions to the estimation problem, but is very slow when done by brute force. Building upon our previous work on piecewise linear two-phase regression models estimation, we develop fast grid search algorithms for two-phase polynomial regression models and demonstrate their performance. Furthermore, we develop bootstrap-based pointwise and simultaneous confidence bands for mean functions. Monte Carlo studies are conducted to demonstrate the computational and statistical properties of the proposed methods. Three real datasets are used to help illustrate the application of two-phase models, with special attention on model choice.
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  • 文章类型: Journal Article
    乙型肝炎(HB)是一个重大的全球性挑战,但缺乏从变化角度对新疆乙型肝炎发病率的流行病学研究。这项研究旨在通过确定重要的变化点和趋势来弥合这一差距。
    数据集从新疆疾病预防控制信息系统获得。使用完整数据集的二元分割和五个年龄组的分段回归模型来确定变化点。
    结果显示了季度HB时间序列的四个变化点,在第一个变化点(2007年3月)和第二个变化点(2010年3月)之间的时间段内,HB报告的平均数量最高。在随后的段中,报告的病例呈明显下降趋势。分段回归模型显示每个年龄组的变化点数量不同,30-50岁、51-80岁和15-29岁年龄组的增长率较高。
    变点分析在流行病学中具有重要的应用价值。这些发现为将来的流行病学研究和HB预警系统提供了重要信息。
    Hepatitis B (HB) is a major global challenge, but there has been a lack of epidemiological studies on HB incidence in Xinjiang from a change-point perspective. This study aims to bridge this gap by identifying significant change points and trends.
    The datasets were obtained from the Xinjiang Information System for Disease Control and Prevention. Change points were identified using binary segmentation for full datasets and a segmented regression model for five age groups.
    The results showed four change points for the quarterly HB time series, with the period between the first change point (March 2007) and the second change point (March 2010) having the highest mean number of HB reports. In the subsequent segments, there was a clear downward trend in reported cases. The segmented regression model showed different numbers of change points for each age group, with the 30-50, 51-80, and 15-29 age groups having higher growth rates.
    Change point analysis has valuable applications in epidemiology. These findings provide important information for future epidemiological studies and early warning systems for HB.
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  • 文章类型: Journal Article
    沙特食品和药物管理局(SFDA)在2018年将普瑞巴林列为受控物质;然而,目前尚不清楚这一政策变化是否影响了普瑞巴林的使用。这项研究检查了SFDA限制前后普瑞巴林处方的趋势。此外,还评估了受控镇痛药的共同处方和普瑞巴林用于批准的适应症的使用。
    对沙特阿拉伯三个医疗中心的门诊普瑞巴林处方进行了横断面研究。中断时间序列分析用于评估普瑞巴林处方随时间的变化和接受普瑞巴林的患者人数。2016年6月至2017年6月被确定为限制前期限,并以2018年7月至2019年7月为限售期后。
    在这项研究中,确定了77,760份普瑞巴林处方。限制前服用普瑞巴林的9,076名患者,处方为16,875张,与7123例患者和19,484例限制后处方相比。普瑞巴林使用者总数在限售后减少21.5%,处方增加了15.5%。限制前后普瑞巴林处方的月趋势没有显着变化。然而,在使用普瑞巴林的患者中,曲马多和对乙酰氨基酚/可待因处方在限制期增加了21%和16.1%,分别。
    实施SFDA强制的处方限制后,普瑞巴林的使用减少。与此同时,在实施后阶段,麻醉品的使用有所增加。
    UNASSIGNED: The Saudi Food and Drug Authority (SFDA) classified pregabalin as a controlled substance in 2018; however, whether this policy change has affected pregabalin use is unclear. This study examined the trends in pregabalin prescriptions before and after the SFDA restriction. In addition, the co-prescription of controlled analgesics and the use of pregabalin for approved indications were also evaluated.
    UNASSIGNED: A cross-sectional study was conducted on outpatient pregabalin prescriptions from three healthcare centers in Saudi Arabia. Interrupted time series analysis was used to assess changes over time in pregabalin prescriptions and the number of patients receiving pregabalin. June 2016 to June 2017 was identified as the pre-restriction period, and July 2018 to July 2019 as the post-restriction period.
    UNASSIGNED: In this study, 77,760 pregabalin prescriptions were identified. There were 9,076 patients on pregabalin in the pre-restriction period with 16,875 prescriptions, compared with 7,123 patients and 19,484 prescriptions post-restriction. The total number of pregabalin users decreased by 21.5% post-restriction, and prescriptions increased by 15.5%. There was no significant change in the monthly trends in pregabalin prescriptions before and after the restriction. However, the of tramadol and acetaminophen/codeine prescriptions in patients who were using pregabalin increased in the post-restriction period by 21% and 16.1%, respectively.
    UNASSIGNED: Pregabalin use was reduced after the SFDA-enforced prescription restriction was implemented. This was accompanied by increased narcotics use in the post-implementation phase.
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  • 文章类型: Journal Article
    中断时间序列(ITS)设计被广泛用于检查大规模公共卫生干预措施的效果,并且具有最高的证据有效性。然而,在解释干预措施滞后效应的方法方面存在显著差距。为了解决这个问题,在滞后期,我们将激活函数(ReLU和Sigmoid)引入了ITS设计的经典分段回归(CSR)。这导致了提出优化分段回归(OSR)的建议,即,OSR-ReLU和OSR-Sig.要比较模型的性能,我们模拟了多种场景下的数据,包括干预措施的积极或消极影响,线性或非线性滞后模式,不同的滞后长度,以及结果时间序列的不同波动程度。根据模拟数据,我们检查了偏见,平均相对误差(MRE),均方误差(MSE),95%置信区间(CI)的平均宽度,以及不同模型之间干预措施长期影响估计的95%CI覆盖率。OSR-ReLU和OSR-Sig对所有情景的长期影响进行了大致无偏的估计,而CSR没有。在准确性方面,OSR-ReLU和OSR-Sig的表现优于CSR,在MRE和MSE中表现出较低的值。随着滞后长度的增加,优化的模型提供了对长期影响的稳健估计。关于精度,OSR-ReLU和OSR-Sig超越了CSR,显示95%CI的较窄平均宽度和较高的覆盖率。我们优化的模型是强大的工具,因为它们可以对干预措施的滞后效应进行建模,并对干预措施的长期影响提供更准确和精确的估计。激活函数的引入为企业社会责任模型的改进提供了新思路。
    The interrupted time series (ITS) design is widely used to examine the effects of large-scale public health interventions and has the highest level of evidence validity. However, there is a notable gap regarding methods that account for lag effects of interventions.To address this, we introduced activation functions (ReLU and Sigmoid) to into the classic segmented regression (CSR) of the ITS design during the lag period. This led to the proposal of proposed an optimized segmented regression (OSR), namely, OSR-ReLU and OSR-Sig. To compare the performance of the models, we simulated data under multiple scenarios, including positive or negative impacts of interventions, linear or nonlinear lag patterns, different lag lengths, and different fluctuation degrees of the outcome time series. Based on the simulated data, we examined the bias, mean relative error (MRE), mean square error (MSE), mean width of the 95% confidence interval (CI), and coverage rate of the 95% CI for the long-term impact estimates of interventions among different models.OSR-ReLU and OSR-Sig yielded approximately unbiased estimates of the long-term impacts across all scenarios, whereas CSR did not. In terms of accuracy, OSR-ReLU and OSR-Sig outperformed CSR, exhibiting lower values in MRE and MSE. With increasing lag length, the optimized models provided robust estimates of long-term impacts. Regarding precision, OSR-ReLU and OSR-Sig surpassed CSR, demonstrating narrower mean widths of 95% CI and higher coverage rates.Our optimized models are powerful tools, as they can model the lag effects of interventions and provide more accurate and precise estimates of the long-term impact of interventions. The introduction of an activation function provides new ideas for improving of the CSR model.
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