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科学通报  2012 

HIV模型的统计诊断

DOI: 10.1360/972011-1978, PP. 666-672

Keywords: HIV,模型,核光滑,影响分析,Cook,距离

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Abstract:

描述HIV的数学模型是一组非线性常微分方程,其中包括CD4+T细胞再感染率和死亡率,HIV病毒死亡率等多个重要未知参数,准确估计这些参数有助于正确了解患者病情发展,以采用个人化治疗方案.针对此模型已提出多个参数估计方法,包括基于数值解的非线性最小二乘,截面似然及两步估计.另一方面,由于客观因素影响,各观测数据对于参数估计的影响大小不同,找出对参数估计影响大的观测值,进一步分析其原因具有重要意义.基于HIV模型的两步估计,构造了用于影响分析的非参数Cook型统计量,并给出其大样本分布.通过模拟数据和临床数据分析发现(1)所构造统计量可以检测中度以上偏移.(2)相对于内点,边界点对HIV模型的参数估计影响更大.基于以上结论,建议对HIV模型进行参数估计时,对边界点应加以格外关注.提出的方法也可以推广到其他线性常微分方程模型的统计诊断问题中.

References

[1]  1 Ho D D, Neumann A U, Perelson A S, et al. Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature, 1995, 373:123-126??
[2]  2 Perelson A S. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev, 1999, 41: 3-44??
[3]  3 Bates D M, Watts D G. Nonlinear Regression and Its Application. New York: John Wiley & Sons, Inc, 1988??
[4]  4 Ramsay J O, Hook G, Campbell , et al. Parameter estimation for differential equation: A generalized smoothing approach. J Roy Stat Soc B, 2007, 69: 741-796??
[5]  5 Cao J, Ramsay J O. Parameter cascades and profiling in functional data analysis. Comput Stat, 2007, 22: 335-351??
[6]  7 Liang H, Wu H L. Parameter estimation for differential equation models using a framework of measurement error in regression models. J Am Stat Assoc, 2008, 103: 1570-1583??
[7]  8 Chen J, Wu H L. Efficient local estimation for time varying coefficients in deterministic dynamic models with applications to HIV-1 dynamics. J Am Stat Assoc, 2008, 103: 369-384??
[8]  10 Liang H, Miao H Y, Wu H L. Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model. Ann Appl Stat, 2010, 4: 460-483??
[9]  11 Fan J, Gijbels I. Local Polynomial Modeling and Its Applications. London: Chapman & Hall, 1996
[10]  14 Miller K S. On the inverse of sum of matrices. Math Mag, 1981, 54: 67-72??
[11]  6 Poyton A A, Varziri M S, McAuley K B, et al. Parameter estimation in continuous time dynamic models using principal differential analysis. Comput Chem Eng, 2006, 30: 698-708??
[12]  9 Chen J, Wu H L. Estimation of time varying parameters in deterministic dynamic models. Statist Sin, 2008, 18: 987-1006
[13]  12 Cook R D, Weisberg S. Residuals and Influence in Regression. London: Chapman & Hall, 1982??
[14]  13 韦博成, 林金官, 解锋昌. 统计诊断. 北京: 高等教育出版社, 2009??

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