2015, 12(5): 937-964. doi: 10.3934/mbe.2015.12.937

Uncertainty quantification in modeling HIV viral mechanics

1. 

Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212

2. 

Center for Research in Scienti c Computation, North Carolina State University, Raleigh, NC 27695-8212, United States, United States, United States, United States, United States, United States

Received  January 2014 Revised  April 2015 Published  June 2015

We consider an in-host model for HIV-1 infection dynamics developed and validated with patient data in earlier work [7]. We revisit the earlier model in light of progress over the last several years in understanding HIV-1 progression in humans. We then consider statistical models to describe the data and use these with residual plots in generalized least squares problems to develop accurate descriptions of the proper weights for the data. We use recent parameter subset selection techniques [5,6] to investigate the impact of estimated parameters on the corresponding selection scores. Bootstrapping and asymptotic theory are compared in the context of confidence intervals for the resulting parameter estimates.
Citation: H. T. Banks, Robert Baraldi, Karissa Cross, Kevin Flores, Christina McChesney, Laura Poag, Emma Thorpe. Uncertainty quantification in modeling HIV viral mechanics. Mathematical Biosciences & Engineering, 2015, 12 (5) : 937-964. doi: 10.3934/mbe.2015.12.937
References:
[1]

S. Abdella, N. Wabe and E. Yesuf, Management of common adverse effects in the era of highly active antiretroviral therapy in south east Ethiopia,, North American Journal of Medical Sciences, 3 (2011), 499. doi: 10.4297/najms.2011.3499.

[2]

B. M. Adams, H. T. Banks, M. Davidian and E. S. Rosenberg, Model fitting and prediction with HIV treatment interruption data,, Center for Research in Scientific Computation Technical Report CRSC-TR05-40, 69 (2007), 05.

[3]

A. Alexaki, Y. Liu and B. Wigdahl, Cellular reservoirs of HIV-1 and their role in viral persistence,, Current HIV Research, 6 (2008), 388. doi: 10.2174/157016208785861195.

[4]

J. Ananworanich, C. Vandergeeten, N. Chomchey and N. Chomont, Early ART Intervention Restricts the Seeding of the HIV Reservoir in Long-Lived Central Memory CD4+ T Cells,, Program and Abstracts of the 20 Conference on Retroviruses and Opportunistic Infections, (2013).

[5]

A. Cintron-Arias, H. T. Banks, A. Capaldi and A. L. Lloyd, A sensitivity matrix based methodology for inverse problem formulation, CRSC Tech. Rep. CRSC-TR09-09, April, 2009;, J. Inverse and Ill-posed Problems, 17 (2009), 545. doi: 10.1515/JIIP.2009.034.

[6]

H. T. Banks, A. Cintron-Arias and F. Kappel, Parameter selection methods in inverse problem formulation,, in Mathematical Modeling and Validation in Physiology, 2064 (2013), 43. doi: 10.1007/978-3-642-32882-4_3.

[7]

H. T. Banks, M. Davidian, S. Hu, G. M. Kepler and E. S. Rosenberg, Modeling HIV immune response and validation with clinical data,, Journal of Biological Dynamics, 2 (2008), 357. doi: 10.1080/17513750701813184.

[8]

H. T. Banks, K. Holm and D. Robbins, Standard error computations for uncertainty quantification in inverse problems: Asymptotic theory vs. bootstrapping,, Mathematical and Computer Modeling, 52 (2010), 1610. doi: 10.1016/j.mcm.2010.06.026.

[9]

H. T. Banks, S. Hu and W. Clayton Thompson, Modeling and Inverse Problems in the Presence of Uncertainty,, CRSC Press/ Taylor and Frances Publishing, (2014).

[10]

H. T. Banks, D. F. Kapraun, W. Clayton Thompson, C. Peligero, J. Argilaguet and A. Meyerhans, A novel statistical analysis and interpretation of flow cytometry data,, Journal of Biological Dynamics, 7 (2013), 96. doi: 10.1080/17513758.2013.812753.

[11]

H. T. Banks and H. T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes,, Taylor Francis/CRC Press, (2009).

[12]

J. N. Blankson, D. Persaud and R. F. Siliciano, The challenge of viral reservoirs in HIV-1 infection,, Annual Review of Medicine, 53 (2002), 557. doi: 10.1146/annurev.med.53.082901.104024.

[13]

R. J. Carroll and D. Ruppert, Transformation and Weighting in Regression,, Chapman & Hall, (1988). doi: 10.1007/978-1-4899-2873-3.

[14]

R. J. Carroll, C. F. J. Wu and D. Ruppert, The effect of estimating weights in weighted least squares,, J. Amer. Statistical Assoc., 83 (1988), 1045. doi: 10.1080/01621459.1988.10478699.

[15]

M. Catalfamo, C. Wilhelm, L. T. Cheung, M. Proschan, T. Friesen, J. H. Park, J. Adelsberger, M. Baseler, F. Maldarelli, R. Davey, G. Roby, C. Rehm and C. Lane, CD4+ and CD8+ T cell immune activation during chronic HIV infection: roles of homeostasis, HIV, type I IFN, and IL-7,, Journal of Immunology, 186 (2011), 2106. doi: 10.4049/jimmunol.1002000.

[16]

N. W. Cummins and A. D. Badley, Anti-apoptotic mechanisms of HIV: lessons and novel approaches to curing HIV,, Cellular and Molecular Life Sciences: CMLS, 70 (2013), 3355.

[17]

C. Dalmasso, W. Carpentier, L. Meyer, C. Rouzioux, C. Goujard, M.-L. Chaix, O. Lambotte, V. Avettand-Fenoel, S. Le Clerc, L. D. de Senneville, C. Deveau, F. Boufassa, P. Debré, J.-F. Delfraissy, P. Broet and I. Theodorou, Distinct genetic loci control plasma HIV-RNA and cellular HIV-DNA levels in HIV-1 infection: the ANRS Genome Wide Association 01 study,, PloS one, 3 (2008).

[18]

M. Davidian, Nonlinear Models for Univariate and Multivariate Response,, ST 762 Lecture Notes, (2007).

[19]

M. Davidian and D. M. Giltinan, Nonlinear Models for Repeated Measurement Data,, Chapman and Hall, (2000).

[20]

B. Descours, V. Avettand-Fenoel, C. Blanc, A. Samri, A. Mélard, V. Supervie, I. Theodorou, G. Carcelain, C. Rouzioux and B. Autran, Immune responses driven by protective human leukocyte antigen alleles from long-term nonprogressors are associated with low HIV reservoir in central memory CD4+ T cells,, Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America, 54 (2012), 1495.

[21]

T. J. DiCiccio and B. Efron, Bootstrap confidence intervals,, Statistical Science, 11 (1996), 189. doi: 10.1214/ss/1032280214.

[22]

B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans,, CBMS 38, (1982).

[23]

M. Egger, M. May, G. Chêne, A. N. Phillips, B. Ledergerber, F. Dabis, D. Costagliola, A. D'Arminio Monforte, F. de Wolf, P. Reiss, J. Lundgren, A. Justice, S. Staszewski, C. Leport, R. Hogg, S. Robert, C. Sabin, M. Gill, B. Salzberger and J. Sterne, Prognosis of HIV-1-infected patients starting highly active antiretroviral therapy: A collaborative analysis of prospective studies,, Lancet, 360 (2002), 119.

[24]

T. H. Finkel, G. Tudor-Williams, N. K. Banda, M. F. Cotton, T. Curiel, C. Monks, T. W. Baba, R. M. Ruprecht and A. Kupfer, Apoptosis occurs predominantly in bystander cells and not in productively infected cells of HIV- and SIV-infected lymph nodes,, Nature Medicine, 1 (1995), 129.

[25]

O. Lambotte, F. Boufassa, Y. Madec, A. Nguyen, C. Goujard, L. Meyer, C. Rouzioux, A. Venet and J.-F. Delfraissy, HIV controllers: A homogeneous group of HIV-1-infected patients with spontaneous control of viral replication,, Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America, 41 (2005), 1053.

[26]

S. Lodi, L. Meyer, A. Kelleher, M. Rosinska, J. Ghosn, M. Sannes and K. Porter, Immunovirologic control 24 months after interruption of antiretroviral therapy initiated close to HIV seroconversion,, Archives of Internal Medicine, 172 (2012), 1251.

[27]

B. Max and R. Sherer, Management of the adverse effects of antiretroviral therapy and medication adherence,, Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America, 30 (2000).

[28]

T. H. Mogensen, J. Melchjorsen, C. S. Larsen and S. R. Paludan, Innate immune recognition and activation during HIV infection,, Retrovirology, 7 (2010).

[29]

N. Ngo-Giang-Huong, C. Deveau, I. Da Silva, I. Pellegrin, A. Venet, M. Harzic, M. Sinet, J. F. Delfraissy, L. Meyer, C. Goujard and C. Rouzioux, Proviral HIV-1 DNA in subjects followed since primary HIV-1 infection who suppress plasma viral load after one year of highly active antiretroviral therapy,, AIDS, 15 (2001), 665.

[30]

T. Schreiber and A. Schmitz, Surrogate time series,, Physica D: Nonlinear Phenomena, 142 (2000), 346. doi: 10.1016/S0167-2789(00)00043-9.

[31]

G. A. F. Seber and C. J. Wild, Nonlinear Regression,, J. Wiley & Sons, (1989). doi: 10.1002/0471725315.

[32]

L. Shan, K. Deng, N. S. Shroff, C. M. Durand, S. A. Rabi, H.-C. Yang, H. Zhang, J. B. Margolick, J. N. Blankson and R. F. Siliciano, Stimulation of HIV-1-specific cytolytic T lymphocytes facilitates elimination of latent viral reservoir after virus reactivation,, Immunity, 36 (2012), 491.

[33]

B. W. Silverman, Density Estimation for Statistics and Data Analysis,, Chapman and Hall, (1986). doi: 10.1007/978-1-4899-3324-9.

[34]

R. M. van der Sluis, T. van Montfort, G. Pollakis, R. W. Sanders, D. Speijer, B. Berkhout and R. E. Jeeninga, Dendritic cell-induced activation of latent HIV-1 provirus in actively proliferating primary T lymphocytes,, PLoS Pathogens, 9 (2013).

[35]

L. Sompayrac, How the Immune System Works,, Wiley, (2003).

[36]

R. Steuer, J. Kurths, C. O. Daub, J. Weise and J. Selbig, The mutual information: Detecting and evaluating dependencies between variables,, Bioinformatics, 18 (2002).

[37]

M. Strain, S. Little, E. Daar, D. Havlir, H. Gunthard, R. Lam, O. Daly, J. Nguyen, C. Ignacio, C. Spina, D. Richman and J. Wong, Effect of treatment, during primary infection, on establishment and clearance of cellular reservoirs of HIV-1,, The Journal of Infectious Diseases, 191 (2005), 1410.

[38]

R. M. Welsh, K. Bahl, H. D. Marshall and S. L. Urban, Type 1 interferons and antiviral CD8+ T cell responses,, PLoS Pathogens, 8 (2012).

[39]

N. Zhang and M. J. Bevan, CD8(+) T cells: Foot soldiers of the immune system,, Immunity, 35 (2011), 161.

show all references

References:
[1]

S. Abdella, N. Wabe and E. Yesuf, Management of common adverse effects in the era of highly active antiretroviral therapy in south east Ethiopia,, North American Journal of Medical Sciences, 3 (2011), 499. doi: 10.4297/najms.2011.3499.

[2]

B. M. Adams, H. T. Banks, M. Davidian and E. S. Rosenberg, Model fitting and prediction with HIV treatment interruption data,, Center for Research in Scientific Computation Technical Report CRSC-TR05-40, 69 (2007), 05.

[3]

A. Alexaki, Y. Liu and B. Wigdahl, Cellular reservoirs of HIV-1 and their role in viral persistence,, Current HIV Research, 6 (2008), 388. doi: 10.2174/157016208785861195.

[4]

J. Ananworanich, C. Vandergeeten, N. Chomchey and N. Chomont, Early ART Intervention Restricts the Seeding of the HIV Reservoir in Long-Lived Central Memory CD4+ T Cells,, Program and Abstracts of the 20 Conference on Retroviruses and Opportunistic Infections, (2013).

[5]

A. Cintron-Arias, H. T. Banks, A. Capaldi and A. L. Lloyd, A sensitivity matrix based methodology for inverse problem formulation, CRSC Tech. Rep. CRSC-TR09-09, April, 2009;, J. Inverse and Ill-posed Problems, 17 (2009), 545. doi: 10.1515/JIIP.2009.034.

[6]

H. T. Banks, A. Cintron-Arias and F. Kappel, Parameter selection methods in inverse problem formulation,, in Mathematical Modeling and Validation in Physiology, 2064 (2013), 43. doi: 10.1007/978-3-642-32882-4_3.

[7]

H. T. Banks, M. Davidian, S. Hu, G. M. Kepler and E. S. Rosenberg, Modeling HIV immune response and validation with clinical data,, Journal of Biological Dynamics, 2 (2008), 357. doi: 10.1080/17513750701813184.

[8]

H. T. Banks, K. Holm and D. Robbins, Standard error computations for uncertainty quantification in inverse problems: Asymptotic theory vs. bootstrapping,, Mathematical and Computer Modeling, 52 (2010), 1610. doi: 10.1016/j.mcm.2010.06.026.

[9]

H. T. Banks, S. Hu and W. Clayton Thompson, Modeling and Inverse Problems in the Presence of Uncertainty,, CRSC Press/ Taylor and Frances Publishing, (2014).

[10]

H. T. Banks, D. F. Kapraun, W. Clayton Thompson, C. Peligero, J. Argilaguet and A. Meyerhans, A novel statistical analysis and interpretation of flow cytometry data,, Journal of Biological Dynamics, 7 (2013), 96. doi: 10.1080/17513758.2013.812753.

[11]

H. T. Banks and H. T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes,, Taylor Francis/CRC Press, (2009).

[12]

J. N. Blankson, D. Persaud and R. F. Siliciano, The challenge of viral reservoirs in HIV-1 infection,, Annual Review of Medicine, 53 (2002), 557. doi: 10.1146/annurev.med.53.082901.104024.

[13]

R. J. Carroll and D. Ruppert, Transformation and Weighting in Regression,, Chapman & Hall, (1988). doi: 10.1007/978-1-4899-2873-3.

[14]

R. J. Carroll, C. F. J. Wu and D. Ruppert, The effect of estimating weights in weighted least squares,, J. Amer. Statistical Assoc., 83 (1988), 1045. doi: 10.1080/01621459.1988.10478699.

[15]

M. Catalfamo, C. Wilhelm, L. T. Cheung, M. Proschan, T. Friesen, J. H. Park, J. Adelsberger, M. Baseler, F. Maldarelli, R. Davey, G. Roby, C. Rehm and C. Lane, CD4+ and CD8+ T cell immune activation during chronic HIV infection: roles of homeostasis, HIV, type I IFN, and IL-7,, Journal of Immunology, 186 (2011), 2106. doi: 10.4049/jimmunol.1002000.

[16]

N. W. Cummins and A. D. Badley, Anti-apoptotic mechanisms of HIV: lessons and novel approaches to curing HIV,, Cellular and Molecular Life Sciences: CMLS, 70 (2013), 3355.

[17]

C. Dalmasso, W. Carpentier, L. Meyer, C. Rouzioux, C. Goujard, M.-L. Chaix, O. Lambotte, V. Avettand-Fenoel, S. Le Clerc, L. D. de Senneville, C. Deveau, F. Boufassa, P. Debré, J.-F. Delfraissy, P. Broet and I. Theodorou, Distinct genetic loci control plasma HIV-RNA and cellular HIV-DNA levels in HIV-1 infection: the ANRS Genome Wide Association 01 study,, PloS one, 3 (2008).

[18]

M. Davidian, Nonlinear Models for Univariate and Multivariate Response,, ST 762 Lecture Notes, (2007).

[19]

M. Davidian and D. M. Giltinan, Nonlinear Models for Repeated Measurement Data,, Chapman and Hall, (2000).

[20]

B. Descours, V. Avettand-Fenoel, C. Blanc, A. Samri, A. Mélard, V. Supervie, I. Theodorou, G. Carcelain, C. Rouzioux and B. Autran, Immune responses driven by protective human leukocyte antigen alleles from long-term nonprogressors are associated with low HIV reservoir in central memory CD4+ T cells,, Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America, 54 (2012), 1495.

[21]

T. J. DiCiccio and B. Efron, Bootstrap confidence intervals,, Statistical Science, 11 (1996), 189. doi: 10.1214/ss/1032280214.

[22]

B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans,, CBMS 38, (1982).

[23]

M. Egger, M. May, G. Chêne, A. N. Phillips, B. Ledergerber, F. Dabis, D. Costagliola, A. D'Arminio Monforte, F. de Wolf, P. Reiss, J. Lundgren, A. Justice, S. Staszewski, C. Leport, R. Hogg, S. Robert, C. Sabin, M. Gill, B. Salzberger and J. Sterne, Prognosis of HIV-1-infected patients starting highly active antiretroviral therapy: A collaborative analysis of prospective studies,, Lancet, 360 (2002), 119.

[24]

T. H. Finkel, G. Tudor-Williams, N. K. Banda, M. F. Cotton, T. Curiel, C. Monks, T. W. Baba, R. M. Ruprecht and A. Kupfer, Apoptosis occurs predominantly in bystander cells and not in productively infected cells of HIV- and SIV-infected lymph nodes,, Nature Medicine, 1 (1995), 129.

[25]

O. Lambotte, F. Boufassa, Y. Madec, A. Nguyen, C. Goujard, L. Meyer, C. Rouzioux, A. Venet and J.-F. Delfraissy, HIV controllers: A homogeneous group of HIV-1-infected patients with spontaneous control of viral replication,, Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America, 41 (2005), 1053.

[26]

S. Lodi, L. Meyer, A. Kelleher, M. Rosinska, J. Ghosn, M. Sannes and K. Porter, Immunovirologic control 24 months after interruption of antiretroviral therapy initiated close to HIV seroconversion,, Archives of Internal Medicine, 172 (2012), 1251.

[27]

B. Max and R. Sherer, Management of the adverse effects of antiretroviral therapy and medication adherence,, Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America, 30 (2000).

[28]

T. H. Mogensen, J. Melchjorsen, C. S. Larsen and S. R. Paludan, Innate immune recognition and activation during HIV infection,, Retrovirology, 7 (2010).

[29]

N. Ngo-Giang-Huong, C. Deveau, I. Da Silva, I. Pellegrin, A. Venet, M. Harzic, M. Sinet, J. F. Delfraissy, L. Meyer, C. Goujard and C. Rouzioux, Proviral HIV-1 DNA in subjects followed since primary HIV-1 infection who suppress plasma viral load after one year of highly active antiretroviral therapy,, AIDS, 15 (2001), 665.

[30]

T. Schreiber and A. Schmitz, Surrogate time series,, Physica D: Nonlinear Phenomena, 142 (2000), 346. doi: 10.1016/S0167-2789(00)00043-9.

[31]

G. A. F. Seber and C. J. Wild, Nonlinear Regression,, J. Wiley & Sons, (1989). doi: 10.1002/0471725315.

[32]

L. Shan, K. Deng, N. S. Shroff, C. M. Durand, S. A. Rabi, H.-C. Yang, H. Zhang, J. B. Margolick, J. N. Blankson and R. F. Siliciano, Stimulation of HIV-1-specific cytolytic T lymphocytes facilitates elimination of latent viral reservoir after virus reactivation,, Immunity, 36 (2012), 491.

[33]

B. W. Silverman, Density Estimation for Statistics and Data Analysis,, Chapman and Hall, (1986). doi: 10.1007/978-1-4899-3324-9.

[34]

R. M. van der Sluis, T. van Montfort, G. Pollakis, R. W. Sanders, D. Speijer, B. Berkhout and R. E. Jeeninga, Dendritic cell-induced activation of latent HIV-1 provirus in actively proliferating primary T lymphocytes,, PLoS Pathogens, 9 (2013).

[35]

L. Sompayrac, How the Immune System Works,, Wiley, (2003).

[36]

R. Steuer, J. Kurths, C. O. Daub, J. Weise and J. Selbig, The mutual information: Detecting and evaluating dependencies between variables,, Bioinformatics, 18 (2002).

[37]

M. Strain, S. Little, E. Daar, D. Havlir, H. Gunthard, R. Lam, O. Daly, J. Nguyen, C. Ignacio, C. Spina, D. Richman and J. Wong, Effect of treatment, during primary infection, on establishment and clearance of cellular reservoirs of HIV-1,, The Journal of Infectious Diseases, 191 (2005), 1410.

[38]

R. M. Welsh, K. Bahl, H. D. Marshall and S. L. Urban, Type 1 interferons and antiviral CD8+ T cell responses,, PLoS Pathogens, 8 (2012).

[39]

N. Zhang and M. J. Bevan, CD8(+) T cells: Foot soldiers of the immune system,, Immunity, 35 (2011), 161.

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