Skip to main content
Top
Published in: BMC Medical Research Methodology 1/2020

Open Access 01-12-2020 | Human Immunodeficiency Virus | Research article

Methods of competing risks flexible parametric modeling for estimation of the risk of the first disease among HIV infected men

Authors: Sahar Nouri, Mahmood Mahmoudi, Kazem Mohammad, Mohammad Ali Mansournia, Mahdi Yaseri, Noori Akhtar-Danesh

Published in: BMC Medical Research Methodology | Issue 1/2020

Login to get access

Abstract

Background

Patients infected with the Human Immunodeficiency Virus (HIV) are susceptible to many diseases. In these patients, the occurrence of one disease alters the chance of contracting another. Under such circumstances, methods for competing risks are required. Recently, competing risks analyses in the scope of flexible parametric models have risen to address this requirement. These lesser-known analyses have considerable advantages over conventional methods.

Methods

Using data from Multi Centre AIDS Cohort Study (MACS), this paper reviews and applies methods of competing risks flexible parametric models to analyze the risk of the first disease (AIDS or non-AIDS) among HIV-infected patients. We compared two alternative subdistribution hazard flexible parametric models (SDHFPM1 and SDHFPM2) with the Fine & Gray model. To make a complete inference, we performed cause-specific hazard flexible parametric models for each event separately as well.

Results

Both SDHFPM1 and SDHFPM2 provided consistent results regarding the magnitude of coefficients and risk estimations compared with estimations obtained from the Fine & Gray model, However, competing risks flexible parametric models provided more efficient and smoother estimations for the baseline risks of the first disease. We found that age at HIV diagnosis indirectly affected the risk of AIDS as the first event by increasing the number of patients who experience a non-AIDS disease prior to AIDS among > 40 years. Other significant covariates had direct effects on the risks of AIDS and non-AIDS.

Discussion

The choice of an appropriate model depends on the research goals and computational challenges. The SDHFPM1 models each event separately and requires calculating censoring weights which is time-consuming. In contrast, SDHFPM2 models all events simultaneously and is more appropriate for large datasets, however, when the focus is on one particular event SDHFPM1 is more preferable.
Appendix
Available only for authorised users
Literature
1.
go back to reference Patel P, Rose CE, Collins PY, Nuche-Berenguer B, Sahasrabuddhe VV, Peprah E, et al. Noncommunicable diseases among HIV-infected persons in low-income and middle-income countries: a systematic review and meta-analysis. AIDS. 2018;32(Suppl 1):S5–20.PubMedCrossRef Patel P, Rose CE, Collins PY, Nuche-Berenguer B, Sahasrabuddhe VV, Peprah E, et al. Noncommunicable diseases among HIV-infected persons in low-income and middle-income countries: a systematic review and meta-analysis. AIDS. 2018;32(Suppl 1):S5–20.PubMedCrossRef
2.
go back to reference Masia M, Padilla S, Moreno S, Barber X, Iribarren JA, Del Romero J, et al. Prediction of long-term outcomes of HIV-infected patients developing non-AIDS events using a multistate approach. PLoS One. 2017;12(9):e0184329.PubMedPubMedCentralCrossRef Masia M, Padilla S, Moreno S, Barber X, Iribarren JA, Del Romero J, et al. Prediction of long-term outcomes of HIV-infected patients developing non-AIDS events using a multistate approach. PLoS One. 2017;12(9):e0184329.PubMedPubMedCentralCrossRef
3.
go back to reference Serrano-Villar S, Perez-Elias MJ, Dronda F, Casado JL, Moreno A, Royuela A, et al. Increased risk of serious non-AIDS-related events in HIV-infected subjects on antiretroviral therapy associated with a low CD4/CD8 ratio. PLoS One. 2014;9(1):e85798.PubMedPubMedCentralCrossRef Serrano-Villar S, Perez-Elias MJ, Dronda F, Casado JL, Moreno A, Royuela A, et al. Increased risk of serious non-AIDS-related events in HIV-infected subjects on antiretroviral therapy associated with a low CD4/CD8 ratio. PLoS One. 2014;9(1):e85798.PubMedPubMedCentralCrossRef
4.
go back to reference Wolbers M, Koller MT, Stel VS, Schaer B, Jager KJ, Heinze G, et al. Statistical tutorials Competing risks analyses : objectives and approaches. Eur Heart J. 2014;35(42):2936–41. Wolbers M, Koller MT, Stel VS, Schaer B, Jager KJ, Heinze G, et al. Statistical tutorials Competing risks analyses : objectives and approaches. Eur Heart J. 2014;35(42):2936–41.
6.
go back to reference Baker JV, Peng G, Rapkin J, Abrams DI, Silverberg MJ, MacArthur RD, et al. CD4+ count and risk of non-AIDS diseases following initial treatment for HIV infection. AIDS. 2008;22(7):841–8.PubMedCrossRef Baker JV, Peng G, Rapkin J, Abrams DI, Silverberg MJ, MacArthur RD, et al. CD4+ count and risk of non-AIDS diseases following initial treatment for HIV infection. AIDS. 2008;22(7):841–8.PubMedCrossRef
7.
go back to reference Serrano-villar S, Pe A, Sainz T, Navas E, Hermida M, Royuela A, et al. Increased Risk of Serious Non-AIDS-Related Events in HIV-Infected Subjects on Antiretroviral Therapy Associated with a Low CD4 / CD8 Ratio. 2014;9(1):e85798. Serrano-villar S, Pe A, Sainz T, Navas E, Hermida M, Royuela A, et al. Increased Risk of Serious Non-AIDS-Related Events in HIV-Infected Subjects on Antiretroviral Therapy Associated with a Low CD4 / CD8 Ratio. 2014;9(1):e85798.
9.
go back to reference Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: competing risks and multi-state models. Stat Med. 2007 May;26(11):2389–430.PubMedCrossRef Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: competing risks and multi-state models. Stat Med. 2007 May;26(11):2389–430.PubMedCrossRef
11.
go back to reference Wolbers M, Koller MT, Stel VS, Schaer B, Jager KJ, Leffondré K, et al. Competing risks analyses: objectives and approaches. Eur Heart J. 2014 Nov;35(42):2936–41.PubMedPubMedCentralCrossRef Wolbers M, Koller MT, Stel VS, Schaer B, Jager KJ, Leffondré K, et al. Competing risks analyses: objectives and approaches. Eur Heart J. 2014 Nov;35(42):2936–41.PubMedPubMedCentralCrossRef
12.
13.
15.
go back to reference Kim HT. Cumulative incidence in competing risks data and competing risks regression analysis. Clin Cancer Res. 2007 Jan;13(2 Pt 1):559–65.PubMedCrossRef Kim HT. Cumulative incidence in competing risks data and competing risks regression analysis. Clin Cancer Res. 2007 Jan;13(2 Pt 1):559–65.PubMedCrossRef
16.
18.
19.
go back to reference Prentice RL, Kalbfleisch JD, Peterson AVJ, Flournoy N, Farewell VT, Breslow NE. The analysis of failure times in the presence of competing risks. Biometrics. 1978;34(4):541–54.PubMedCrossRef Prentice RL, Kalbfleisch JD, Peterson AVJ, Flournoy N, Farewell VT, Breslow NE. The analysis of failure times in the presence of competing risks. Biometrics. 1978;34(4):541–54.PubMedCrossRef
21.
go back to reference Lau B, Cole SR, Gange SJ. Parametric mixture models to evaluate and summarize hazard ratios in the presence of competing risks with time-dependent hazards and delayed entry. Stat Med. 2011;30(6):654–65.PubMedCrossRef Lau B, Cole SR, Gange SJ. Parametric mixture models to evaluate and summarize hazard ratios in the presence of competing risks with time-dependent hazards and delayed entry. Stat Med. 2011;30(6):654–65.PubMedCrossRef
22.
23.
go back to reference Larson MGDG. A mixture model for the regression analysis of competing risks data. J R Stat Soc Ser C. 1985;34:201–11. Larson MGDG. A mixture model for the regression analysis of competing risks data. J R Stat Soc Ser C. 1985;34:201–11.
25.
go back to reference Nicolaie MA, van Houwelingen HCPH. Vertical modeling: a pattern mixture approach for competing risks modeling. Stat Med. 2010;29:1190–205.PubMed Nicolaie MA, van Houwelingen HCPH. Vertical modeling: a pattern mixture approach for competing risks modeling. Stat Med. 2010;29:1190–205.PubMed
26.
go back to reference Haller B, Schmidt G, Ulm K. Applying competing risks regression models: an overview. Lifetime Data Anal. 2013;19(1):33–58.PubMedCrossRef Haller B, Schmidt G, Ulm K. Applying competing risks regression models: an overview. Lifetime Data Anal. 2013;19(1):33–58.PubMedCrossRef
30.
go back to reference Mozumder SI, Rutherford M, Lambert P. Direct likelihood inference on the cause-specific cumulative incidence function: a flexible parametric regression modelling approach. Stat Med. 2018;37(1):82–97.PubMedCrossRef Mozumder SI, Rutherford M, Lambert P. Direct likelihood inference on the cause-specific cumulative incidence function: a flexible parametric regression modelling approach. Stat Med. 2018;37(1):82–97.PubMedCrossRef
31.
go back to reference Royston P, Parmar MKB. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat Med. 2002;21(15):2175–97.PubMedCrossRef Royston P, Parmar MKB. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat Med. 2002;21(15):2175–97.PubMedCrossRef
33.
go back to reference Hernan MA, Brumback B, Robins JM. Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology. 2000;11(5):561–70.PubMedCrossRef Hernan MA, Brumback B, Robins JM. Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology. 2000;11(5):561–70.PubMedCrossRef
34.
go back to reference Graham NM, Zeger SL, Kuo V, Jacobson LP, Vermund SH, Phair JP, et al. Zidovudine use in AIDS-free HIV-1-seropositive homosexual men in the multicenter AIDS cohort study (MACS), 1987-1989. J Acquir Immune Defic Syndr. 1991;4(3):267–76.PubMed Graham NM, Zeger SL, Kuo V, Jacobson LP, Vermund SH, Phair JP, et al. Zidovudine use in AIDS-free HIV-1-seropositive homosexual men in the multicenter AIDS cohort study (MACS), 1987-1989. J Acquir Immune Defic Syndr. 1991;4(3):267–76.PubMed
35.
go back to reference Hessol NA, Kalinowski A, Benning L, Mullen J, Young M, Palella F, et al. Mortality among participants in the multicenter AIDS cohort study and the Women’s interagency HIV study. Clin infect dis [internet]. 2007;44(2):287–94 Available from: https://doi.org/10.1086/510488.CrossRef Hessol NA, Kalinowski A, Benning L, Mullen J, Young M, Palella F, et al. Mortality among participants in the multicenter AIDS cohort study and the Women’s interagency HIV study. Clin infect dis [internet]. 2007;44(2):287–94 Available from: https://​doi.​org/​10.​1086/​510488.CrossRef
36.
go back to reference Cole SR, Hernán MA, Robins JM, Anastos K, Chmiel J, Detels R, et al. Effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome or death using marginal structural models. Am J Epidemiol [internet]. 2003;158(7):687–694. Available from: https://doi.org/10.1093/aje/kwg206.PubMedCrossRef Cole SR, Hernán MA, Robins JM, Anastos K, Chmiel J, Detels R, et al. Effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome or death using marginal structural models. Am J Epidemiol [internet]. 2003;158(7):687–694. Available from: https://​doi.​org/​10.​1093/​aje/​kwg206.PubMedCrossRef
39.
40.
go back to reference Hinchliffe SR. Advancing and appraising competing risks methodology for better communication of survival statistics. [Internet] [Doctoral dissertation]. University of Leicester; 2013. Available from: http://hdl.handle.net/2381/28176. Hinchliffe SR. Advancing and appraising competing risks methodology for better communication of survival statistics. [Internet] [Doctoral dissertation]. University of Leicester; 2013. Available from: http://​hdl.​handle.​net/​2381/​28176.
41.
go back to reference Mozumder SI. Development of flexible parametric models for competing risks and tools to facilitate in the understanding and communication of Cancer survival [internet] [doctoral dissertation]. University of Leicester; 2018. Available from: https://hdl.handle.net/2381/42864 Mozumder SI. Development of flexible parametric models for competing risks and tools to facilitate in the understanding and communication of Cancer survival [internet] [doctoral dissertation]. University of Leicester; 2018. Available from: https://​hdl.​handle.​net/​2381/​42864
42.
go back to reference Geskus RB. Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. Biometrics. 2011;67(1):39–49.PubMedCrossRef Geskus RB. Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. Biometrics. 2011;67(1):39–49.PubMedCrossRef
43.
go back to reference Mozumder SI, Rutherford MJ, Lambert PC. stpm2cr: a flexible parametric competing risks model using a direct likelihood approach for the cause-specific cumulative incidence function. Stata J. 2017;17(2):462–89.PubMedPubMedCentralCrossRef Mozumder SI, Rutherford MJ, Lambert PC. stpm2cr: a flexible parametric competing risks model using a direct likelihood approach for the cause-specific cumulative incidence function. Stata J. 2017;17(2):462–89.PubMedPubMedCentralCrossRef
44.
go back to reference Harrell FE. Regression modeling strategies. With applications to linear models, logistic regression, and survival analysis. 2nd ed. New York, Berlin, Heidelberg: Springer International Publishing; 2015. Harrell FE. Regression modeling strategies. With applications to linear models, logistic regression, and survival analysis. 2nd ed. New York, Berlin, Heidelberg: Springer International Publishing; 2015.
45.
47.
48.
go back to reference Pettit AC, Giganti MJ, Ingle SM, May MT, Shepherd BE, Gill MJ, et al. Increased non-AIDS mortality among persons with AIDS-defining events after antiretroviral therapy initiation. J Int AIDS Soc. 2018;21(1).PubMedCentralCrossRef Pettit AC, Giganti MJ, Ingle SM, May MT, Shepherd BE, Gill MJ, et al. Increased non-AIDS mortality among persons with AIDS-defining events after antiretroviral therapy initiation. J Int AIDS Soc. 2018;21(1).PubMedCentralCrossRef
49.
go back to reference Greenland S, Mansournia MA, Altman DG. Sparse data bias: a problem hiding in plain sight. BMJ. 2016;352:i1981.PubMedCrossRef Greenland S, Mansournia MA, Altman DG. Sparse data bias: a problem hiding in plain sight. BMJ. 2016;352:i1981.PubMedCrossRef
Metadata
Title
Methods of competing risks flexible parametric modeling for estimation of the risk of the first disease among HIV infected men
Authors
Sahar Nouri
Mahmood Mahmoudi
Kazem Mohammad
Mohammad Ali Mansournia
Mahdi Yaseri
Noori Akhtar-Danesh
Publication date
01-12-2020
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2020
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/s12874-020-0900-z

Other articles of this Issue 1/2020

BMC Medical Research Methodology 1/2020 Go to the issue