1. Introduction
y disrupting the immune system, Acquired Immunodeficiency Syndrome (AIDS) exposes individuals to Tuberculosis (TB) absorbing state and increases the death rate [1, 2]. The global incidence of Human Immunodeficiency Virus (HIV) and TB equals 0.44%; in Iran, 0.037% of deaths occur due to HIV and TB [2, 3]. Survival modeling can estimate the survival function for each individual at any given time [4, 5]. 
An intermediate state is a flexible tool, that practically, can easily examine the results of different survival models by fully considering the intermediate event [6]. The simplest form of this model involves describing the process of health to disease and death, i.e., called the disease-death model [7]. Intermediate states are used to estimate the transition odds and the factors affecting each transition [6, 7, 8, 9, 10, 11, 12]. In the present study, an intermediate state was used to examine the progression of HIV infection to death.
2. Materials and Methods
In this retrospective study, patients’ information was extracted from their treatment records using a checklist that included demographic, behavioral, and disease transmission information. The intermediate state, at each stage, measured the impact of factors affecting the progression of the disease [13]. The time of diagnosis of HIV was considered as the baseline, the death as the absorbing state, and the stages of AIDS, TB, and the simultaneous infection of HIV/TB as intermediate states (Figure 1).  To estimate the odds of transition between states, we used the Allen-Johnson estimator probability of staying (Formula 1) [7]:


I represent the same matrix, and  is a matrix in which in its non-diameter elements, the momentary hazards of transition from the g-state to the h-state are  Instantaneous hazards were estimated as Formula 2:


Yg(s)Yg(s) reflects the number of individuals who are at risk in a state other than g at time s in a state other than dgh(s) dgh(s) represents the number of subjects that have entered stated h from state g at the s time.
To examine the effect of auxiliary variables on cause-specific risk for the individual, a proportional risk model was used (Formula 3):


The estimation of parameters was performed using the partial odds method, as Formula 4 [10]:


To analyze the obtained data, mState and msSurv packages were used in R software version 3.3.3.
3. Results
The Mean±SD age of examined 2185 participants was 33.9±10.3 years. Of the 1195(54.7%) subjects infected with HIV, 619(51.7%) received antiretroviral treatment and 342(28.6%) patients received isoniazid prophylaxis.
Approximately 20% of the explored participants were expired within the first 10 years after being diagnosed with HIV. In this time, about 40% of the subjects remained HIV-positive, and about 40% of those experienced AIDS.
In the first transition from the primary state (HIV diagnosis) to state 2 (AIDS diagnosis) (Figure 1), the variables of age, isoniazid intake, CD4 count, and the routes of transmission were influential. In this study, the transitions of HIV to TB, AIDS to death, and TB to TB/AIDS were not included in Tables 1 and 2 due to the lack of significance of the variables. 


The variables affecting the third transition (transition from HIV to death, Figure 1) were also a history of imprisonment, age, and the use of antiretroviral drugs, respectively (P<0.05).
The variables affecting the fourth transition (transition from AIDS to TB, Figure 1) also significantly influenced disease progression and TB, respectively, which included gender, prison history, age, isoniazid intake, CD4, and antiretroviral treatment (Table 2).


The effective variables in the fifth transition (transition from AIDS to death) were gender, imprisonment, isoniazid intake, CD4, and antiretroviral therapy, in sequence (Table 1).
4. Discussion
In our study, the risk of death was higher in HIV-infected patients who did not receive antiretroviral therapy than in those who expired. Other studies indicated that antiretroviral therapy reduces the burden of disease in HIV-infected patients [11, 12, 13]. A prognostic factor of HIV disease is the number of CD4 cells [14]. Our study also confirmed its effects on AIDS, post-AIDS TB development, and AIDS-related deaths. Low CD4 cell count is a direct factor in the development of TB in individuals living with HIV [15, 16]. In our study, the age of individuals was significantly associated with AIDS, HIV-related death, and AIDS-related death, i.e., consistent with other studies [13، 16, 17, 18, 19, 20]. The effect of gender was approved on TB generated after AIDS and AIDS-induced death [21, 22]. However, the effect of gender has not been confirmed in some studies n this respect [20]. Prison history was influential in our study on HIV-related deaths, post-AIDS TB, and AIDS-induced deaths, i.e., consistent with other studies [23, 24]. The main risk factor for the spread of HIV and AIDS in Iran is injection drug use. The most common cause of disease transmission in men is injecting drugs and in women, is sexual intercourse [13, 25, 26]. Isoniazid intake was effective in the progression of HIV to AIDS, AIDS to TB, and death from AIDS [28 ,27 ,18]. 
The current study results indicated the effects of different clinical and baseline variables on the natural course of this disease. Therefore, preventing the further spread of the disease to the community and controlling the disease in patients requires targeted educational and therapeutic interventions that familiarize community members with the routes of transmission and the prevention of the disease and encourage patients to visit medical centers early.

Ethical Considerations
Compliance with ethical guidelines
This study was approved by the Research Ethics Committee of Hamadan University of Medical Sciences (Code: IR.UMSHA.REC.1396.117).

Funding
This research did not receive any grant from funding agencies in the public, commercial, or non-profit sectors. 

Authors' contributions
All authors equally contributed to preparing this article.

Conflicts of interest
The authors declared no conflicts of interest.

Acknowledgements
We appreciate the cooperation of the Vice Chancellor for Research and Technology of Hamadan University of Medical Sciences.


References

1. Oladejo N, John A. A steady state solution method for HIV/AIDS model for the assesment, monitoring, control and evaluation of confirmed status with vertical transmission in Nigeria. J Virol Antivir Res. 2017;6:1. [DOI:10.4172/2324-8955.1000166]
2. Bernstein L, Ross RK. Endogenous hormones and breast cancer risk. Epidemiol Rev. 1993; 15(1):48-65. [DOI:10.1093/oxfordjournals.epirev.a036116][PMID]
3. Hatami H, Yadegarfar G, Meshkati M. [Investigation of survival rate among HIV-positive individuals identified in Isfahan Province, 1997-2013 (Iran) (Persian)]. Qom Univ Med Sci J. 2017; 11(8):66-75. http://journal.muq.ac.ir/article-1-499-en.html
4. Hosseini M, Mohammad K, Rahimzadeh Kivi M, Mahmoodi M. [Comparison of survival models in studying breastfeeding duration (Persian)]. Hakim. 2007; 1(10);66-71. http://hakim.hbi.ir/article-1-336-fa.html
5. Sainani KL. Introduction to survival analysis. PM R. 2016; 8(6):580-5. [DOI:10.1016/j.pmrj.2016.04.003][PMID]
6. Meira-Machado L, de Uña-Álvarez J, Cadarso-Suárez C, Andersen PK. Multi-state models for the analysis of time-to-event data. Stat Methods Med Res. 2019; 18(2):195-222. [DOI:10.1177/0962280208092301] [PMID] [PMCID]
7. Putter H, van der Hage J, de Bock GH, Elgalta R, van de Velde CJ. Estimation and prediction in a multi-state model for breast cancer. Biom J. 2006; 48(3):366-80. [DOI:10.1002/bimj.200510218]
8. Hougaard P. Multi-state models: A review. Lifetime Data Anal. 1999; 5(3):239-64. [DOI:10.1023/A:1009672031531][PMID]
9. Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: Competing risks and multi-state models. Stat Med. 2007; 26(11):2389-430. [DOI:10.1002/sim.2712]
10. Geskus RB. Data analysis with competing risks and intermediate states. Taylor & Francis Group: New York; 2020. https://books.google.com/books?id=bq73zQEACAAJ&dq
11. Haghighat S. Survival rate and its correlated factors in breast cancer patients referred to breast cancer research center. Iran J Breast Dis. 2013; 6(3):28-36. http://ijbd.ir/article-1-291-en.html
12. Cui Z, Lin M, Nie S, Lan R. Risk factors associated with Tuberculosis (TB) among people living with HIV/AIDS: A pair-matched case-control study in Guangxi, China. PloS One. 2017; 12(3):e0173976. [DOI:10.1371/journal.pone.0173976][PMID][PMCID]
13. Yaghoobi H, Ahmadiniya H, Shabani Z, Vazirinejad R, Zolfizadeh F, Rezaeian M. [The epidemiological investigation of patients with HIV/AIDS in Bandar Abbas behavioral disorders counseling center during 2005-2015 (Persian)]. J Rafsanjan Univ Med Sci. 2018; 16(10):969-82. http://journal.rums.ac.ir/browse.php?a_id=3815&sid=1&slc_lang=en
14. Lanoy E, May M, Mocroft A, Phillip A, Justice A, Chene G, et al. Prognosis of patients treated with cART from 36 months after initiation, according to current and previous CD4 cell count and plasma HIV-1 RNA measurements. AIDS. 2019; 23(16):2199-208. [DOI:10.1097/QAD.0b013e3283305a00][PMID][PMCID]
15. Mokarian F, Mokarian S, Ramezani A. [Relations of disease-free survival and overall survival with age and primary metastases in patients with breast cancer (Persian)]. J Isfahan Med Sch. 2013; 31(225):112-20. http://jims.mui.ac.ir/index.php/jims/article/view/1827
16. Akbarzadeh Baghban A, Zaeri F, Hashemi Nazari SS, Jambarsang S, Nikfarjam A, Moradi A. [Estimation of the CD4 cells recovery probability following long term HAART in HIV positive patients using a non-homogenous Markov model (Persian)]. J Clin Res Paramed Sci. 2017; 5(4):293-301. https://sites.kowsarpub.com/jcrps/articles/81553.html
17. Ghorbani N, Yazdani Cherati J, Anvari K, Ghorbani N. [Factors affecting recurrence in breast cancer using Cox model (Persian)]. J Mazandaran Univ Med Sci. 2015; 25(131):32-9. http://jmums.mazums.ac.ir/article-1-6567-en.html
18. Rampisheh Z, Motamed N, Amiri M, Ostovar A, Azarnoush A, Bahramian F, et al. [Breast cancer survival rate according to data of cancer registry and death registry systems in Bushehr Province, 2001-2013 (Persian)]. Iran South Med J. 2015; 18(4):729-37. http://ismj.bpums.ac.ir/article-1-715-en.html
19. Swain PK, Grover G. Determination of predictors associated with HIV/AIDS patients on ART using accelerated failure time model for interval censored survival data. Curr Res Biostat. 2016; 6(1):12-9. [DOI:10.3844/amjbsp.2016.12.19]
20. Saatchi M, Roshanaei G, Khazaei S, Zahiri A, Bathaei J. [Assessment of Epidemiology extra pulmonary tuberculosis in Hamadan province 2006-2012 (Persian)]. Pajouhan Sci J 2014; 12(3):1-11. https://psj.umsha.ac.ir/article-1-25-en.html
21. Akbari M, Gharibi M, Modi K, Vaziri Mehr V. Tuberculosis and epidemiology in Bu Ali Hospital of Zahedan from March 2013 to the end of October 2013. Paper presented at: 6^th National Congress of Biology and Natural Sciences of Iran. 13 February 2019; Tehran, Iran. https://civilica.com/l/9503/
22. Umeh EU, Ishaleku D, Iheukwumere CC. HIV/Tuberculosis co-infection among patients attending a referral chest clinic in Nasarawa State, Nigeria. J Appli Sci. 2020; 7(6):933-5. [DOI:10.3923/jas.2007.933.935]
23. Kassira EN, Bauserman RL, Tomoyasu N, Caldeira E, Swetz A, Solomon L. HIV and AIDS surveillance among inmates in Maryland prisons. J Urban Health. 2001; 78(2):256-63. [DOI:10.1093/jurban/78.2.256][PMID][PMCID]
24. Afsar Kazeroni P, Amini Lari M, Joulayi H, Sabet M, Hasanabadi AR, Naghshvarian M, et al. [Prevalence of human immunodeficiency virus infection and related risk factors among injective substance abusers in Shiraz, Southern part of Iran (Persian)]. J Fundam Ment Health. 2009; 11(43):175-84. [DOI:10.22038/JFMH.2009.1549]
25. World Health Organization (WHO). Global update on HIV treatment 2013: Results, impact and opportunities [Internet]. 2013 [Updated 2013 June]. Available from: https://www.who.int/hiv/data/global_treatment_report_presentation_2013.pdf
26. Mirahmadizadeh A, Kadivar MR, Ghane Shirazi R, Fararoei M. Prevalence of human immunodeficiency virus infection and related risk factors among injective substance abusers in Shiraz, Southern part of Iran. Sci J Gorgan Uni Med Sci. 2001; 3(8):39-42. https://www.sid.ir/fa/journal/ViewPaper.aspx?ID=14187
27. Cohen T, Lipsitch M, Walensky RP, Murray M. Beneficial and perverse effects of isoniazid preventive therapy for latent tuberculosis infection in HIV-tuberculosis coinfected populations. Proc Natl Acad Sci U S A. 2006; 103(18):7042-7. [DOI:10.1073/pnas.0600349103] [PMID][PMCID]
28. Lakzaei M, Salarilak S, Khalkhali H R, Maleki D, Esnaashari O. [Association between age of morbidity and prognosis of breast cancer (Persian)]. Stud Med Sci. 2015; 26(7):625-33. http://umj.umsu.ac.ir/article-1-3035-en.html