

ORIGINAL ARTICLE 

Year : 2016  Volume
: 7
 Issue : 1  Page : 101 

Estimating the transitional probabilities of smoking stages with crosssectional data and 10year projection for smoking behavior in Iranian adolescents
Ahmad Khosravi^{1}, Mohammad Ali Mansournia^{1}, Mahmood Mahmoodi^{1}, Ali Akbar Pouyan^{2}, Kourosh HolakouieNaieni^{1}
^{1} Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran ^{2} Department of Computer Engineering and Information Technology, Shahrood University of Technology, Shahrood, Iran
Date of Submission  23Jan2016 
Date of Acceptance  18Jul2016 
Date of Web Publication  17Aug2016 
Correspondence Address: Kourosh HolakouieNaieni Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran Iran
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/20087802.188602
Background: Cigarette smoking is one of the most important healthrelated risk factors in terms of morbidity and mortality. In this study, we introduced a new method for deriving the transitional probabilities of smoking stages from a crosssectional study and simulated a longterm smoking behavior for adolescents. Methods: In this study in 2010, a total of 4853 high school students were randomly selected and were completed a selfadministered questionnaire about cigarette smoking. We used smoothed age and sexspecific prevalence of smoking stages in a probabilistic discrete event system for estimating of transitional probabilities. A nonhomogenous discrete time Markov chain analysis was used to model the progression of the smoking in 10 years ahead in the same population. The mean age of the students was 15.69 ± 0.73 years (range: 1419). Results: The smoothed prevalence proportion of current smoking varies between 3.58 and 26.14%. The ageadjusted odds of initiation in boys is 8.9 (95% confidence interval [CI]: 7.910.0) times of the odds of initiation of smoking in girls. Our study predicted that the prevalence proportion of current smokers increased from 7.55% in 2010 to 20.31% (95% CI: 19.4421.37) for 2019. Conclusions: The present study showed a moderately but concerning prevalence of current smoking in Iranian adolescents and introduced a novel method for estimation of transitional probabilities from a crosssectional study. The increasing trend of cigarette use among adolescents indicated the necessity of paying more attention to this group. Keywords: Adolescents, discrete event system, projection, smoking stages, transitional probability
How to cite this article: Khosravi A, Mansournia MA, Mahmoodi M, Pouyan AA, HolakouieNaieni K. Estimating the transitional probabilities of smoking stages with crosssectional data and 10year projection for smoking behavior in Iranian adolescents
. Int J Prev Med 2016;7:101 
How to cite this URL: Khosravi A, Mansournia MA, Mahmoodi M, Pouyan AA, HolakouieNaieni K. Estimating the transitional probabilities of smoking stages with crosssectional data and 10year projection for smoking behavior in Iranian adolescents
. Int J Prev Med [serial online] 2016 [cited 2020 Jul 5];7:101. Available from: http://www.ijpvmjournal.net/text.asp?2016/7/1/101/188602 
Introduction   
Cigarette smoking is one of the most important healthrelated risk factors in terms of morbidity and mortality. ^{[1],[2]} As the World Health Organization reports, tobacco use is increasing in countries with low and middle income, and in highincome and developed countries, it is slowly declining with a constant slope. ^{[3]} The prevalence of cigarette smoking has decreased among the USA high school students in recent years. Demonstrating a decrease from 15.8% in 2011, in 2014, almost 9.2% of high school students reported that they had smoked cigarettes in the past 30 days. ^{[4]} Recent Iranian studies showed an increase in cigarette smoking among Iranian adolescents between 2002 and 2012. ^{[5],[6],[7]}
Due to a large health and economic consequence of cigarette smoking, it is important to delineate the future trends of cigarette smoking proportion among high school students as a highrisk group for transient over smoking stages and starting of smoking. ^{[5],[8]} Many of the studies conducted in Iran are crosssectional and there are not a longterm cohort study for assessing the smoking behavior in adolescents. Considering the lack of information about the future trends of smoking behavior in a large cohort study in Iran, we use a Markov chain model for projection of smoking behavior among an adolescents cohort for 10 years. Our main purpose was to estimate the agespecific transitional probability for never smoker (NS), current smoker (CS), and exsmoker within a crosssectional study, and in the second phase, we used these probabilities for longterm smoking behavior projections. Traditionally, such transitional probabilities are estimated by longitudinal studies, but there is some additional information in crosssectional studies that can allow us to calculate the transitional probabilities. In this study, we introduced a new method for deriving the transitional probabilities of smoking stages from a crosssectional study.
Methods   
Data
For estimation of ageadjusted 1year transitional probabilities of smoking stages, we used a crosssectional data. At first, in 2010, 57 high schools of Tabriz city were randomly selected and 82 boy and 114 girl classes regarding the number of students were randomly selected. The total number of presented students completed a selfadministered multiplechoice anonym questionnaire. To determine the reliability of the cigarette smoking stages questionnaire, we administrated it in 154 students twice with a 2week interval. Intraclass correlation coefficient was found to be 0.929 (confidence interval [CI] 95%: 0.900.95). The validity of the algorithm of smoking stages assessment was approved by Mohammadpoorasl et al. ^{[8]} This study have been approved by the Ethics Committee of Tabriz University of Medical Sciences.
For estimating the transitional probabilities, we used age and sexspecific prevalence of smoking stages from 4853 subjects. The mean age of the students was 15.69 ± 0.73 years (range: 1419).
The observed changes in smoking stages prevalence after 1 year in the same students were assessed 1 year later (2011). For validation of predictions, we compared the observed smoking stages prevalence for the same students in 2011 with our predicted smoking stages prevalence from the Markov model.
Study tools
In this study, we used less errorprone questions about smoking patterns such as smoking in the past 7 days and past 30 days and when tried a cigarette for the first time or the last time. Students were classified into three stages of cigarette smoking continuum ^{[4],[9],[10],[11]} as follows: (a) NS: Adolescents who have never smoked (even a puff); (b) CS: Adolescents who have tried the cigarette (even a puff) and smoked in the past 30 days; and (c) exsmoker (XS): Adolescents who have smoked cigarettes and did not smoked for 30 days ago. [Figure 1] shows an algorithm for classifying students into different stages of smoking. As shown in this algorithm, exsmokers (XS) in each specific age are consisted of three subcategories; (a) NXS = NS who progressed to exsmoker (students that smoked and quitted in the same age); (b) CS who progressed to exsmoker1 year ago; and (c) XXS = exsmoker that remained as exsmoker in the past year.  Figure 1: Algorithm for classifying participants into different stages of smoking
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Estimating of state probability and transitional probability
The state probabilities of smoking were computed by age and sexspecific prevalence proportions for NS, CS, and exsmokers. Our approaches for estimating transitional probabilities consist of two steps: (1) Smoothing of age and sexspecific prevalence of cigarette smoking stages which can remove the noise of proportions, (2) estimating transitional probabilities between smoking stages with a new and detectable approach as probabilistic discrete event systems (PDESs). According to the classification of smoking behavior, the PDES model is illustrated in [Figure 2]. The arrowed line in [Figure 2] indicates the 7 transition paths. Each σ_{i} (i = 1, 2, ,7) representing the transition from one state to another state during a 1year period. As shown in [Figure 2], σ_{1} indicates the probability for an NS remaining as an NS. σ_{2} indicates the transitional probability of NS to CS (initiation); σ_{4} indicates the transitional probability of CS to an exsmoker (quitting); σ_{5} indicates the transitional probability of exsmoker to CS (relapsing); σ_{7} indicates the transitional probability of NS to exsmoker (experimenter); σ_{3} and σ_{6} indicate the probability of CS and exsmoker remain on their primary stages. To estimate the mentioned transitional probabilities σ_{i} (i = 1, 2, 3,7), we first estimate the smoothed proportion of smoking stages using a multinomial Psplines. The Pspline smoothing can remove the noise from proportions. Fitting Pspline model provides a functional relation between age and prevalence proportions. In consequence, we can calculate CI for proportions. ^{[12]} Given the estimation of transitional probabilities calculated from prevalence proportions of two consecutive ages, removing noise from the data is necessary. ^{[12]}
Projection for smoking behavior
In this study, the smoking progression is assumed to follow a discrete time Markov chain with nonhomogenous transitional probabilities. The probability p _{ij} to move from state s _{i} to state s _{j} in one step is named transitional probability. A tenstep sequence from a nonhomogeneous Markov chain was used for simulation of smoking behavior. For projection, we used 5 transition matrix (transition from 14 to 15, 1516, 1617, 1718, and 1819 years) underlying transitional probabilities as time goes on. ^{[13]} In this method for every student according to the sex and age, a tenstep random sequence was predicted. We assume that a cohort sample of 1419yearold students with the starter state at 2011 projected until 2019. We assumed that transitional probability until 19 years is coincident with our predicted transition matrix and in 1926 years the risk of smoking stages acquiring is constant.
Statistical analysis
All calculations were carried out in the statistical software environment R. For fitting a Pspline on multinomial data, we used the codes that written by Kassteele et al. ^{[12]} The Markov chain package provides functions for projection the smoking behavior. ^{[13]}
Results   
Of the 4853 sample students, 2087 (43%) were boys and 2766 (57%) were girls. [Table 1] shows the frequency distribution of the cigarette smoking stages by age and sex. [Table 2] shows the smoothed prevalence of the cigarette smoking stages by age. The overall observed prevalence of current smoking among the students was 6.7% (95% CI: 6.07.4). The smoothed prevalence proportion of current smoking varies between 3.58 and 26.14%.  Table 1: Frequency distribution of cigarette smoking and quitting stages by age and sex2010
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 Table 2: The smoothed prevalence of smoking stages in various ages with a multinomial Pspline fitting
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[Figure 3] shows the multinomial Pspline fit through the observed prevalence proportions of the data. We use the smoothed prevalence of various stages (NS, CS, XS [, XS, NXS]) as the state probabilities. We calculated the sex and agespecific transitional probabilities from 14 to 19 years in [Table 3] using the PDES model. The results of [Table 3] indicated that the transitional probability of NS to CS (initiation) for boys is higher than girls. The ageadjusted odds of initiation in boys is 8.9 (95% CI: 7.910.0) times of the odds of initiation in girls. The mean incidence of becoming a CS after 1 year in NS students (initiation) was estimated as 3.5%.  Figure 3: Smoothed prevalence of cigarette smoking and quitting states in adolescents
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 Table 3: Estimated transitional probabilities with probabilistic discrete event systems method (%)
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Based the Markov chain model described before, predicted number of students with history of smoking in the past month (CS) and exsmokers (XS) was projected for 10 years ahead in the same populations [Table 4].  Table 4: Predicted smoking stages prevalence among adolescent for a 10year period with a Markov chain model
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Our study predicted that the prevalence proportion of CSs increased from 7.55% in 2010 to 20.31% (95%CI: 19.4421.37) for 2019 if the same students have the predicted patterns of smoking. The smoothed 10year predicted prevalence of smoking stages is illustrated in [Figure 4].  Figure 4: Predicted prevalence of smoking stages for adolescents from 2010 to 2019
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Computed results from the Markov chain modeling were compared with 1year later prevalence of smoking stages from the second phase of the study to assess how accurately the model is predicting the smoking behavior. The result of the second phase (smoking stages prevalence after 1 year in 2011) of this study showed that 74.1% of the participants were NSs (95% CI: 72.875.2), 10.7% were CS (95% CI: 9.811.6), and 15.1% were exsmokers (95% CI: 14.116.4). For 1year followup, 833 (17.2%) of participants were nonresponse. The comparison of the projected and direct estimated prevalence of current smoking in 2011 indicated that our projection is close but slightly lower than the observed (9.5 vs. 10.7).
Discussion   
The probability of a person being in a different stage at 1 year ahead is defined as transitional probability. Estimates of transitional probabilities are ideally attained from longitudinal studies, in which cigarette smoking stages are assessed in subjects repeatedly over time. There are also some limitations to cigaretterelated longitudinal studies, such as loss to followup, inaccuracy of survey time, and repeated survey effect (repeatedly asking a question for several times). ^{[12],[14]} Compared to longitudinal study, conducting a crosssectional study is more costeffective and collection of data will be easier. There are some ways for extracting the transitional probabilities from repeated crosssectional data. ^{[15]} There are two new methods for this purpose. The first method is PDES that was introduced in 2010 by Lin et al. ^{[14]} and the second method is based on the two steps (smoothing and solving the net transition as a transportation problem). ^{[12]} The base of these methods is that data from a crosssectional study are analogs to data from a longitudinal survey that follows a sample of birth cohort for multiple years. ^{[12],[14]} In our model, we assumed that over time, there is only one path of changes in smoking behavior. In these two methods, under the assumption that transitions remain stable over time, agespecific prevalence data were used for estimations. In this paper, we used a modified PDES model (for the first time introduced in this paper) with seven transitional probabilities. Chen pointed caution when there are sudden and substantial changes in population size. ^{[10]} Findings of this study showed that there are noises in the agespecific prevalence of smoking stages and because of imbalance in the number of students that were sampled, we use a multinomial Pspline method for smoothing of age and sexspecific prevalence. After the smoothing the age and sexspecific prevalence of smoking stages, we estimated the transitional probabilities from NS to CS and exsmoker (σ_{1} , σ_{7} ) and CS to exsmoker (σ_{4} ) and relapsing from exsmoker to cigarette smoking (σ_{6} ). Comparison of projected and observed prevalence of smoking stages 1 year after the first phase of the study showed that estimation with modified PDES method is close to those computed from the longitudinal study. The validity of this method was evaluated in the other studies. ^{[10],[14]}
The overall prevalence of cigarette use among the students was 6.7% (95% CI: 6.07.4), and 1year later in 2011, the observed prevalence of current smoking increased to 10.7 (95% CI: 9.811.6). The observed prevalence of the past 30 days cigarette smoking in our study is identical to the study of Shahroud (Northeast of Iran) (7.1% [95% CI: 510]). ^{[16]} In another study which was conducted on 1064 male students in Zanjan (Northwest of Iran), almost 23.4% were experimenter and 10.8% were regular smoker. ^{[17]} In a crosssectional study on 1925yearold youngsters of the Isfahan and NajafAbad cities, 11.8% of them smoked. ^{[18]} Compared with what has internationally been reported, the prevalence of adolescent cigarette smoking in our study was considerably small. The prevalence of current smoking in the past 30 days in the USA high school students ^{[4]} has reported to be 9.2%. According to the 2009 National Youth Tobacco Survey, 17.2% (15.019.4) of high school students (9 ^{th} 12 grades) were current cigarette smoker. ^{[19]}
There is evidence that youth are sensitive to nicotine and sooner than adults can feel dependency on nicotine. ^{[20]} The 1year incidence of becoming a cigarette smoker among nonsmoker adolescents in our study was high (3.5%). The increasing trend of smoking in adolescents is worrying because individuals' behavior and lifestyle are significantly formed during adolescence.
According to the 2010 National Survey on Drug Use and Health, the prevalence of current cigarette smoking among USA young adults (1825yearold) was 34.2% (35.335.2). ^{[19]} In our study, the projected prevalence of current smoking for young adults (1824 years) was 15.71% (15.2016.20) and for ages between 24 and 28 years was 20.31% (19.4421.27). The increasing trend of cigarette use among adolescents indicated the necessity of paying more attention to this group as the future constructing generation. ^{[16]} Cigarette smoking is a process that begins in adolescence and less older ages, and probability of initiation of smoking grows into a young adult and in older ages either stabilizes or declines with time. ^{[21]} The projected trends of smoking [Figure 4] obviously showed the mentioned pattern for cigarette smoking.
Sampling from grade 10 students and selection of a limited age range for this study violated our observed prevalence proportions despite using quite satisfactory sampling and design. With this limited range, we obtained transitional probability for 5 years consecutive. Hence, our forecasting after 19 can be violated. However, we assumed a constant transitional probability after 19 years. Another limitation of this study was lack of access to longitudinal data with more than two waves for comparison between the predicted and observed smoking stages.
Conclusions   
The result of this study showed a moderate but worrying prevalence of current smoking in Iranian adolescents and introduced a novel method for estimation of transitional probabilities from a crosssectional study and introduced a Markov chain simulation for projection of smoking behavior for transition from adolescence through young adulthood.
Acknowledgements
We wish to thank all of the students, teachers, and principals of Tabriz high schools for their valuable collaboration.
Financial support and sponsorship
This study was a PhD thesis in Epidemiology supported by Tehran University of Medical Sciences. We would like to thank the Deputy of Research and Technology of Tehran University of Medical Sciences.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2], [Table 3], [Table 4]
