Abstract

Introduction

Lung cancer accounts for 1.6 million deaths per year according to the World Health Organization (WHO) ¹1. Ferlay J, Soerjomataram I, Ervik M, Dikshit R, Eser S, Mathers C, et al. GLOBOCAN 2012 v1.0, cancer incidence and mortality worldwide. Lyon: International Agency for Research on Cancer; 2013. (IARC CancerBase, 11).. In Chile, cancer of the trachea, bronchi, and lungs (hereinafter “lung cancer”) is the second cause of cancer mortality, following gastric cancer (Departamento de Estadísticas e Información en Salud, Ministerio de Salud. Mortalidad. http://www.deis.cl/?p=51, accessed on 23/Jul/2013).

In developed countries, lung cancer incidence and mortality rates are declining in men and stabilizing in women thanks to changes in smoking prevalence. However, according to estimates in developing countries, incidence and mortality continue to increase due to endemic smoking prevalence ²2. Youlden DR, Cramb SM, Baade PD. The international epidemiology of lung cancer. J Thorac Oncol 2008; 3:818-31..

In Chile, the lung cancer mortality rate showed an upward trend in females and a slightly downward trend in males from 2001 to 2008 ³3. Icaza G, Núñez L, Torres-Avilés F, Díaz N, Villarroel JE, Soto A, et al. Atlas de mortalidad en Chile, 2001-2008. Talca: Editorial Universidad de Talca; 2013.. The increase in the female population can be explained by the late adoption of smoking by women, due to sociocultural issues and exploitation of this characteristic by the tobacco industry ⁴4. Nerín I. El tabaquismo en la mujer: una atracción fatal. Arch Bronconeumol 2005; 41:360-2..

Time trend analysis of indicators like mortality is useful for monitoring a country’s health status and the impact of health interventions ⁵5. Puig X, Ginebra J, Gispert R. Análisis de la evolución temporal de la mortalidad mediante modelos lineales generalizados. Gac Sanit 2005; 19:481-5.. Together with time trend analyses, it is useful to estimate the magnitude of the disease in the future, thus allowing optimization of resource allocation, services planning, and public policymaking ⁶6. Mistry M, Parkin DM, Ahmad AS, Sasieni P. Cancer incidence in the United Kingdom: projections to the year 2030. Br J Cancer 2011; 105:1795-803..

The current study aimed to analyze trends in the lung cancer mortality rate in men and women in Chile from 1990 to 2009 and to conduct projections for the next six years, using Bayesian dynamic linear models.

Methods

Data source

Data on lung cancer mortality [International Classification of Diseases, 9^th revision (ICD-9): 162 from the year 1990 to 1996 and C33-C34 from the 10^th revision (ICD-10): for the years 1997 to 2009], data were obtained from the available databases of the Department of Health Statistics and Information (DEIS) of the Ministry of Health of Chile, 1990-2009 (http://www.deis.cl/?p=51, accessed on 23/Jul/2013). Population data were obtained from projections based on the 2002 Census conducted by the Chilean National Institute of Statistics and the Latin American and Caribbean Demographic Center ⁷7. Instituto Nacional de Estadística; Centro Latinoamericano y Caribeño de Demografía. Chile: proyecciones y estimaciones de población. Total país 1950-2050. Santiago: Instituto Nacional de Estadística/Centro Latinoamericano y Caribeño de Demografía; 2004..

Time trend models

Standardized annual mortality rates were calculated by five-year age groups from 1990 to 2009 for men and women. The standardization method was direct adjustment, using the world standard as the reference population ⁸8. Doll R, Payne P, Waterhouse JAH. Cancer incidence in five continents. v. I. Geneva: Union Internationale Contre le Cancer; 1966..

The study used Bayesian dynamic linear models (DLM), whereY_t represents the log of the mortality rate in time t and the model can be represented by the following system of equations:

Where, F_t is a vector of orderP x 1 which is formed by co-variables,Ɵ_t is the vector of the model’s unknown parameters p,G_t is ap x p order matrix that describes the trend of the parameters contained inƟ_t over time, e_t and w_t represent random errors that are assumed to have typically normal distribution with mean 0, and variance-covariance matrices (depending on the structure of G_t )V_t andW_t respectively.

For the study’s analyses, we specifically used two structures forF_t andG_t.

First-order model: F_t=1, G_t=1 and Ɵ_t =Ɵ_1t.

Second-order model: F_t=[1 0], andF_t= [1 0]Ɵ_t = [Ɵ_1tƟ_2t].

What distinguishes DLM from ordinary time-series models is the specification of the autocorrelation order for the model’s structural parameters, making them more flexible. If there is a degree of autocorrelation, the second-order model is the most adequate.

Estimation of Bayesian DLM requires a stepwise filtering and smoothing process, in addition to defining a priori distributions for the unknown parameters that intervene in the models. When using the Bayesian paradigm in the estimation process, it is necessary to define knowledge a priori through distributions for the unknown parameters that intervene in the models. Thus, one assumes that the variances are independent and follow non-informative inverse gamma distributions. Additionally, one includes an a priori distribution for the series’ baseline structural parameter,Ɵ_o. The literature suggests specifying a normal distribution for the target parameter. Theoretical details on such models can be found in West & Harrison ⁹9. West M, Harrison J. Bayesian forecasting and dynamic models. 2nd Ed. New York: Springer; 1999. and Gamerman & Lopes ¹⁰10. Gamerman D, Lopes, H. Markov chain Monte Carlo: stochastic simulation for Bayesian inference. 2nd Ed. Boca Raton: Chapman & Hall/CRC Press; 2006..

Computational implementation

Adjustment of these models used the code’s implementation in Winbugs 1.4.3 (http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml). Nevertheless, it is possible to use the dlm library from the R software package (http://www.r-project.org/), whose functions dlmModPoly and dlmModSeas are designed to estimate dynamic linear models ¹¹11. Petris G. An R package for dynamic linear models. J Stat Softw 2010; 36:1-16.. To perform inference, chains of 60,000 iterations were generated, excluding the first 40,000 to eliminate the influence of baseline values and autocorrelation, which would allow ensuring the parameters’ convergence in the MCMC strategy (Markov chain Monte Carlo stochastic simulation) used. Having estimated the models’ parameters, one evaluates their goodness of fit using the deviance information criterion (DIC), the effective number of parameters (pD) ¹²12. Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc B 2002; 64:583-639., the magnitude of the discrepancy observed a posteriori between the data expected by the models and the observed data (SCEp), and the model’s predictive capacity based on the prediction error.

The model’s projection was also compared to the data for 2010-2012, recently published by DEIS (http://www.deis.cl/?p=51, accessed on 23/Jul/2013). The study provides results of the best model, and based on which, projections of lung cancer mortality rates for the next six years in men and women in Chile, with the respective credible intervals.

Results

Time trend analysis of standardized lung cancer mortality rates in men and women in Chile from 1990 to 2009 showed a reduction of 19.9% in men, while in women there was an upward trend, namely a 28.4% increase (Figure 1).

The second-order DLM was the model with the best fit for the trend of standardized mortality rates in men, according to Bayesian goodness of fit criteria. Meanwhile, in women the first-order DLM showed the best fit (Table 1). Mortality data for the years 2010 to 2012 were used to obtain age-adjusted rates for both males and females, the value of which is contained in both models’ confidence intervals (Table 2). Meanwhile, the differences between the expected and observed mortality rates were less than one (Table 2).

Based on each model, the study provided the six-year projections and credible intervals (Figures 2 and 3). In men, the downward trend observed in 1990-2009 was maintained. In women, the six-year projection showed stabilization of the lung cancer mortality rates, thereby interrupting the upward trend observed in the period under study.

Discussion

Chile is considered to have world-standard vital statistics ¹³13. Mahapatra P, Shibuya K, Lopez AD, Coullare F, Notzon FC, Rao C, et al. Civil registration systems and vital statistics: successes and missed opportunities. Lancet 2007; 370:1653-63. thanks to a systematic effort by the DEIS under the Ministry of Health of Chile in terms of coding and processing death certificates. Nevertheless, on-going efforts are needed to reduce the differences observed between urban and rural areas, counties, males and females, and age groups ¹⁴14. Núñez L, Icaza G. Calidad de las estadísticas de mortalidad en Chile, 1997-2003. Rev Méd Chile 2006; 134:1191-6..

One of the methods current employed to analyze trends in mortality rates is joinpoint regression ¹⁵15. Kim H-J, Fay M, Feuer E, Midthune D. Permutation tests for joinpoint regression with applications to cancer rates. Stat Med 2000; 19:335-51., useful for identifying changes in trends over time. The currently study used Bayesian DLM, which have been applied to a wide range of situations due to their predictive power, since the models’ parameters are updated with each new observation, allowing them to adapt to the series’ evolution and capturing changes in their behavior. Bayesian DLM are thus flexible for detecting change points and useful for forecasting ¹⁶16. Fonseca F, Soares A, Telles P, Williamson D. Dynamic linear model and SARIMA: a comparison of their forecasting performance in epidemiology. Stat Med 2001; 20:3051-69..

The downward trend in lung cancer in men has been described in developed countries, as has the upward trend in women, reflecting smoking prevalence at the population level ²2. Youlden DR, Cramb SM, Baade PD. The international epidemiology of lung cancer. J Thorac Oncol 2008; 3:818-31.. In the case of women, a plateau effect has been seen following the upward trend, as described in the current study.

In Chile, the downward trend in men can be attributed not only to changes in smoking prevalence, but also to the longstanding exposure to arsenic in drinking water in the northern region of the country, followed by the installation of the first water treatment plants in 1971 ¹⁷17. Steinmaus CM, Ferreccio C, Acevedo J, Yuan Y, Cortes S, Marshall G, et al. Drinking water arsenic in northern Chile: high cancer risks 40 years after exposure cessation. Cancer Epidemiol Biomarkers Prev 2013; 22:623-30..

One of study’s limitations is that these rates are a summary measure for Chile as a whole and do not consider geographic differences, found in the relative risk of this disease due to the presence of arsenic in the north of the country ³3. Icaza G, Núñez L, Torres-Avilés F, Díaz N, Villarroel JE, Soto A, et al. Atlas de mortalidad en Chile, 2001-2008. Talca: Editorial Universidad de Talca; 2013.. Spatiotemporal studies are planned to take this phenomenon into account.

Another limitation is that the projections fail to consider changes in incidence of the disease or the incorporation of preventive strategies, so the results must be interpreted in the context of status quo. Importantly, Chile has adopted a series of changes in its anti-tobacco legislation which are expected to contribute to the decrease in mortality. Meanwhile, according to data from Chile’s National Health Surveys, smoking prevalence in individuals more than 15 years of age decreased in males from 48.3% in 2003 to 44.2% in 2010, while in females it increased from 36.8% to 37.1% in the same period ¹⁸18. Ministerio de Salud. Resultados: I Encuesta de Salud, Chile 2003. http://epi.minsal.cl/epi/html/invest/ens/informefinalens.pdf (accedido el 11/May/2013).
http://epi.minsal.cl/epi/html/invest/ens... ^,1919. Ministerio de Salud. Encuesta Nacional de Salud 2009-2010. http://www.minsal.gob.cl/portal/url/item/bcb03d7bc28b64dfe040010165012d23.pdf (accedido el 11/May/2013).
http://www.minsal.gob.cl/portal/url/item... . An aggravating factor is that Chilean schoolchildren (13 to 15 years of age) have the highest smoking rates in the Americas for their age group ²⁰20. Schmidt MTV. Chile: situación del tabaquismo a cinco años de la ratificación del Convenio Marco para el Control del Tabaco y los desafíos pendientes. http://www.chilelibredetabaco.cl/descargas/Informe_Chile_5_anos_CMCT_EPES_2010.pdf (accedido el 16/Ene/2013).
http://www.chilelibredetabaco.cl/descarg... . At the local level, studies on the general adult population in Santiago that evaluate the national trend reported 47% smoking prevalence in men and 27% in women in 1971. In 1984, the prevalence rates were 44% and 39%, respectively ²¹21. Medina E, Kaempffer AM. Tabaquismo y salud en Chile. Bol Oficina Sanit Panam 1991; 111:112-21.. Finally, a study in 2003 found smoking prevalence rates of 46.5% in men and 39.4% in women ²²22. Rojas G, Gaete J, González I, Ortega M, Figueroa A, Fritsch R, et al. Tabaquismo y salud mental. Rev Méd Chile 2003; 131:873-80..

The current study used a methodology that allows modeling lung cancer mortality rates and producing projections. The methodology can be replicated to forecast mortality rates from other diseases in the population and make adjustments in public policies and implement surveillance systems for chronic non-communicable diseases and evaluate appropriate preventive strategies.

Acknowledgments

The authors wish to thank Prof. Abel Valdebenito S. for validating the fit in the models used in the current study. To Fondo Nacional de Desarrollo Científico y Tecnológico (Fondecyt) for the financial support to Francisco Torres-Avilés (Fondecyt Iniciación 11110119).

References

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