Salud Pública de México

Breast cancer mortality in Mexico. An age-period-cohort analysis

Breast cancer mortality in Mexico. An age-period-cohort analysis


Francisco Franco-Marina MC, MPH, MHSc,(1) Eduardo Lazcano-Ponce, Dr SP,(2) Lizbeth López-Carrillo QBP, Dr PH.(2)

(1) División de Epidemiología. Instituto Nacional de Rehabilitación. México.
(2) Instituto Nacional de Salud Pública. México.


Objetivo. Evaluar efectos de edad-periodo-cohorte en la mortalidad por cáncer de mama (CaMa) en México. Material y métodos. Las tendencias de los efectos de edad-periodo-cohorte fueron estimados mediante un modelo de regresión de Poisson propuesto por Holford. Resultados. Las tasas de mortalidad por CaMa se han estabilizado en la mayoría de los grupos de edad desde 1995 y están determinadas principalmente por efectos de cohorte y edad. Las mujeres nacidas entre 1940 y 1955 muestran los mayores aumentos en la mortalidad en comparación con las nacidas después de este período. La mamografía y la terapia adyuvante han tenido un impacto limitado sobre la mortalidad. Se discuten posibles explicaciones de las tendencias observadas. En las siguientes décadas se espera continúe aumentando la mortalidad por CaMa. Conclusiones. El acceso a mamografía y a tratamiento oportuno y efectivo debieran ser una prioridad para revertir la tendencia creciente esperada de la mortalidad por CM.

Palabras claves: mortalidad por cáncer de mama, análisis edad-periodo-cohorte, México


Objective. To assess the age, period and cohort effects on breast cancer (BC) mortality in Mexico. Material and Methods. Age, period and cohort curvature trends for BC mortality were estimated through the Poisson Regression model proposed by Holford. Results. Nationally, BC death rates have leveled off since 1995 in most age groups. BC mortality trends are mainly determined by birth cohort and age effects in Mexico. Women born between 1940 and 1955 show the highest rate of increase in BC mortality. Women born afterwards still show an increasing trend but at a much lower rate. Mammography and adjuvant therapy have had a limited impact on mortality. Potential reasons for observed patterns are discussed. An increase in BC mortality in Mexico is expected in the following decades. Conclusions. Mammography screening programs and timely access to effective treatment should be a national priority to reverse the expected increasing BC mortality trend.

Keywords: breast cancer mortality, age-period-cohort analysis, Mexico

Address reprint requests to: Francisco Franco-Marina. Instituto Nacional de Rehabilitación. División de Epidemiología. Calz. México-Xochimilco 289 Col. Arenal de Guadalupe, Tlalpan, 14389 México, DF. E-mail:


Breast cancer became the leading cause of female cancer deaths after cervical cancer in 2005, with a steadily increasing trend in Mexico.1 Breast cancer death rates vary by a factor of four between the highest and lowest rates in the world and Mexico has a low breast cancer death rate on a worldwide scale.2 However, breast cancer mortality is increasing more rapidly in countries in Latin America and Asia which have the lowest incidence rates (7 to 14/100000) compared to those with the highest rates (17 to 27/100000).3

The interpretation of breast cancer mortality trends is complicated because they might be the combined result of changes in risk factors and screening practices as well as better survival due to treatment improvements. One way of disentangling these effects consists in attempting to separate age, period and cohort effects implied in the trends through an appropriate statistical model. In such analysis, period effects may capture mainly the effects on breast cancer death rates of factors related to improved survival such as screening and adjuvant therapy, whereas cohort effects may give some clues of risk factors changing the incidence of the disease.

The aim of this paper is to characterize the age, period and cohort effects of breast cancer mortality in Mexico and to better explain the role of advances in early detection and treatment and changes in reproductive and other breast cancer risk factors that may have taken in place in the country over the past three decades.

Material y Métodos

Mortality data

Individual BC deaths occurring in women between 1980 and 2005 were obtained from the official mortality databases generated by Mexico’s National Institute of Geography and Statistics (INEGI, per its abbreviation in Spanish). The basic cause of death was coded in these databases using the ninth revision of the International Classification of Diseases (ICD-9) between 1980 and 1997 and the tenth revision afterwards (ICD-10). According to a WHO ICD translator,4 ICD-9 breast cancer codes (174.0-174.9) map only to ICD-10 breast cancer codes (C50.0-C50.9) and vice versa.

Official mid-year female population estimates at the state level were obtained from the Mexico’s National Population Council (CONAPO, per its abbreviation in Spanish) for 1980 through 2005.5 Population estimates were available in five-year age groups throughout the analyzed period and in single-year of age for 2005. Some of the statistical analyses presented in this study required population estimates by single-year of age. Thus, for 1980 through 2004 we generated such estimates by applying the single-year of age proportions within each five-year age group observed in 2005 to the five-year age groups population estimates observed in each year between 1980 and 2004.

Statistical analysis

All statistical analyses were confined to women aged 25 and older. Age adjusted death rates were calculated through the direct method6 using, in all instances, the national population estimates for 2005 broken down by five-year age groups.

Trends in the absolute number of breast cancer deaths or the corresponding death rates were modeled through joinpoint Poisson regression using the Joinpoint Regression Program.7 Joint point regression is a non-linear statistical technique aimed at identifying changes in trends in the response variable over the analyzed period (i.e. deaths or death rates).8 Unknown points in time at which the response changes in trend (joinpoints) are identified by the grid search method. Models with a variable number of joinpoints (0 through 4) are then compared through permutation tests with p-values found by Monte Carlo methods and a Bonferroni correction to maintain an overall asymptotic significance level. The final model consists of a series of lines with different slopes connected together at the joinpoints.

Age (a), period (p) and cohort (c) curvature trends for breast cancer mortality  were estimated through the following Poisson Regression Age-Period-Cohort (APC) model, proposed by Holford:9

where a’ and c’ are the curvature components of the age and cohort effects, is called the “net drift parameter” indicating the overall direction in which the mortality trend is moving, and and y are the parameters describing the age, period and curvature trends. The net drift parameter was extracted using Holford’s naive average. The model was fitted so that age effects are presented as death rates for the reference cohort. Additionally, cohort effects represent death rate ratios relative to the reference cohort, whereas period effects are constrained to be 0 on average with 0 slope.

The APC model just described was fitted using national information on deaths and population between 1980 and 2005 for women aged 25 through 85 years and born between 1905 and 1975. The model was fit on a tabulation of deaths and populations using single-years of age and period to avoid overlapping cohorts and to give more detail to the trends. Natural splines with seven parameters for the age, period and cohort terms were incorporated in the APC modeling to reduce random variation due to the use of such detailed tabulation. The same APC model was also fit for four Mexican state clusters, created from an analysis published by Tuiran et al. for the calendar year in which each state reached an overall fertility rate of three children or less.10 Using the results from these models, directly age-adjusted death rates were calculated for the analyzed birth cohorts using the 2005 national population as standard.

All APC modeling was performed using the implementation provided by Carstensen11 in the R Statistical Package.12


Between 1980 and 2005, a total of 67 854 breast cancer deaths were observed in Mexican women. Only 172 (0.25%) of those occurred in women younger than 25 years of age and 199 (0.25%) had an unknown age. Over the analyzed period, the mean age at death from breast cancer remained very close to an average of 57.3 years (standard deviation= 0.38). In addition, the population age distribution for Mexican women aged 25 and older over the analyzed period has also remained close to an average age of 44.7 years (standard deviation= 0.24).

Figure 1 plots the annual number of breast cancer deaths in Mexican women aged 25 and older as well as their fitted trends. Three trend periods with slopes

Figure 1. Annual breast cancer deaths in Mexican women aged 25 years and older. Dots represent the observed number of breast cancer deaths. Lines were obtained using joinpoint Poisson regression on death counts. Continuous lines are line segments with year slopes significantly difffferent from zero. Annual percent change is provided for significant line segments

significantly different from zero are identified. Between 1982 and 1987 the absolute number of breast cancer deaths in Mexican women aged 25 and older grew 8.3% annually. After this period, breast cancer deaths have increased at increasingly lower rates (5.6% between 1987 and 1995 and 3.6% between 1995 and 2005).

Age-specific breast cancer death rate trends for five age groups are shown in figure 2. A clear gradient of higher breast cancer death rates with increasing age is observed throughout the analyzed period. The four younger age groups comprising Mexican women between 25 and 74 years of age show very similar trends between 1980 and 2005. In these age groups death rates increased annually between 2.6 and 3.5% during the first 13 to 15 years of the analyzed period, but afterwards death rates show annual increases not statistically significant from zero. On the other hand, Mexican women aged 75 years and older show an annual death rate increase of 4.9% between 1980 and 1987 and a 1.2% increase between 1987 and 2005.

Figure 3 graphically presents the estimated age, period and cohort female breast cancer mortality effects. Death rates by age for the 1940-1941 birth cohorts are plotted on a logarithmic scale. Breast cancer death rates increase very fast between 25 and 35 years of age and continue to increase with increasing age, albeit at lower rates. The fitted APC model implies that this age effect is constant among birth cohorts and periods. The

Figure 2. Breast cancer death rate trends in Mexican women by age group. Lines were obtained using joinpoint Poisson regression. Continuous lines are line segments with statistically significant year slopes. Annual percent change is provided for significant line segments

Figure 3. Age, period and cohort effffects for femamale breast cancer mortality in Mexico, using the Holford Age-Period-Cohort model. Age effffects are death rates per 100 000 person-years for the reference cohort. Cohort effffects represent death rate ratios relative to the reference cohort (1940-1941). Period effffects are also death rate ratios relative to a zero slope. The net drift paramameter was estimamated at 1.017

birth cohort effect on breast cancer death rates is shown as death rate ratios with respect to the 1940-1941 birth cohorts. It consists of higher breast cancer death rates in the more recent cohorts born after that period (1940-1941) in contrast to earlier cohorts born at the beginning of the 20th century; the latter are estimated to have almost one-half the breast cancer death rates estimated for the 1940-1941 birth cohorts and almost one-third of those estimated for the 1975 birth cohort. In addition, breast cancer death rates increase more rapidly in women born between 1935 and 1950 and considerably more slowly in women born afterwards. Finally, as it was expected, the estimated period effect, also expressed as death rate ratios, shows a much lower intensity than the age and cohort effects. Nevertheless, breast cancer death rates show a slight increase during the 1980s, a leveling off during the first half of the 1990s and a continuous slight decrease afterwards.

Using information on the year that Mexican states reached a global fertility rate of three children per woman we created four state clusters with a roughly similar population. Table I summarizes fertility and breast cancer mortality patterns for the created clusters. All state clusters had similar fertility patterns in 1965, but global fertility rates in states belonging to cluster A had a faster decline in fertility than those observed in the other state clusters, especially cluster D. Additionally, states in cluster A also showed the lowest marginality index and those in cluster D, the highest. Cluster states B and C showed an intermediate average marginality and also higher variability in marginality than regions A and D. Between 1980 and 2005, all state clusters showed a non-linear adjusted death trend with a progressively decreasing slope. Annual percent changes in age-adjusted death rates during the most recent analyzed decade (1996 to 2005) differ between state clusters. Cluster B shows a significant rising trend, whereas the rest of the clusters show no significant trend. Nevertheless, cluster A may possibly have a slight decrease in breast cancer mortality and clusters C and D a slight increase during the last analyzed decade.

Figure 4 plots the age-adjusted breast cancer death rates for birth cohorts for women aged 25 and older derived from fitting the Holford Age-Period-Cohort model in each of the state clusters. These rates can be compared to the observed breast cancer death rate in Mexico in 2005 of 15.5 per 100 000 women for this age group. In all cohorts, breast cancer death rates are higher in cluster states with faster fertility declines. Also, the most recently born cohorts show less variability in breast cancer death rates among state clusters. Additionally, the rising trend of breast mortality in the most recently born cohorts is seen in all state clusters but it is more


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Salud Pública de México es una publicación periódica electrónica, bimestral, publicada por el Instituto Nacional de Salud Pública (con domicilio en Avenida Universidad núm. 655, col. Santa María Ahuacatitlán, Cuernavaca, Morelos, C.P. 62100, teléfono 329-3000, página web,, con ISSN: 1606-7916 y Reserva de Derechos al Uso Exclusivo con número: 04-2012-071614550600-203, ambos otorgados por el Instituto Nacional del Derecho de Autor. Editor responsable: Carlos Oropeza Abúndez. Responsable de la versión electrónica: Subdirección de Comunicación Científica y Publicaciones, Avenida Universidad núm. 655, planta baja, col. Santa María Ahuacatitlán, Cuernavaca, Morelos, C.P. 62100, teléfono 329 3000. Fecha de última modificación: 7 de junio de 2018. D.R. © por el sitio: Instituto Nacional de Salud Pública.

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