Abstracts

Introduction

Among Latin American women, breast cancer is one of the most common causes of malignant tumors, surpassing cervical uterine cancer ¹1 . Lozano-Ascencio R, Gómez-Dantés H, Lewis S, Torres-Sánchez L, López-Carrillo L. Tendencias del cáncer de mama en América Latina y el Caribe. Salud Pública Méx 2009; 52 Suppl 2:S147-56. . Patient survival rates have been related to the stage at diagnosis, therefore early detection of a growing breast tumor is of vital importance. Regular participation in exploration activities such as mammography is known to increase the likelihood of early diagnosis, thereby increasing the survival rate by up to 98.1% within at least 5 years of breast cancer identification ²2 . American Cancer Society. Breast cancer facts & figures: 2007-2008. Atlanta: American Cancer Society; 2007. ^{, 3}3 . Ries LAG, Harkins D, Krapcho M, Mariotto A, Miller BA, Feuer EJ, et al. SEER cancer statistics review. Bethesda: National Cancer Institute; 2005. . Nevertheless, in Mexico 80% of diagnosed cases are at advanced stages ⁴4 . Mohar A, Bargalló E, Ramírez MT, Lara F, Beltrán-Ortega A. Recursos disponibles para el tratamiento del cáncer de mama en México. Salud Pública Méx 2009; 52 Suppl 2:S263-9. .

In Mexican populations, breast cancer detection coverage between 2007 and 2012 was below the national target of 21.6% for females aged between 45 and 64 ⁵5 . Martínez-Montañez OG, Uribe-Zúñiga P, Hernández-Ávila M. Políticas públicas para la detección del cáncer de mama en México. Salud Pública Méx 2009; 52 Suppl 2:S350-60. . In 2007, a low rate of mammography of only 16% was reported in rural areas among women between the ages of 40 and 49 ⁶6 . Sosa-Rubí S, Walker D, Serván E. Práctica de mastografías y pruebas de Papanicolaou entre mujeres de áreas rurales de México. Salud Pública Méx 2009; 52 Suppl 2:S236-45. . Understanding the reasons for the low participation rate in mammography among the Mexican female population is needed to change people’s attitudes and resolve institutional problems in promoting screening tests. The identification of the socio-ecological (individual, interpersonal and intermediate/community) factors involved in the adoption of mammography is vital for three reasons: (1) to attain optimal survival outcomes, (2) to identify the crucial socio-ecological factors towards maximizing the efficiency of Social Marketing Campaigns and (3) to define whether Social Marketing Campaigns should be focused at the public health level, i.e. behavior affected by income, and/or at individual level i.e. behavior influenced by attitudes ⁷7 . Somers TJ. Risk behaviors in a community sample of women with a family history of breast cancer [Doctoral Dissertation]. Pittsburgh: University of Pittsburgh; 2006. .

In situations that require expert judgment, i.e. the socio-ecological factors that affect mammography participation, some uncertainty and ambiguity is to be expected because of the disparity between meanings and interpretations of opinions ⁸8 . Glumac B, Han Q, Smeets JJAM, Schaefer WF. Brownfield redevelopment features: applying Fuzzy Delphi. Journal of European Real Estate Research 2011; 4:145-59. ^{, 9}9 . Hsu Y, Lee C, Kreng VB. The application of Fuzzy Delphi Method and Fuzzy AHP in lubricant regenerative technology selection. Expert Syst Appl 2010; 37:419-25. . Thus, these conjectures cannot be accurately represented quantitatively ⁹9 . Hsu Y, Lee C, Kreng VB. The application of Fuzzy Delphi Method and Fuzzy AHP in lubricant regenerative technology selection. Expert Syst Appl 2010; 37:419-25. . The combination of the Fuzzy Set Theory and Delphi Method, named the Fuzzy Delphi Method ¹⁰10 . Murray TJ, Pipino LL, Gigch JP. A pilot study of fuzzy set modification of Delphi. Human Systems Management 1985; 5:76-80. , models the uncertainty and vagueness mathematically, addressing the inaccuracy which is intrinsic in human reasoning from using linguistic terms, i.e. “not important”, “less important”, so as to reflect their preferences ⁹9 . Hsu Y, Lee C, Kreng VB. The application of Fuzzy Delphi Method and Fuzzy AHP in lubricant regenerative technology selection. Expert Syst Appl 2010; 37:419-25. ^{, 11}11 . Kahraman C, Cebeci U, Ruan D. Multi-attribute comparison of catering service companies using fuzzy AHP: the case of Turkey. International Journal of Production Economics 2004; 87:171-84. . A fuzzy set is a collection of elements characterized by a membership function. The grade of membership is defined as a possibility distribution and ranges between zero and one ¹²12 . Zadeh LA. Fuzzy sets. Information Control 1965; 8:338-53. . The nearer the value to unity, the greater the degree of belonging. For example, consider a fuzzy set as an application in supporting medical diagnosis for five diseases, where we have a set of symptoms S = {chest-pain, cough, stomach pain, headache, temperature} and a set of diagnoses D = {fever, malaria, typhoid, stomach problem, chest problem}. The state of a patient is determined by his/her medical test results. However, sometimes there is lack of knowledge, thus the information cannot be classified. Therefore, a solution is derived from the use of a degree of membership ¹³13 . Ju H, Wang F. A similarity measure for interval-valued Fuzzy Sets and its application in supporting medical diagnostic reasoning. In: Proceedings of the 10th International Symposium on Operations Research and Its Applications (ISORA 2011. Dunhunag: World Publishing Corporation; 2011. p. 251-7. . The Fuzzy Set Theory is designed to extract a primary possible outcome resembling human reasoning. The Fuzzy Set Theory rationalizes uncertainty to generate and solve the group decision ¹⁰10 . Murray TJ, Pipino LL, Gigch JP. A pilot study of fuzzy set modification of Delphi. Human Systems Management 1985; 5:76-80. ^{, 12}12 . Zadeh LA. Fuzzy sets. Information Control 1965; 8:338-53. ^{, 14}14 . Qiu J, Sun T, Shi, Y. The absolute continuity of fuzzy complex measures. ICIC Express Letters 2007; 1:27-32. . Consequently, to obtain a more representative description of the significance of the factors in reduced mammography participation, this study applies the Fuzzy Delphi Method which is optimized by the consistency aggregation method. The consistency aggregation method aggregates the fuzzy individual opinions into a group consensus using a consistency index. It is based on similarity and distance indices for the comparison between experts’ fuzzy opinions ¹⁵15 . Lu C, Lan J, Wang Z. Aggregation of fuzzy opinions under group decision-making based on similarity and distance. Journal of Systems Science and Complexity 2006; 19:63-71. .

Our study design overcomes variations in medical opinions in Mexican breast cancer by implementing Fuzzy Set Theory through the following objectives: (1) to review the literature in order to generate a list of various features influencing mammography attendance and; (2) to apply the Fuzzy Delphi Method via the Consistency Aggregation Method to form a consensus of expert opinion and determine the most significant factors that affect breast cancer screening participation or avoidance behavior. The results therefore represent the first step of an investigation with two goals: (1) to guide the implementation of theoretically designed educational programs and (2) to provide the authorities responsible for breast cancer detection programs in Mexico with a view of the procedures to be optimized and target the areas in which to encourage investment. The aim is to raise awareness about breast cancer and the benefits of early diagnosis.

Methodology

A detailed list of possible determining factors for women’s participation in early mammography detection screening was created through an exhaustive review of literature and based on the spatial interaction model of mammography use ¹⁶16 . Mobley LR, Kuo M, Driscoll D, Clayton L, Anselin C. Heterogeneity in mammography use across the nation: separating evidence of disparities from the disproportionate effects of geography. Int J Health Geogr 2008; 7:1-18. ( Table 1 ). This model considers the effects of hypothetical constructs – those that cannot be directly observed and are measured indirectly by means of observable items in a questionnaire – therein called latent variables ¹⁷17 . MacCallum RC, Austin JT. Applications of structural equation modeling in psychological psychological research. Annu Rev Psychol 2000; 51:201-26. , at the political, cultural, social and institutional level. On an individual level the model evaluates the characteristics which enable or prohibit mammography participation: the interpersonal level (locality) includes vicinity specificity which impacts perceived individual risk or the search for health care information; the intermediate level (municipality) covers the physical and social environment affected by infrastructure resources supporting community life ¹⁸18 . Schulz A, Kannan S, Dvonch J, Israel B, Allen A, James S, et al. Social and physical environments and disparities in risk for cardiovascular disease: the healthy environments partnership conceptual model. Environ Health Perspect 2005; 113:1817-25. . The fourth level (state) is omitted from this investigation, because at present the data is available for 13 out of 32 states. The variables used herein, corresponding to each latent variable of the spatial model, are shown in Table 1 .

The Fuzzy Delphi Method

The creation of a large number of variables complicates the construction and assessment of models ¹⁹19 . Secretaría de Desarrollo Social. Evaluación externa, bases de datos y cuestionarios. Encuesta de Evaluación de los Hogares 2007: ENCEL 2007. http://evaluacion.oportunidades.gob.mx:8010/es/bases_cuan_c.php (accessed on 15/May/2011).
http://evaluacion.oportunidades.gob.mx:8... . The Delphi Method has been widely used to obtain a constant flow of expert opinions through survey. Questions come from related literature and those recommended by experts. The Delphi approach has three characteristics: anonymous responses, interaction and controlled feedback, as well as a statistical group response ⁹9 . Hsu Y, Lee C, Kreng VB. The application of Fuzzy Delphi Method and Fuzzy AHP in lubricant regenerative technology selection. Expert Syst Appl 2010; 37:419-25. . The questionnaire procedure requires asking the opinion of experts on multiple occasions, which results in certain difficulties, such as: (1) failure to take fuzziness into account leading to misinterpretation of the opinions; (2) systematic suppression of variables, i.e. sometimes the factors that are selected by at least 50% of the experts are retained; (3) process losses in coordination and communication; (4) repeatedly surveying the experts is more costly and time-consuming ¹⁰10 . Murray TJ, Pipino LL, Gigch JP. A pilot study of fuzzy set modification of Delphi. Human Systems Management 1985; 5:76-80. . Furthermore, there is a noteworthy problem to solve the fuzziness (expected ambiguity) of common understanding of expert opinions (Dirección General de Información en Salud. Recursos Humanos, Físicos y Materiales de la Secretaría de Salud y los Servicios Estatales de Salud . http://www.sinais.salud.gob.mx/bases dedatos/recursos.html; Unidades Médicas del Sector Público . http://www.sinais.salud.gob.mx/basesdedatos/unidadesmedicas.html, accessed on 15/May/2011) ⁸8 . Glumac B, Han Q, Smeets JJAM, Schaefer WF. Brownfield redevelopment features: applying Fuzzy Delphi. Journal of European Real Estate Research 2011; 4:145-59. . To overcome these difficulties, Murray et al. ¹⁰10 . Murray TJ, Pipino LL, Gigch JP. A pilot study of fuzzy set modification of Delphi. Human Systems Management 1985; 5:76-80. proposed to apply the Fuzzy Delphi Method to group decisions. This method is based on a similarity function to assess the level of agreement between experts. The Fuzzy Delphi Method assures no misinterpretation of expert opinions since it considers the fuzziness that every survey process has to deal with ⁸8 . Glumac B, Han Q, Smeets JJAM, Schaefer WF. Brownfield redevelopment features: applying Fuzzy Delphi. Journal of European Real Estate Research 2011; 4:145-59. . Thus, more objective evaluation factors can be determined through statistical analysis since the efficiency and quality of questionnaires are enhanced ⁸8 . Glumac B, Han Q, Smeets JJAM, Schaefer WF. Brownfield redevelopment features: applying Fuzzy Delphi. Journal of European Real Estate Research 2011; 4:145-59. ^{, 9}9 . Hsu Y, Lee C, Kreng VB. The application of Fuzzy Delphi Method and Fuzzy AHP in lubricant regenerative technology selection. Expert Syst Appl 2010; 37:419-25. . Some of the more representative strengths of the Fuzzy Delphi Method are: time saving, fewer surveys, increased recovery rate, and guarantee of completeness and consistency of the group opinion ¹⁹19 . Secretaría de Desarrollo Social. Evaluación externa, bases de datos y cuestionarios. Encuesta de Evaluación de los Hogares 2007: ENCEL 2007. http://evaluacion.oportunidades.gob.mx:8010/es/bases_cuan_c.php (accessed on 15/May/2011).
http://evaluacion.oportunidades.gob.mx:8... . Additionally, the Similarity Aggregation Method was suggested to help solve the fuzziness problem in the consensus of experts (Consejo Nacional de Evaluación de la Política de Desarrollo Social. Índice de Rezago Social 2005 a Nivel Municipal y por Localidad . http://www.co neval.gob.mx/cmsconeval/rw/pages/medicion/cifras/indicederezago.es.do, accessed on 01/Jun/2011). The Similarity Aggregation Method procedure introduces a similarity index to measure consistency among survey responders. Lu et al. ¹⁵15 . Lu C, Lan J, Wang Z. Aggregation of fuzzy opinions under group decision-making based on similarity and distance. Journal of Systems Science and Complexity 2006; 19:63-71. enriched the methodology through the Consistency Aggregation Method to improve the way in which similarity between fuzzy numbers is calculated. In this research, modified measures of similarity and distance were thus combined to obtain the weights of each individual opinion and finally the aggregation weights were determined through the algorithm stated as follows.

• Adapted Consistency Aggregation Method ¹⁵15 . Lu C, Lan J, Wang Z. Aggregation of fuzzy opinions under group decision-making based on similarity and distance. Journal of Systems Science and Complexity 2006; 19:63-71.

Step 1: calculate the similarity between each pair of experts’ opinions and for the 13 experts by:

where the triangular membership function is given by:

where λ - α = α_i, λ = b_i, λ + β = c_i ( Figure 1 ). Let us consider as an example for only two experts’ opinions, and . Now using the membership function equation (2) we obtain:

however, for a left ( a _i, b _i, 0) or right (0, b _i, c _i) triangular fuzzy set the respective membership function defined also by Park et al. ²⁰ was applied. If a _i = b _i = c _i in a triangular fuzzy number, we obtain a real crisp number ¹⁵, therefore its membership function is equal to 1 for the given real number and 0 for all other real numbers ²¹.

Step 2: calculate the distance between each pair of and by :

where is the normalized distance measure defined as follows:

with the Hamming distance based on the weighted one defined by Merigó ²² and are calculated between any two fuzzy numbers = a ₁, b ₁, c ₁ and = a ₂, b ₂, c ₂ as follows:

represents the largest distance,

by our distance measure equation (3), we have:

Step 3: given , let and calculate the consistency degree between each pair of experts by:

Step 4: let the degrees of importance of thirteen experts be e _i , i = 1,..., 13.

The degrees of importance are defined according to the years of experience reported by each expert in mammography studies, getting the percentage for each expert over the total years of experience. Then calculate the weighted consistency degree C ( E _i) for each expert E_i by:

Using equation (9) and a given e ₁ = 0.04, e ₂ = 0.08 the weighted consistency degrees are C ( E ₁) = 0.04, C ( E ₂) = 0.08

Step 5: calculate the aggregation weight w ( E _i)of expert E _i as follows:

Step 6: aggregate each fuzzy opinion for each feature k into a group fuzzy opinion as:

where (•) is the fuzzy multiplication operator ²³23 . Kaufman A, Gupta MM. Introduction to fuzzy arithmetic: theory and applications. 2ndEd. New York: van Nostrand Reinhold; 1985. .

Thus, the fuzzy opinion for feature k = 1 is

The Fuzzy Delphi Method with the Simple Center of Gravity Method proposed by Glumac et al. ⁸8 . Glumac B, Han Q, Smeets JJAM, Schaefer WF. Brownfield redevelopment features: applying Fuzzy Delphi. Journal of European Real Estate Research 2011; 4:145-59. and Hsu et al. ⁹9 . Hsu Y, Lee C, Kreng VB. The application of Fuzzy Delphi Method and Fuzzy AHP in lubricant regenerative technology selection. Expert Syst Appl 2010; 37:419-25. was used to achieve consensus regarding the importance of the identified variables. The Simple Center of Gravity Method is the most common method for creating a quantifiable result in fuzzy logic (defuzzification), computing the weighted average of the membership function ²⁴24 . Bai Y, Zhuang H, Wang D. Advanced fuzzy logic technologies in industrial applications. London: Springer; 2006. , as follows.

• Deffuzification ⁹9 . Hsu Y, Lee C, Kreng VB. The application of Fuzzy Delphi Method and Fuzzy AHP in lubricant regenerative technology selection. Expert Syst Appl 2010; 37:419-25.

The value S _k is obtained by:

A modified approach for Fuzzy Delphi Method is illustrated in Figure 2 with a flow chart for this study. The analysis was performed with R software (The R Foundation for Statistical Computing, Vienna, Austria; http://www.r-project.org ). The methodology with the corresponding modifications, consisted of the following steps:

• First panel evaluation: definition of items

Validation of a predefined list of variables: in a preliminary survey, experts were asked to approve or, failing that, add the variables they considered pertinent to the initial proposed list, based on the literature review.

• Second panel evaluation: item evaluation by some criterion of importance

Collection of experts’ opinions: in a second survey, the triangular fuzzy number was obtained for each expert, which represented the respondents’ rate and range of importance of each variable, i.e. the expert gave three values (minimum – a _i, optimal – b _i and maximum level – c _i of importance) on a scale of 0 to 10 related to a linguistic description (“very unimportant” to “very important”). In this study, a triangular membership function was implemented, to provide the experts with a simpler evaluation procedure. The three scores obtained per variable and per expert generated a more reliable data analysis ⁸8 . Glumac B, Han Q, Smeets JJAM, Schaefer WF. Brownfield redevelopment features: applying Fuzzy Delphi. Journal of European Real Estate Research 2011; 4:145-59. .

• Consistency Aggregation Method algorithm

Setting up overall triangular fuzzy number: separately examining the evaluation of each variable provided by the group of experts and aggregate the individual fuzzy opinions into a group fuzzy opinion through the modified Consistency Aggregation Method. By the method, the group consensus opinion is achieved based on similarity and distance indices. The aggregation of the fuzzy opinions is calculated from the weighted consistency degree for each expert and aggregated weight ¹⁵15 . Lu C, Lan J, Wang Z. Aggregation of fuzzy opinions under group decision-making based on similarity and distance. Journal of Systems Science and Complexity 2006; 19:63-71. . An algorithm is illustrated in item Adapted Consistency Aggregation Method to determine the aggregation weights of each individual opinion. The first modification to the original algorithm was the adjustment of the Consistency Aggregation Method, considering either a left or right triangular fuzzy set, to model the unusual answer pattern given by some experts. The second modification was the distance definition in Consistency Aggregation Method, using the Hamming distance for calculation optimization.

• Simple Center of Gravity Method

Defuzzification: the aim was to convert the overall triangular number to a real number ⁸8 . Glumac B, Han Q, Smeets JJAM, Schaefer WF. Brownfield redevelopment features: applying Fuzzy Delphi. Journal of European Real Estate Research 2011; 4:145-59. . The Simple Center of Gravity Method ²⁵25 . Agudelo M, Aguirre A, Dávila C. Variaciones en los años de vida perdidos por cánceres de mama y cérvico uterino en México según grado de marginación estatal, 1997 y 2007. Rev Chil Salud Pública 2010; 14:8-17. for each group fuzzy opinion was used to derive a definite value for each feature. The procedure is shown in item Deffuzification .

• Ho et al. ²⁶26 . Ho YF, Wang HL, Lu CH. The dynamic simulation model for the sustainable development of taichung city. Journal of Architecture 2002; 41:107-28. thresholds setting

Choice of the relatively important variables: variables that presented a value greater than each separately set threshold for each latent variable based on the method of Ho et al. ²⁶26 . Ho YF, Wang HL, Lu CH. The dynamic simulation model for the sustainable development of taichung city. Journal of Architecture 2002; 41:107-28. applied by Ho & Wang ²⁷27 . Ho YF, Wang HL. Applying fuzzy Delphi method to select the variables of a sustainable urban system dynamics model. In: Proceedings of the 26th International Conference of System. http://www.systemdynamics.org/conferences/2008/proceed/ (accessed on 15/May/2011).
http://www.systemdynamics.org/conference... , were retained. The cut-off point was determined using the arithmetic mean and the standard deviation of the internal variables in each latent variable. The threshold settings were made following Ho et al.’s ²⁶26 . Ho YF, Wang HL, Lu CH. The dynamic simulation model for the sustainable development of taichung city. Journal of Architecture 2002; 41:107-28. methodology for variable selection, which avoided the subjectivity in the specification.

Survey design

The first selection of variables to be evaluated relied mainly on the availability of data taken at individual, local and municipal levels in the rural homes survey (ENCEL 2007) ¹⁹19 . Secretaría de Desarrollo Social. Evaluación externa, bases de datos y cuestionarios. Encuesta de Evaluación de los Hogares 2007: ENCEL 2007. http://evaluacion.oportunidades.gob.mx:8010/es/bases_cuan_c.php (accessed on 15/May/2011).
http://evaluacion.oportunidades.gob.mx:8... , from the National Health Information System (Dirección General de Información en Salud. Recursos Humanos, Físicos y Materiales de la Secretaría de Salud y los Servicios Estatales de Salud . http://www.sinais.salud.gob.mx/basesdedatos/recursos.html; Unidades Médicas del Sector Público . http://www.sinais.salud.gob.mx/basesdedatos/unidadesmedicas.html, accessed on 15/May/2011) and datasets from the National Council for Evaluation of Social Development Policies (Consejo Nacional de Evaluación de la Política de Desarrollo Social. Índice de Rezago Social 2005 a Nivel Municipal y por Localidad . http://www.coneval.gob.mx/cmsconeval/rw/pages/medicion/cifras/indicederezago.es.do, accessed on 01/Jun/2011). The ENCEL survey was carried out on women who lived in impoverished areas. This research is focused on rural areas because women living in more deprived areas present additional challenges in terms of the access to health systems, related payment capacity, timely attention, treatment from health care staff and geographical difficulties in reaching care centers, among others ²⁵25 . Agudelo M, Aguirre A, Dávila C. Variaciones en los años de vida perdidos por cánceres de mama y cérvico uterino en México según grado de marginación estatal, 1997 y 2007. Rev Chil Salud Pública 2010; 14:8-17. .

The two surveys were carried out by sending an e-mail questionnaire to experts and academics in the following fields, viz. epidemiology, demography, economics, sociology, oncology, public health and health sciences. The goal of the first instrument was to refine and validate the initial list of factors obtained from the literature review. For that purpose the survey was submitted to three experts for evaluation, namely an epidemiologist, a demographist and a marketer. Hence, 52 variables corresponding to 9 constructs of the spatial interaction model of mammography use were proposed ( Table 1 ) as inputs for the second questionnaire. A total of 20 experts were contacted to participate in the second stage, 13 of whom agreed, a response rate of 65%. Three sections were included, following the methodology employed by Ho & Wang ²⁷27 . Ho YF, Wang HL. Applying fuzzy Delphi method to select the variables of a sustainable urban system dynamics model. In: Proceedings of the 26th International Conference of System. http://www.systemdynamics.org/conferences/2008/proceed/ (accessed on 15/May/2011).
http://www.systemdynamics.org/conference... : basic information (gender, area of specialization, years of specialization in breast cancer and in mammography), questionnaire instructions and finally the definition of variables and responses. The focus of the survey was to ask experts to estimate the importance of each variable as a determining factor in the use of mammography by allocating three values: minimum, optimal and maximum, by means of a 7-point Likert scale (0 = very unimportant, 1 = quite unimportant, 3 = unimportant, 5 = neutral, 7 = important, 9 = quite important and 10 = very important).

The structure of the experts’ disciplines comprised epidemiology (31%), sociology (23%), public health (15%), oncology (15%), demographics (8%) and health sciences in the workplace (8%); 76.92% were women. The respondents had an average of 10.12 years’ experience in breast cancer research, with a minimum of 3 years and a maximum of 38. The mean number of years of mammography-related research was 6.58, with a minimum of 2 and a maximum of 15. Based on this information, the degrees of importance of 13 experts (Step 4, item Adapted Consistency Aggregation Method ) are shown in Table 2 . After eliminating the missing values obtained in the ranking of the variables in the second questionnaire, the sample size varied between 9 and 13 experts.

Results

Those features which showed a real score higher than the threshold value after defuzzification were retained and the remainder discarded. The 20 relatively important factors resulting from the examination process are shown in Table 1 and Figure 3 . A description of the variables selected from the expert survey are given and correspond to nine latent variables considered from the spatial interaction model of mammography use:

1) Enabling/disabling: of the eight variables, three were retained, insurance status having the highest score, with 8.90, followed by asset index and number of children aged 12 and under.

2) Predisposing: only level of education was retained with 8.91.

3) Need: of the nine characteristics, three were retained, preventive medical consultation having the highest value with 8.17, followed by Pap smear and age at first childbirth.

4) Stressors: of the three variables, only the social gap index was retained with 9.01.

5) Social integration, support and behavioral settings: Of the four factors, only women who have worked at some time was retained with 5.97.

6) Social relationships: of the five variables only two remained, being accompanied to the doctor is seen as the most important with 7.18 followed by women who are listened to.

7) Population health behaviors or norms: only four of the eight variables remained, follow-up of abnormal mammogram results was the most relevant with 9.52, preceded by following the doctor’s advice, trusting the doctor and follow-up of abnormal Pap results.

8) Proximity and density of facilities, physicians: of the nine variables, four were retained, the availability of mammographs having the highest score with 9.44, followed by health communication through workshops, density of radiologists and availability of health centers.

9) Crowding, scheduling and convenience latent variable: the longer than average waiting time for a consultation was the factor retained with 7.10.

Discussion

The theory proposes that a variety of contextual factors operating at different levels of influence can help explain female participation in breast cancer screening. This study has examined the theoretical model of the ecological environment for mammography use proposed by Mobley et al. ¹⁶16 . Mobley LR, Kuo M, Driscoll D, Clayton L, Anselin C. Heterogeneity in mammography use across the nation: separating evidence of disparities from the disproportionate effects of geography. Int J Health Geogr 2008; 7:1-18. in the Mexican context.

The selection procedure and importance of the factors which affect the screening uptake was determined by expert survey, i.e. having experts from the practice validate it, and Fuzzy Delphi Method analysis. The use of the Fuzzy Delphi Method helps to solve the uncertainty of an accurate expert distinction in the examination of the features during the survey process, ensuring a better quality of survey analysis. One of the great advantages of the Fuzzy Delphi Method is the time saved in obtaining results, compared to the classic Delphi. The degrees of importance of participants affected the group decision-making, i.e. some experts are more experienced with breast cancer screening studies than others. Thus, by applying the Consistency Aggregation Method the fuzzy individual opinions are combined to obtain group consensus opinions, considering the relative weight of each expert according to their years of experience in mammography studies.

Several authors mentioned that the use of mammography can be determined by the term and type of medical insurance ⁶6 . Sosa-Rubí S, Walker D, Serván E. Práctica de mastografías y pruebas de Papanicolaou entre mujeres de áreas rurales de México. Salud Pública Méx 2009; 52 Suppl 2:S236-45. ^{, 28}28 . Couture MC, Nguyen CT, Alvarado BE, Velasquez LD, Zunzunegui MV. Inequalities in breast and cervical cancer screening among urban Mexican women. Prev Med 2008; 47:471-6. ^{, 29}29 . Naivar CK. Factors associated with mammography utilization in Sao Paulo and Mexico city elderly females [Doctoral Dissertation]. Houston: University of Texas School of Public Health; 2008. . De Alba et al. ³⁰30 . De Alba I, Hubbell AF, McMullin JM, Sweningson JS, Saitz R. Impact of U.S. citizenship status on cancer screening among immigrant women. J Gen Intern Med 2005; 20:290-6. and Garbers et al. ³¹31 . Garbers S, Jessop DJ, Foti H, Uribelarrea M, Chiasson MA. Barriers to breast cancer screening for low-income Mexican and Dominican women in New York City. J Urban Health 2003; 80:81-91. reported that lower participation rates are primarily associated with low socio-economic levels and health care barriers. Women believe that child-care issues influence the lack of follow-up mammograms ³²32 . Livaudais J, Coronado GD, Espinoza N, Islas I, Ibarra G, Thompson B. Educating Hispanic women about breast cancer prevention: evaluation of a home-based promotora-led intervention. J Womens Health 2010; 19:2049-56. ^{, 33}33 . Salazar MK. Hispanic women’s beliefs about breast cancer and mammography. Cancer Nurs 1996; 19:437-46. ^{, 34}34 . Thomas E. From qualitative data to instrument development: the women’s breast conflict scale. Qual Rep 2011; 16:908-32. ^{, 35}35 . Wall KM, Núñez-Rocha GM, Salinas-Martínez AM, Sánchez-Peña SR. Determinants of the use of breast cancer screening among women workers in urban Mexico. Prev Chronic Dis 2008; 5:1-8. . Our results of asset index and having children, as factors influencing mammography participation are consistent with previous studies ⁶6 . Sosa-Rubí S, Walker D, Serván E. Práctica de mastografías y pruebas de Papanicolaou entre mujeres de áreas rurales de México. Salud Pública Méx 2009; 52 Suppl 2:S236-45. ^{, 28}28 . Couture MC, Nguyen CT, Alvarado BE, Velasquez LD, Zunzunegui MV. Inequalities in breast and cervical cancer screening among urban Mexican women. Prev Med 2008; 47:471-6. ^{, 29}29 . Naivar CK. Factors associated with mammography utilization in Sao Paulo and Mexico city elderly females [Doctoral Dissertation]. Houston: University of Texas School of Public Health; 2008. ^{, 30}30 . De Alba I, Hubbell AF, McMullin JM, Sweningson JS, Saitz R. Impact of U.S. citizenship status on cancer screening among immigrant women. J Gen Intern Med 2005; 20:290-6. ^{, 32}32 . Livaudais J, Coronado GD, Espinoza N, Islas I, Ibarra G, Thompson B. Educating Hispanic women about breast cancer prevention: evaluation of a home-based promotora-led intervention. J Womens Health 2010; 19:2049-56. ^{, 33}33 . Salazar MK. Hispanic women’s beliefs about breast cancer and mammography. Cancer Nurs 1996; 19:437-46. ^{, 34}34 . Thomas E. From qualitative data to instrument development: the women’s breast conflict scale. Qual Rep 2011; 16:908-32. ^{, 35}35 . Wall KM, Núñez-Rocha GM, Salinas-Martínez AM, Sánchez-Peña SR. Determinants of the use of breast cancer screening among women workers in urban Mexico. Prev Chronic Dis 2008; 5:1-8. . As Brouwers et al. ³⁶36 . Brouwers MC, De Vito C, Bahirathan L, Carol A, Carroll JC, Cotterchio M, et al. Effective interventions to facilitate the uptake of breast, cervical and colorectal cancer screening: an implementation guideline. Implement Sci 2011; 6:112. reported, there is no evidence that group education has an effect on mammography adherence. However other studies reported a link between having a higher level of education and being receptive to mammography ⁷7 . Somers TJ. Risk behaviors in a community sample of women with a family history of breast cancer [Doctoral Dissertation]. Pittsburgh: University of Pittsburgh; 2006. ^{, 28}28 . Couture MC, Nguyen CT, Alvarado BE, Velasquez LD, Zunzunegui MV. Inequalities in breast and cervical cancer screening among urban Mexican women. Prev Med 2008; 47:471-6. ^{, 29}29 . Naivar CK. Factors associated with mammography utilization in Sao Paulo and Mexico city elderly females [Doctoral Dissertation]. Houston: University of Texas School of Public Health; 2008. ^{, 35}35 . Wall KM, Núñez-Rocha GM, Salinas-Martínez AM, Sánchez-Peña SR. Determinants of the use of breast cancer screening among women workers in urban Mexico. Prev Chronic Dis 2008; 5:1-8. .

Participation in mammography screening by the women in this study appears determined by “need factors”. Age of first childbirth is one of the risk factors for breast cancer ³⁷37 . Fitzpatrick JJ, Wallace M. Encyclopedia of nursing research. 2ndEd. New York: Springer; 2006. . Sclowitz et al. ³⁸38 . Sclowitz ML, Baptista AM, Petrucci D, Tessaro S. Condutas na prevenção secundária do câncer de mama e fatores asociados. Rev Saúde Pública 2005; 39:340-9. concluded that, at least with regard to the clinical breast exam, having a higher risk is positively related to the test. A number of preventive care variables such as influenza vaccination, bone density screening, Pap or gynecologic exam ³⁹39 . Wilkinson JE, Lauer E, Freund KM, Rosen AK. Determinants of mammography in women with intellectual disabilities. J Am Board Fam Med 2011; 24:693-703. and other disease prevention behaviors ³⁷37 . Fitzpatrick JJ, Wallace M. Encyclopedia of nursing research. 2ndEd. New York: Springer; 2006. were strongly associated with mammography. Moreover, in a study of Mexican women aged between 20 and 49, undergoing at least one Pap test was found to be linked with the carrying out of mammograms ⁶6 . Sosa-Rubí S, Walker D, Serván E. Práctica de mastografías y pruebas de Papanicolaou entre mujeres de áreas rurales de México. Salud Pública Méx 2009; 52 Suppl 2:S236-45. . Our research is the first study to use fuzzy logic that has identified the Pap smear as a factor that may affect screening rates. This finding is consistent with mathematical modeling studies among Mexican women ⁶6 . Sosa-Rubí S, Walker D, Serván E. Práctica de mastografías y pruebas de Papanicolaou entre mujeres de áreas rurales de México. Salud Pública Méx 2009; 52 Suppl 2:S236-45. and elsewhere ⁴⁰40 . González P, Borrayo EA. Role of physician involvement on Latinas’ mammography screening adherence. Womens Health Issues 2011; 21:165-70. ^{, 41}41 . Otero-Sabogal R, Owens D, Canchola J, Golding JM, Tabnak F, Fox P. Mammography rescreening among women of diverse ethnicities: patient, provider, and health care system factors. J Health Care Poor Underserved 2004; 15:390-412. . There is general agreement with the broad conclusions of the Canadian Cancer Society study, which reported that improved health care systems, strategies and policies must include the integration of primary cancer prevention with other chronic disease prevention activities ⁴²42 . Nigenda G, Caballero M, González-Robledo LM. Access barriers in early diagnosis of breast cancer in the Federal District and Oaxaca. Salud Pública Méx 2009; 52 Suppl 2:S254-62 .

Our study confirms that among the barriers to the best breast cancer healthcare in developing countries, more so at low income levels, are lack of knowledge of the disease, socio-economic and cultural barriers, organizational problems, poor quality health services and limited resources ³⁵35 . Wall KM, Núñez-Rocha GM, Salinas-Martínez AM, Sánchez-Peña SR. Determinants of the use of breast cancer screening among women workers in urban Mexico. Prev Chronic Dis 2008; 5:1-8. ^{, 37}37 . Fitzpatrick JJ, Wallace M. Encyclopedia of nursing research. 2ndEd. New York: Springer; 2006. ^{, 40}40 . González P, Borrayo EA. Role of physician involvement on Latinas’ mammography screening adherence. Womens Health Issues 2011; 21:165-70. ^{, 41}41 . Otero-Sabogal R, Owens D, Canchola J, Golding JM, Tabnak F, Fox P. Mammography rescreening among women of diverse ethnicities: patient, provider, and health care system factors. J Health Care Poor Underserved 2004; 15:390-412. . Case studies supporting our findings, have suggested that the synergy between elements such as: anti-poverty strategies, collaboration of NGOs with the government, empowerment through employment ⁴²42 . Nigenda G, Caballero M, González-Robledo LM. Access barriers in early diagnosis of breast cancer in the Federal District and Oaxaca. Salud Pública Méx 2009; 52 Suppl 2:S254-62 , participative development and active health programs may be the most effective in improving health and development outcomes ³⁷37 . Fitzpatrick JJ, Wallace M. Encyclopedia of nursing research. 2ndEd. New York: Springer; 2006. . However, besides raising women’s income-generating capacity, it is also necessary to increase their autonomy, decision-making authority, mobility and power in the home.

Other mamography participation studies have also found a lack of health-related social support as a barrier for the use of early detection tests ⁴⁰40 . González P, Borrayo EA. Role of physician involvement on Latinas’ mammography screening adherence. Womens Health Issues 2011; 21:165-70. ^{, 41}41 . Otero-Sabogal R, Owens D, Canchola J, Golding JM, Tabnak F, Fox P. Mammography rescreening among women of diverse ethnicities: patient, provider, and health care system factors. J Health Care Poor Underserved 2004; 15:390-412. ^{, 42}42 . Nigenda G, Caballero M, González-Robledo LM. Access barriers in early diagnosis of breast cancer in the Federal District and Oaxaca. Salud Pública Méx 2009; 52 Suppl 2:S254-62 . Health-related social support may be forthcoming from a regular doctor, but also refers to engaging in conversations with other women about health-related issues, for example providing information and clearing up any doubts about the exam.

Our findings related to the association between screening uptake and health behaviors, proximity-density of facilities and stressors, are consistent with the results documented by Brouwers et al. ³⁶36 . Brouwers MC, De Vito C, Bahirathan L, Carol A, Carroll JC, Cotterchio M, et al. Effective interventions to facilitate the uptake of breast, cervical and colorectal cancer screening: an implementation guideline. Implement Sci 2011; 6:112. and the Canadian Cancer Society ⁴³43 . Canadian Cancer Society; Cancer Care Ontario. Targeting cancer: an action plan for cancer prevention and detection (Cancer 2020). Toronto: Cancer Care Ontario; 2003. . In a cohort of women with initial ages of 35 to 39 years, those who had false-positive mammography outcomes showed less risk of non-participation in the future, compared to those who had true-negative outcomes ³⁷37 . Fitzpatrick JJ, Wallace M. Encyclopedia of nursing research. 2ndEd. New York: Springer; 2006. . Similarly, women with abnormal Pap smears were significantly more adherent to mammography than those with normal results ³⁷37 . Fitzpatrick JJ, Wallace M. Encyclopedia of nursing research. 2ndEd. New York: Springer; 2006. . Particularly in the clinical breast exam ⁴⁰40 . González P, Borrayo EA. Role of physician involvement on Latinas’ mammography screening adherence. Womens Health Issues 2011; 21:165-70. and breast cancer screening ⁴¹41 . Otero-Sabogal R, Owens D, Canchola J, Golding JM, Tabnak F, Fox P. Mammography rescreening among women of diverse ethnicities: patient, provider, and health care system factors. J Health Care Poor Underserved 2004; 15:390-412. ^{, 42}42 . Nigenda G, Caballero M, González-Robledo LM. Access barriers in early diagnosis of breast cancer in the Federal District and Oaxaca. Salud Pública Méx 2009; 52 Suppl 2:S254-62 , one barrier which dampens demand is users’ confidence in health care personnel and in the organizational aspects of the institutions which provide the service. Furthermore, the recommendation of doctors is vital because the physician’s advice to have a mammogram persuades individuals to adopt that preventive health behavior ³⁷37 . Fitzpatrick JJ, Wallace M. Encyclopedia of nursing research. 2ndEd. New York: Springer; 2006. ^{, 40}40 . González P, Borrayo EA. Role of physician involvement on Latinas’ mammography screening adherence. Womens Health Issues 2011; 21:165-70. ^{, 41}41 . Otero-Sabogal R, Owens D, Canchola J, Golding JM, Tabnak F, Fox P. Mammography rescreening among women of diverse ethnicities: patient, provider, and health care system factors. J Health Care Poor Underserved 2004; 15:390-412. ^{, 42}42 . Nigenda G, Caballero M, González-Robledo LM. Access barriers in early diagnosis of breast cancer in the Federal District and Oaxaca. Salud Pública Méx 2009; 52 Suppl 2:S254-62 . Unger-Saldaña & Infante-Castañeda ⁴⁴44 . Unger-Saldaña K, Infante-Castañeda C. Delay of medical care for symptomatic breast cancer: a literature review. Salud Pública Méx 2009; 52 Suppl 2:S270-85. maintain that the national screening program implies the equitable cost and distribution of mammography equipment, in addition to the training and adequate distribution of personnel to perform and interpret the test. The perception that the health system has sufficient equipment, staff and time to carry out the test also bore a significant relation to the breast cancer screening ³⁵35 . Wall KM, Núñez-Rocha GM, Salinas-Martínez AM, Sánchez-Peña SR. Determinants of the use of breast cancer screening among women workers in urban Mexico. Prev Chronic Dis 2008; 5:1-8. ^{, 37}37 . Fitzpatrick JJ, Wallace M. Encyclopedia of nursing research. 2ndEd. New York: Springer; 2006. .

Our findings support the argument that the lack of effective communication in health care ⁴²42 . Nigenda G, Caballero M, González-Robledo LM. Access barriers in early diagnosis of breast cancer in the Federal District and Oaxaca. Salud Pública Méx 2009; 52 Suppl 2:S254-62 and lack of knowledge about cancer ³⁵35 . Wall KM, Núñez-Rocha GM, Salinas-Martínez AM, Sánchez-Peña SR. Determinants of the use of breast cancer screening among women workers in urban Mexico. Prev Chronic Dis 2008; 5:1-8. ^{, 45}45 . Bird Y, Banegas MP, Moraros J, King S, Prapasiri S, Thompson B. The Impact of family history of breast cancer on knowledge, attitudes, and early detection practices of Mexican women along the Mexico-US border. J Immigr Minor Health 2011; 13:867-75. are determining factors for poor mammography participation ⁴⁰40 . González P, Borrayo EA. Role of physician involvement on Latinas’ mammography screening adherence. Womens Health Issues 2011; 21:165-70. . Thus, a reduction of structural barriers, giving provider assessment and feedback is recommended to improve screening rates ³⁹39 . Wilkinson JE, Lauer E, Freund KM, Rosen AK. Determinants of mammography in women with intellectual disabilities. J Am Board Fam Med 2011; 24:693-703. as well as ensuring an adequate supply of cancer prevention scientists and practitioners ⁴²42 . Nigenda G, Caballero M, González-Robledo LM. Access barriers in early diagnosis of breast cancer in the Federal District and Oaxaca. Salud Pública Méx 2009; 52 Suppl 2:S254-62 . Disparities in access to and quality of health services, for example, and an acceptable waiting time for obtaining a breast cancer exam ³⁵35 . Wall KM, Núñez-Rocha GM, Salinas-Martínez AM, Sánchez-Peña SR. Determinants of the use of breast cancer screening among women workers in urban Mexico. Prev Chronic Dis 2008; 5:1-8. have been identified in and within various regions of Mexico, affecting poorer women to a greater degree ⁴¹41 . Otero-Sabogal R, Owens D, Canchola J, Golding JM, Tabnak F, Fox P. Mammography rescreening among women of diverse ethnicities: patient, provider, and health care system factors. J Health Care Poor Underserved 2004; 15:390-412. . Our result of consultation wait times as a possible determinant of mammography utilization is consistent with this finding.

Examination of the threshold values showed that experts generally ranked highly those variables that related to predisposing and proximity-density of facilities and physicians. Early diagnosis, therefore, requires a process of effective communication and education which inculcates the medical culture of prevention in the population ⁴⁶46 . Morales A, Morimoto S, Natsuko O, Díaz V. Cáncer de glándula mamaria parte II. Revista de la Escuela de Medicina “Dr. José Sierra Flores” 2009; 23:16-22. Consequently, the best alternative is to renew early cancer detection strategies and programs rather than continuing the identification of patients in later stages when there will be insufficient resources for adequate treatment ⁴4 . Mohar A, Bargalló E, Ramírez MT, Lara F, Beltrán-Ortega A. Recursos disponibles para el tratamiento del cáncer de mama en México. Salud Pública Méx 2009; 52 Suppl 2:S263-9. . The findings described above coincide with some of today’s challenges for the efficient detection of breast cancer such as: (1) promoting equal investment in human resources, infrastructure and screening equipment, (2) improving information and target population awareness-raising about the benefits associated with early detection, (3) training enough radiology technicians, oncology specialist nurses among others and (4) promoting a culture of quality and excellence in the provision of services ⁵5 . Martínez-Montañez OG, Uribe-Zúñiga P, Hernández-Ávila M. Políticas públicas para la detección del cáncer de mama en México. Salud Pública Méx 2009; 52 Suppl 2:S350-60. .

Conclusion

The present study suggests that population health behaviors, i.e. follow-up of abnormal mammogram results and/or abnormal Pap results, following the doctor’s advice and trusting the doctor, is the most relevant latent variable that could determine women’s mammography participation. This shows, therefore, that some women may be less willing and less concerned about their health, demonstrating a bigger risk of non-participation in preventive health behavior in the future. According to the next highest scores obtained from the Consistency Aggregation Method, proximity-density of facilities and physicians, as well as stressors, are also relevant latent variables associated with adherence to early breast cancer detection. Additional research to balance and increase the number of experts in the various areas of specialization to obtain more reliable conclusions, to use other transformation methods for defuzzification in the proposed algorithm and to study the risk of breast cancer through Fuzzy Rule-Based System, is also needed. Moreover, additional studies addressing factors like quality and optimization of health services, training of personnel at all levels, formality and seriousness when dealing with patients, self-esteem, body image, taboos and psycho-social factors are suggested.

References

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