Abstract

OBJECTIVE:

to introduce the methodology used to calculate post-stratification weights of the 2012 Surveillance System for Risk and Protective Factors for Chronic Diseases by Telephone Survey (Vigitel) and to compare the trends of indicators estimated by cell-by-cell weighting and raking methods.

METHODS:

in this panel of cross-sectional studies, the prevalences of smokers, overweight, and intake of fruits and vegetables from 2006 to 2012 were estimated using the cell-by-cell weighting and raking methods.

RESULTS:

there were no differences in time trends of the indicators estimated by both methods, but the prevalence of smokers estimated by the raking method was lower than the estimated by cell-by-cell weighting, whilst the prevalence of fruit and vegetable intake was higher; for overweight, there was no difference between the methods.

CONCLUSION:

raking method presented higher accuracy of the estimates when compared to cell-by-cell weighting method, proving to be most convenient, although it presents register coverage bias.

Keywords:
Health Surveys; Telephone; Bias; Surveillance; Serial Cross-Sectional Studies

Introduction

The Surveillance System of Risk and Protective Factors for Chronic Diseases by Telephone Survey (Vigitel), implemented in 2006, is consolidated as a surveillance and management system.¹1. Ministério da Saúde (BR). Secretaria de Vigilância em Saúde. Secretaria de Gestão Estratégica e Participativa. Vigitel Brasil 2006: vigilância de fatores de risco e proteção para doenças crônicas por inquérito telefônico [Internet]. Brasília: Ministério da Saúde, 2007 [citado 2017 ago 23]. 297 p. Disponível em: Disponível em: http://bvsms.saude.gov.br/bvs/publicacoes/vigitel_brasil_2006.pdf
http://bvsms.saude.gov.br/bvs/publicacoe...

2. Ministério da Saúde (BR). Secretaria de Vigilância em Saúde. Secretaria de Gestão Estratégica e Participativa. Vigitel Brasil 2007: vigilância de fatores de risco e proteção para doenças crônicas por inquérito telefônico [Internet]. Brasília: Ministério da Saúde , 2008 [citado 2017 ago 23]. 136 p. Disponível em: Disponível em: http://bvsms.saude.gov.br/bvs/publicacoes/vigitel_brasil_2007.pdf
http://bvsms.saude.gov.br/bvs/publicacoe...

3. Ministério da Saúde (BR). Secretaria de Vigilância em Saúde. Secretaria de Gestão Estratégica e Participativa. Vigitel Brasil 2008: vigilância de fatores de risco e proteção para doenças crônicas por inquérito telefônico [Internet]. Brasília: Ministério da Saúde , 2009 [citado 2017 ago 23]. 112 p. Disponível em: Disponível em: http://bvsms.saude.gov.br/bvs/publicacoes/vigitel_brasil_2008.pdf .
http://bvsms.saude.gov.br/bvs/publicacoe...

4. Ministério da Saúde (BR). Secretaria de Vigilância em Saúde. Secretaria de Gestão Estratégica e Participativa. Vigitel Brasil 2009: vigilância de fatores de risco e proteção para doenças crônicas por inquérito telefônico [Internet]. Brasília: Ministério da Saúde , 2010 [citado 2017 ago 23]. 150 p. Disponível em: Disponível em: http://www.abeso.org.br/uploads/downloads/75/553a24c01eb80.pdf .
http://www.abeso.org.br/uploads/download...

5. Ministério da Saúde (BR). Secretaria de Vigilância em Saúde. Secretaria de Gestão Estratégica e Participativa. Vigitel Brasil 2010: vigilância de fatores de risco e proteção para doenças crônicas por inquérito telefônico [Internet]. Brasília: Ministério da Saúde , 2011 [citado 2017 ago 23]. 152 p. Disponível em: Disponível em: http://bvsms.saude.gov.br/bvs/publicacoes/vigitel_2010.pdf .
http://bvsms.saude.gov.br/bvs/publicacoe... ^-66. Ministério da Saúde (BR). Secretaria de Vigilância em Saúde. Secretaria de Gestão Estratégica e Participativa. Vigitel Brasil 2011: vigilância de fatores de risco e proteção para doenças crônicas por inquérito telefônico [Internet]. Brasília: Ministério da Saúde , 2012 [citado 2017 ago 23]. 132 p. Disponível em: Disponível em: http://bvsms.saude.gov.br/bvs/publicacoes/vigitel_brasil_2011_fatores_risco_doencas_cronicas.pdf
http://bvsms.saude.gov.br/bvs/publicacoe... Vigitel target-population is composed of adults aged 18 years or over, who live in households with or without landline, in the 26 Brazilian state capitals and the Federal District (FD). Its information is used for planning public policies, guidelines and specific actions for health promotion and prevention of risks and diseases.⁷7. Ministério da Saúde (BR). Secretaria de Vigilância em Saúde. Departamento de Análise de Situação de Saúde. Plano de ações estratégicas para o enfrentamento das doenças crônicas não transmissíveis (DCNT) no Brasil 2011-2022 [Internet]. Brasília: Ministério da Saúde , 2011 [citado 2017 ago 23]. 148 p. Disponível em: http://bvsms.saude.gov.br/bvs/publicacoes/plano_acoes_enfrent_dcnt_2011.pdf.
http://bvsms.saude.gov.br/bvs/publicacoe...

In the sampling process, Vigitel uses the registers of household telephone numbers, in order to randomly select household samples. Data of the Household Budget Survey (POF), conducted by the Brazilian Institute of Geography and Statistics (IBGE) between 2008 and 2009, point that 66.7% of the families who lived in Brazilian state capitals and the FD had expenses related to landlines in the 30 days previous to the study, and this coverage had remained stable in the previous six years (2003 to 2008).⁸8. Instituto Brasileiro de Geografia e Estatística. Microdados da pesquisa de orçamentos familiares [Internet]. 2014 [citado 2013 maio 14]. Disponível em: Disponível em: http://downloads.ibge.gov.br/downloads_ estatisticas.htm
http://downloads.ibge.gov.br/downloads_ ... Data of the 2010 Demographic Census⁸8. Instituto Brasileiro de Geografia e Estatística. Microdados da pesquisa de orçamentos familiares [Internet]. 2014 [citado 2013 maio 14]. Disponível em: Disponível em: http://downloads.ibge.gov.br/downloads_ estatisticas.htm
http://downloads.ibge.gov.br/downloads_ ... show that 61.0% of the private households located in the 26 state capitals and the FD had at least one landline. However, the landline coverage was not homogeneous throughout the country: the regions North and Northeast presented coverages of 38.0% and 44.0%, respectively, whilst the Midwest, South and Southeast had coverages of 56.0%, 70.0% and 74.0%, respectively.

When part of the study population is excluded from the sample due to the low coverage of the register used to select the sample, some non-sample biases may appear.⁹9. Kish L. Survey sampling. New York: John Wiley & Sons; 1965.

10. Cochran WG. Sampling techniques. 3rd ed. New York: John Wiley & Sons; 1977.^-1111. Kalton G. Compensating for missing survey data. Michigan: Institute for Social Research, The University of Michigan; 1983. Such situation happens at Vigitel survey, and is especially relevant in the capitals of the North and Northeast regions, whose landline coverage was under 50% in 2010. Bernal et al. show that this is a minor bias in regions with coverage over 70%.¹²12. Bernal R, Silva NN. Cobertura de linhas telefônicas residenciais e vícios potenciais em estudos epidemiológicos. Rev Saúde Pública. 2009;43(3):421-6.

The post-stratification weighting to compensate low coverage is commonly used in order to minimize these potential biases.¹³13. Battaglia MP, Frankel MR, Link MW. Improving standard poststratification techniques for random-digit-dialing telephone surveys. Surv Res Methods [Internet]. 2008 [cited 2013 Nov 24];2(1):11-9. Available from: Available from: https://ojs.ub.uni-konstanz.de/srm/ article/view/597 .
https://ojs.ub.uni-konstanz.de/srm/ arti...

14. Lepkowsky JM, Tucker NC, Brick JM, Leeuw E, Japec L, Lavraskas PJ, et al. Advances in telephone survey methodology. Hoboken (NJ): John Wiley & Sons; 2008.

15. Flores-Cervantes I, Brick JM, Jones ME, Westat J, DiSogra C, Yen W. Weighting for nontelephone household in the 2001 California Health Interview Survey [Internet]. In: Proceedings of the Joint Statistical Meetings Section on Survey Research Methods; 2002 Aug 11-15; New York. p.1002-7 [cited 2013 May 14]. Available from: Available from: http://www.amstat.org/sections/srms/Proceedings/y2002/Files/JSM2002-000661.pdf .
http://www.amstat.org/sections/srms/Proc... ^-1616. Bernal RTI, Malta DC, Araújo TS, Silva NN. Inquérito por telefone: pesos de pós-estratificação para corrigir vícios de baixa cobertura em Rio Branco, AC. Rev Saúde Pública. 2013 abr;47(2):316-25. Such procedure uses variables available in the sample and in the reference population, obtained from external sources to adjust the distribution of the sample with landline to what was verified for the whole set of the reference population.The choice of variables used in the construction of weights takes into consideration the characteristics of the population excluded, so the bias can be minimized.

Since the first edition of Vigitel, cell-by-cell weighting¹⁷17. Moura EC, Morais Neto OL, Malta DC, Moura L, Silva NN, Bernal R, et al. Vigilância de fatores de risco para doenças crônicas por inquérito telefônico nas capitais dos 26 Estados brasileiros e no Distrito Federal (2006). Rev Bras Epidemiol. 2008;11 (supl 1):20-37. had been adopted to calculate post-stratification weights, for each capital, using the population data from the 2000 Demographic Census as basis.⁸8. Instituto Brasileiro de Geografia e Estatística. Microdados da pesquisa de orçamentos familiares [Internet]. 2014 [citado 2013 maio 14]. Disponível em: Disponível em: http://downloads.ibge.gov.br/downloads_ estatisticas.htm
http://downloads.ibge.gov.br/downloads_ ... The combinations of categories of variables associated with landline - according to age group (18 to 24; 25 to 34; 35 to 44; 45 to 54; 55 to 64; 65 or over), sex (male, female) and education level (0 to 8; 9 to 11; 12 years or more of schooling) - compose the 36 cells used to calculate the weights, through the ratio between the relative frequency of each cell, the population from 2000 Demographic Census and the sample weighted by the basic design weights.⁸8. Instituto Brasileiro de Geografia e Estatística. Microdados da pesquisa de orçamentos familiares [Internet]. 2014 [citado 2013 maio 14]. Disponível em: Disponível em: http://downloads.ibge.gov.br/downloads_ estatisticas.htm
http://downloads.ibge.gov.br/downloads_ ...

However, at Vigitel recent measurements, there has been high variability of post-stratification weighting due to the presence of some cells with little sample information.The cells that compose the young population strata (18 to 24 years old) and with low education level (0 to 8 years of schooling) present the highest weights, due to the low frequency of the sample, because of the sociodemographic changes occurred in the period from 2000 to 2010.

In face of these results and after the population data of the 2010 Demographic Census was released, the researchers chose to review the methodology used to calculate post-stratification weighting, trying to find alternative methods that could minimize the effect of weighting in the estimates accuracy and could consider the sociodemographic transitions experienced by the Brazilian population between the 2000 and 2010 Demographic Censuses.

The raking method¹¹11. Kalton G. Compensating for missing survey data. Michigan: Institute for Social Research, The University of Michigan; 1983.^,1818. Izrael D, Hoaglin DC, Battaglia MP. A SAS macro for balancing a weighted sample [Internet]. In: Proceedings of the Twenty-Fifth Annual SAS Users Group International Conference, Paper 275, 2000 [cited 2010 Dec 12]. Available from: http://www2.sas.com/proceedings/sugi29/207-29.pdf.
http://www2.sas.com/proceedings/sugi29/2... was selected to calculate Vigitel post-stratification weighting. This method uses the simple frequency distribution of each variable, such as age group, sex and education level for each state capital, and allows the utilization of different external sources in the inter-census period, to calculate the weights.The main advantage of this method is the use of univariate distributions from different external sources, in different periods of time. A disadvantage of raking method is the need of an algorithm to calculate the weights. The advantage of cell-by-cell weighting method is the easiness to calculate weights, but its disadvantage is the need of databases to generate the contingency table used to calculate weights.¹¹11. Kalton G. Compensating for missing survey data. Michigan: Institute for Social Research, The University of Michigan; 1983.

The objective of this study was to present the methodology used to create post-stratification weights of the 2012 Vigitel and to compare the trend of indicators estimated by the cell-by-cell weighting and raking methods.

Methods

In this panel of cross-sectional studies, the prevalences of smokers, overweight, and regular intake of fruits and vegetables for five or more days a week were estimated using Vigitel data from 2006 to 2012, using cell-by-cell weighting and raking methods.

The raking method¹¹11. Kalton G. Compensating for missing survey data. Michigan: Institute for Social Research, The University of Michigan; 1983.^,1818. Izrael D, Hoaglin DC, Battaglia MP. A SAS macro for balancing a weighted sample [Internet]. In: Proceedings of the Twenty-Fifth Annual SAS Users Group International Conference, Paper 275, 2000 [cited 2010 Dec 12]. Available from: http://www2.sas.com/proceedings/sugi29/207-29.pdf.
http://www2.sas.com/proceedings/sugi29/2... was used as an alternative to calculate post-stratification weighting to increase Vigitel sample. This method uses the annual frequency distribution of the variables ‘age group’, ‘sex’ and ‘education level’ of the population. Due to the absence of annual projections of the population’s education level, we chose to estimate the education level, sex and age group using data of the 2000 and 2010 Censuses.

The procedures used to calculate the projections and to calculate weights using the raking method for each capital are presented below. Initially, we considered the microdata of the 2000¹⁸18. Izrael D, Hoaglin DC, Battaglia MP. A SAS macro for balancing a weighted sample [Internet]. In: Proceedings of the Twenty-Fifth Annual SAS Users Group International Conference, Paper 275, 2000 [cited 2010 Dec 12]. Available from: http://www2.sas.com/proceedings/sugi29/207-29.pdf.
http://www2.sas.com/proceedings/sugi29/2... and 2010¹⁹19. Ministério da Saúde (BR). Portal da saúde. Datasus. Demográficas e socioeconômicas [Internet]. 2012 [citado 2013 dez 12]. Disponível em: http://www2.datasus.gov.br/DATASUS/ index.php?area=0206.
http://www2.datasus.gov.br/DATASUS/ inde... Demographic Censuses for each state capital (i), in the calculation of the geometric mean rate (rg_(i)) of the annual growth of the adult population used for population projections during the inter-census period - Expression 1:

For each capital, we calculated the population growth rate, stratified by sex, for each of the six age groups (18 to 24; 25 to 34; 35 to 44; 45 to 54; 55 to 64; and 65 or over), and for four education levels (no schooling or incomplete Primary School; complete Primary School or incomplete High School; complete High School or incomplete Higher Education; Higher Education degree). Due to changes in the questions of 2000 and 2010 Censuses, IBGE provided the combinations of the classification variables of education level for each census.The use of the data imputation technique was necessary for the category ‘Not mentioned’ of the variable ‘education level’, by adopting the most frequent value within each age group - stratified by sex - for the missing cases.

The estimates of the adult population of each state capital, during the inter-census period (t), were obtained from the geometric mean rate of annual growth estimated for each one of the 14 population groups (six age groups for the total population and four education levels for each sex). Moreover, the total estimate of Vigitel population by age was adjusted using the total population from IBGE, provided by the Department of the Brazilian National Health System (Datasus)¹⁹19. Ministério da Saúde (BR). Portal da saúde. Datasus. Demográficas e socioeconômicas [Internet]. 2012 [citado 2013 dez 12]. Disponível em: http://www2.datasus.gov.br/DATASUS/ index.php?area=0206.
http://www2.datasus.gov.br/DATASUS/ inde... for each surveyed year. This adjustment resulted from the multiplication of the total frequency per age, stratified by sex, by the total number of adults aged 18 or over in the population. The same procedure was used for education level, stratified by sex. In both cases, the total population, estimated from the adults’ sample was adjusted to the total size of the population.

For each capital, the population estimates were calculated per age groups (six categories) and per education level, stratified by sex (eight categories), in the period from 2006 to 2011 - except for 2010. This information was used to calculate Vigitel post-stratification weights by raking method.¹¹11. Kalton G. Compensating for missing survey data. Michigan: Institute for Social Research, The University of Michigan; 1983.^,1818. Izrael D, Hoaglin DC, Battaglia MP. A SAS macro for balancing a weighted sample [Internet]. In: Proceedings of the Twenty-Fifth Annual SAS Users Group International Conference, Paper 275, 2000 [cited 2010 Dec 12]. Available from: http://www2.sas.com/proceedings/sugi29/207-29.pdf.
http://www2.sas.com/proceedings/sugi29/2... This method works with one variable at a time, leveling the distribution of the total variable in the sampling weights by the sample weights and in the population, through itineration procedure. This process is repeated to each one of the variables used to calculate the weights, so the sample distribution becomes identical to the population for these variables. The new post-stratification weights for each capital were calculated using the statistical software SAS (macro function Rakinge.sas²¹21. Bernal RTI. Inquéritos por telefone: inferências válidas em regiões com baixa taxa de cobertura de linhas residenciais [tese]. São Paulo (SP): Universidade de São Paulo, 2011.).

Vigitel sample weights, in each capital, are calculated by the ratio between the number of adults and the number of landlines, due to the random sampling, in two stages: first, the registers of household telephones are used so the household samples can be drawn; second, one adult resident of the picked household is also randomly selected.

The analyses of Vigitel data require the survey sampling complex plan (SCP) to be considered. The measure used to assess the impact of weights in the prevalence accuracy is the design effect (deff),⁹9. Kish L. Survey sampling. New York: John Wiley & Sons; 1965. which expresses the ratio between the variance of estimates calculated with weights and the simple casual sample. A deff value equals 1 indicates that the weights did not change the estimate accuracy, whilst deff values over 1 indicate loss of accuracy due to the use of post-stratification weighting. Deff was calculated for each indicator using the post-stratification weights by the cell and raking methods. The deff obtained from the raking method is expected to be lower than the one obtained by cell-by-cell weighting.

The following stages will be described, in order to present the raking methodology applied in Vigitel after 2012:

This study used secondary data, with no identification of subjects, in accordance with the ethical principles established at the Resolution of the National Health Council (CNS) No. 510, dated April 7^th 2016.

Results

From 2000 to 2010, the adult population living in Belém-PA increased, on average, 1.2% per year, although in stratification per age, the variation rate of the population size from 18 to 24 years old has been negative. A bigger growth was observed in the age group from 55 to 64 years old. The population with no schooling or incomplete Primary School decreased 1.7% per year, whilst the population with complete High School or incomplete Higher Education increased, on average, 5.5% per year. The population with Higher Education degree increased almost 7% per year, with higher growth among women: 7.6% (Table 1).

In 2011, the outputs of the program Rakinge.sas carried out for Belém-PA (Figure 1) shows, for example, the results for the first and last iteration to calculate post-stratification weights.The first variable to calculate the weights is the age group, presented in column (1), with six categories (18 to 24; 25 to 34; 35 to 44; 45 to 54; 55 to 64; and 65 years or over). In the first iteration of age group, we can observe that the number of adults weighted by the base sampling weight is equal to 6,116.75 (2); and in the population, equals to 999,061 adults (3). When the sample relative distribution is compared (4) with the population (5), we can notice that Vigitel has less adults aged 18 to 44, and more adults aged 45 or over (6). The second variable is education level stratified by sex (7), with eight categories:

In this stage the total expanded sample of Vigitel (8) is already equal to the total population, according to IBGE (9); however, when the relative distribution of the sample and education level are compared in Vigitel we observe a difference of -8.8% of men and -5.9% of women, both with no schooling or with incomplete Primary School. In turn, there are more adults with Higher Education degree.In the second iteration, the weighted sample of the variable ‘age group’ is the same as the population; however, the difference between the relative distributions of the population and the sample differs from zero. This procedure is repeated until the relative difference between Vigitel and the population is equal to zero. In this example, to meet the convergence criterion, seven iterations were necessary until the age groups (10) and education level stratified by sex (11) were equal to zero. At the end of the process, a file with post-stratification weighting is generated.

The evaluation of weighting impact in the accuracy of smokers prevalence, presented by the measure of design effect (deff) showed deff values >1; this means there was accuracy loss in the use of post-stratification weighting.Deff values produced by cell-by-cell weightingwere higher than those produced by raking method, for all capitals and years. The higher the deff value is, the lower the estimate accuracy will be (Table 2). The accuracy loss happens due to the change in the sample size, expressed by the following formula:

For example, in 2006, the state capital Palmas-TO presents a deff of 5.12 and 2.54 - which corresponds to the effective sample size of 391 (2,000/5.12) and 787 (2,000/2.54), respectively. That is, the weighting makes the sample size equal to 2,000 correspond to the effective sample size, equivalent to 391 and 787 interviews, respectively (Table 2).

When we compare the historical series of adult smokers prevalences, for all the state capitals and the FD, estimated by cell and raking methods, we observe a decreasing trend for both methods; however, in raking method, this trend was more marked, with prevalences lower than those estimated by the cell-by-cell weighting. For the overweight estimates, we did not observe any difference between the methods. The prevalence estimates of regular intake of fruits and vegetables for five or more days a week presented increasing trend, and the prevalences estimated by the raking method were higher than those in the cell method (Figure 2).

Discussion

This is the first study that compared two post-stratification methods: cell-by-cell weighting and raking. Raking method was first adopted in Vigitel in 2012 and presents advantages over cell-by-cell weighting, because it uses annual population data, which reflect the changes occurred in the Brazilian population, whilst cell-by-cell weighting uses the same population data for different years of research. Although raking method does not eliminate the register coverage bias, it produces estimates that express more accurately the trends of risk factor indicators in the population, when comparing with cell-by-cell weighting.This new weighting method has already been used to produce new estimates based on Vigitel data, for the period from 2006 to 2011.

There are several methods to calculate post-stratification weighting. Among them, the cell-by-cell weighting is widely used due to its simple weight calculation, which uses the cells of the population and sample contingency tables.¹¹11. Kalton G. Compensating for missing survey data. Michigan: Institute for Social Research, The University of Michigan; 1983. This method has a limitation regarding the need of available data to create the contingency table of the variables, since this information is available only every ten years (IBGE Demographic Census). The Brazilian population has been going through a demographic and socioeconomic transition,²⁰20. Alves JED, Cavenaghi S. Tendências demográficas, dos domicílios e das famílias no Brasil [Internet]. Aparte: inclusão social em debate. 2012 [citado 2013 out 11]. Disponível em: Disponível em: http://www.ie.ufrj.br/aparte/pdfs/tendencias_ demograficas_e_de_familia_24ago12.pdf .
http://www.ie.ufrj.br/aparte/pdfs/tenden... and this large period of one decade constitutes a limitation for this method.In turn, raking method uses only the simple frequencies of each variable of population and sample, which enables the use of population information from different external sources, as well as interpolation of the population variables during the inter-census period, covering the changes in the population occurred in the period. The limitation of the raking method is the higher complexity of weighting calculation, because it needs an algorithm which is available in the statistics package for post-stratification weighting.

In the comparison between the estimates of both weighting methods, the trends of the three indicators were similar; however, the values of the prevalences were different comparing the raking and cell-by-cell weighting. We noticed differences in the prevalences of smokers and fruits and vegetable intake, whereas overweight prevalence did not show any difference. The differences observed may be explained by the association between the indicators, regarding having a landline.²¹21. Bernal RTI. Inquéritos por telefone: inferências válidas em regiões com baixa taxa de cobertura de linhas residenciais [tese]. São Paulo (SP): Universidade de São Paulo, 2011.^,2222. Malta DC, Iser BPM, Sá NNB, Yokota RTC, Moura L, Claro RM, et al. Tendências temporais no consumo de tabaco nas capitais brasileiras, segundo dados do Vigitel, 2006 a 2011. Cad Saúde Pública [Internet]. 2013 abr [citado 2013 set 01];29(4):812-22. Disponível em: Disponível em: http://www.scielo.br/scielo.php?script=sci_ arttext&pid=S0102-311X2013000400018&lng=en &nrm=iso
http://www.scielo.br/scielo.php?script=s...

In the case of indicators positively associated to education level, the increase in schooling by the population in the inter-census decade, as well as its aging, might have led to the higher decrease of those indicators, as shown by this study.Other studies point that the smoking prevalence is associated to low schooling.²³23. Giovino GA, Mirza SA, Samet JM, Gupta PC, Jarvis MJ, Bhala N, et al. Tobacco use in 3 billion individuals from 16 countries: an analysis of nationally representative cross-sectional household surveys. Lancet. 2012 Aug;380(9842):668-79. The increase in the education level of the Brazilians during the inter-census period justifies the reduction in the prevalence of smokers, which could be more consistently noticed by the raking weighting, since this method updates the population estimates of sex, age and education level. Thus, the raking method could reveal smaller prevalences; and a trend of sharper decrease of smoking among the Brazilian population, confirmed by the National Health Survey (PNS), conducted by the Ministry of Health in a partnership with IBGE, which pointed to a 20% reduction in smoking prevalence in the Brazilian population from 2008 to 2013.²⁴24. Malta DC, Vieira ML, Szwarcwald CL, Caixeta R, Brito SMF, Reis AAC. Tendência de fumantes na população brasileira segundo a pesquisa nacional de amostra de domicílios 2008 e a pesquisa nacional de saúde 2013. Rev Bras Epidemiol. 2015 dez;18(suppl 2);45-56. Therefore, the raking method could obtain more accurate estimates using Vigitel data.

Similarly, in the United States, Battaglia et al.¹³13. Battaglia MP, Frankel MR, Link MW. Improving standard poststratification techniques for random-digit-dialing telephone surveys. Surv Res Methods [Internet]. 2008 [cited 2013 Nov 24];2(1):11-9. Available from: Available from: https://ojs.ub.uni-konstanz.de/srm/ article/view/597 .
https://ojs.ub.uni-konstanz.de/srm/ arti... evaluated the post-stratification weighting of 2003 data provided by the Behavioral Risk Factor Surveillance System (BRFSS), whose response rate was lower than 50%. The estimates obtained by the weighting and raking method were compared, both using population data from the Current Population Survey (CPS) to calculate post-stratification weighting, in order to minimize non response bias. The results of the North American study showed that the BRFSS tended to underestimate the indicators of risk factors of the population due to the low response rate, fewer than 50%, especially among the low income population, who presented higher prevalence of risk factors. And the estimates of prevalences obtained from the raking method were higher, when compared to those provided by the cell-by-cell weighting, given the association between the variables used to calculate weights and risk factors.

In 2011, the Centers for Disease Control and Prevention (USA/CDC) implemented many changes in the BRFSS.²⁵25. Center for Disease Control and Prevention. Behavioral risk factor surveillance system: BRFSS 2011 survey data and documentation [Internet]. Atlanta: Center for Disease Control and Prevention; 2011 [cited 2017 May 17]. Available from: Available from: http://www.cdc.gov/brfss/ annual_data/ annual_2011.htm
http://www.cdc.gov/brfss/ annual_data/ a... The CDC/USA included in its survey sample the population that uses only mobile phones (added to the population that uses landline) and changed the weighting method.The system started using the raking method to calculate post-stratification weighting, due to the double register (landline and mobile phones), the reduction of non response bias and the improve in the estimates accuracy. The methodology changing process adopted by BRFSS was recommended by experts, with the release of studies that evaluated different variables used in the construction of post-stratification weights, in order to reduce the bias generated by the low response rate.²⁶26. Brennan N, Kenney G, Rajan S, Scheuren F, Wang K, Zuckerman S, et al. 1997 NASF technical papers: report no 16: assessing the new federalism an urban institute program to assess changing social policies. Washington: Urban Institute; 2001.^,2727. Link MW et al. Reaching the U.S. cell phone generation: comparison of cell phone survey results with an ongoing landline telephone survey. Public Opin Q [Internet]. 2007 [cited 2013 Nov 24];71(5):814-39. Available from: Available from: http://www.bebr.ufl.edu/files/ Reaching%20the%20US%20Cell%20Phone%20 Generation.pdf
http://www.bebr.ufl.edu/files/ Reaching%...

Regarding Vigitel, the post-stratification methods used aim to reduce possible distortions in the estimates associated to the method of participants’ selection, through landline, which generates a selection bias. To eliminate this bias, Vigitel should introduce in its research individuals without landline.

While Vigitel sampling process does not change we recommend the use o raking method. It enables the collection of more accurate prevalence estimates - when comparing with the cell-by-cell weighting -, making them closer to the reality presented in the 2010 Census. Thereby, it is possible to support the monitoring of risk and protective factors for chronic non-communicable diseases, besides subsidizing, more adequately, public policies for health promotion.

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