Section on Survey Research Methods JSM 2008

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1 Secton on Survey Research Methods JSM 008 Mnmzng Condtonal Global MSE for Health Estmates from the Behavoral Rs Factor Survellance System for U.S. Countes Contguous to the Unted States-Mexco Border Joe Fred Gonzalez, Jr. a, Machell Town b, Jay J. Km a Centers for Dsease Control and Preventon a Natonal Center for Health Statstcs, 33 Toledo Rd, Hyattsvlle, MD 078 b Natonal Center for Chronc Dsease Preventon and Health Promoton, 770 Buford Hwy, NE MS K-0 Atlanta, GA Abstract The Behavoral Rs Factor Survellance System (BRFSS) s a State-based telephone survey of the adult cvlan non-nsttutonalzed populaton resdng n the Unted States. Consequently, the BRFSS fnal weghts that are currently avalable n the publc use data fles are desgned to produce unbased estmates of health condtons by soco-demographc characterstcs at the State level. In addton to State level BRFSS estmates, there s nterest n the health status of adults resdng n the 5 U.S. countes contguous to the Unted States - Mexco border. The purpose of ths paper s to apply an alternatve approach of poststratfcaton by mnmzng condtonal global mean squared error of BRFSS health estmates for adults resdng n the combned 5 countes contguous to the Unted States - Mexco border. Keywords: unbased estmaton, root mean squared error, poststratfcaton. Introducton The Behavoral Rs Factor Survellance System (BRFSS) s a State-based telephone survey of the cvlan non-nsttutonalzed adult (8 years and over) populaton resdng n the Unted States. However, there s also nterest n another geographcal subpopulaton, the combned 5 U.S. countes contguous to the Unted States-Mexco Border States (Arzona, Calforna, New Mexco, and Texas.). The map n Fgure dsplays the sster ctes along both sdes of the Unted States-Mexco Border. Fgure shows a map of the actual countes that are contguous to the Unted States-Mexco Border. It was determned that t would be worthwhle to produce BRFSS estmates for the adult populaton n the border regon by certan age-sex-ethncty/race cells. The desred sx age groups were: 8-, 5-3, 35-, 5-5, 55-6, and 65 and over. The desred three ethncty/race groups were: Hspanc, Non-Hspanc Whte, and Non-Hspanc Blac/Multracal and others. In prevous wor (Gonzalez, et al, 005, 006, and 007), BRFSS sample counts were tabulated for the year 00 by age-sex-ethncty/race wthn each border county. Although sample counts were nsuffcent for some cells wthn each border county for the current estmaton research, BRFSS county level estmaton technques have been developed (Ja, et al, 00) and have been produced (Ja, et al, 006). For detaled documentaton for producng county level estmates, the reader s referred to: BRFSS's SMART (Selected Metropoltan/Mcropoltan Area Rs Trends) data from metropoltan/mcropoltan statstcal areas ( For the current estmaton research, sample szes were aggregated by the target age-sex-ethncty/race cells for the combned 5 countes contguous to the Unted States-Mexco Border (Arzona, Calforna, New Mexco, and Texas.). At the border regon level, sample szes were suffcently large for the desred agesex-ethncty/race cells for both Hspancs and Non-Hspanc Whtes, and n a few nstances for Non- Hspanc Blac/Multracal and others. Hereafter, the Unted States-Mexco Border Regon wll be smply referred to as the border regon. In addton, the same age-sex-ethncty/race crosstabulaton that was used for determnng sample sze suffcency was also used as the weghtng matrx for ths nvestgaton. Dsclamer: Ths paper represents the vews of the authors and should not be nterpreted as representng the vews, polces or practces of the Centers for Dsease Control and Preventon, Natonal Center for Health Statstcs, or the Natonal Center for Chronc Dsease Preventon and Health Promoton. 868

2 Secton on Survey Research Methods JSM 008 Ths paper wll focus on a condtonal global mnmum MSE strategy for calculatng 00 poststratfcaton factors by nvestgatng alternatve ways of collapsng cells by age-sex-ethncty/race for producng fnal weghts and estmates of health condtons of U.S. adults (8+ years) along the border regon. Then, the effect of ths alternatve collapsng approach on the MSE and root mean squared error (RMSE) of health estmates wll be determned.. Sample Weghtng Procedures for the Border Regon Post-stratfcaton s used for ncorporatng populaton dstrbutons of ey soco-demographc varables nto survey estmates. For a reference on poststratfcaton, see Km (00) Effect of Collapsng Rows/Columns of Weghtng Matrx on Weghts. The varable _WT, whch s the ntal sample weght from the BRFSS data sets, s defned as follows: where, _WT _STRWT * NAD / NPH STRWT wthn State stratum weght, NAD number of adults n household, and NPH number of phones n the household. The ntal sample weght (_WT) was used to create the ntal poststratfcaton factors (PSF) whch were calculated by age (6 groups)-sex ()-ethncty/race (Hspanc, Non-Hspanc Whte, and Non-Hspanc Blac/Multracal and Others) as follows: PSF Census pop. count wthn an -th cell / sum of _WT wthn same -th cell. The ntal poststratfed Fnal Weghts used n ths nvestgaton were calculated for the year 00 as follows: Fnal_Weght _WT*PSF. In ths paper two approaches are compared. The frst approach s conventonal cell collapsng. Ths approach s usually drven by sample sze consderatons (here, mnmum cell count, raw cell count 0), and maxmum rato crtera (orgnal PSF) by domans, and row adjacency. The second approach, the condtonal global mnmum MSE method, also employs the prevously mentoned crtera. The Fnal_Weghts were used to produce the 00 BRFSS prevalence estmates of the followng condtons among adults (8+ years of age): Ever had Asthma Ever had hgh blood pressure Hgh cholesterol Dabetes Havng health nsurance Current smoer Any exercse. 3. Bacground of Post Stratfcaton Strateges and Prevous Wor A.) Weghtng class methods have tradtonally been used based on the mnmum sample counts for the cell/row/column and the rato factor or post stratfcaton factor (PSF) wthn a cell; B.) The post stratfcaton factor s the rato of the control count to the ntally weghted sample count or the nverse of the coverage rato; C.) Tradtonal approach combnes homogeneous cells whch are smlar n content and characterstcs. D.) However, Km (00) dscovered a potental problem wth combnng cells that have dfferent coverage ratos. 869

3 Secton on Survey Research Methods JSM 008 E.) Gonzalez, et al (005) nvestgated a heurstc approach and condtonal local bas approach (006, 007) and found out that ths approach performs better than the conventonal approach n bas and MSE. 3. Condtonal Global Mnmum Mean Squared Error (MSE) Analyss Frst, we wll ntroduce the notaton nvolved n performng a mean square error (MSE) analyss as follows: MSE (p) [Bas (p)] + [se (p)] where p percent estmator of a health condton, bas P - p, where P populaton parameter, and se (p) standard error estmator for the percent estmator of the same health condton. Also, root mean squared error of p RMSE (p) MSE (p). The prevalence of health condtons usng the ntal poststratfed Fnal_Weghts are unbased estmates and treated as parameters, that s, as true values of health condtons for the adult populaton for ths mean square error (MSE) analyss. Snce we are usng estmates as parameters, ths bas and RMSE analyss s condtonal on our sample. The bas and RMSE analyss was performed by comparng these parameters of health condtons wth correspondng prevalence estmates of health condtons generated by Mnmzng Condtonal Global MSE analyss descrbed later followed by nvestgatng the effects on the RMSE of the same estmates. New PSF, correspondng Fnal Weghts, and correspondng percent estmates were produced by usng the above approach.. Methodology for Collapsng Two or More Cells Let N c N, where c s a constant and N s the control count for cell,,. Let f / ˆ N N be the post stratfcaton factor (PSF) for cell. N ˆ s the ntally weghted sample count for cell. Collapsng Adjustment Factor (CAF) for cell s defned as f( + c) β, cf+ f and CAF for cell, f( + c) β. cf + f. Two Cells Are Collapsed Suppose cells are collapsed wth another cells. σ V V β N x β N,,. () n Let [ ] Note than σ are the cell varances based on the global (over entre weghtng matrx) mean and x s the sample mean for cell. Let,,, be further adjustment factors for the collapsng adjustment factors. The s can be found by mnmzng the followng mean square error, assumng only two cells need to be collapsed wth another two cells, as before. V + V+ V 3+ V + βnx+ βnx + β3n3x3+ βnx Nx () 870

4 Secton on Survey Research Methods JSM 008 Dfferentatng expresson () wth respect to and and solvng a system of two equatons n the two unnowns and, we have β Nx Nx β Nx β Nx β Nx V and ( β N x ) β Nx Nx β Nx β Nx β Nx. () V ( β N x ) To smplfy further, let I β Nx,,, 3,, Then from equaton (3), I Nx I I I V + I 3 ( ) Smlarly, from equaton (), we have I Nx I I I V + I 3 ( ) 3 3 Denotng Nx I I by A, and after some algebra, equatons (5) and (6) can be smplfed to as AIV 3 VV 3+ I3V+ V3I AI V 3 VV 3+ I3V+ V3I. Three or More Cells Are Collapsed If there are sx cells and three of whch are collapsed wth another three, we have V+ V + V+ V + V+ V + β Nx βnx + β3nx 3 3+ βnx + 3β5Nx β6nx Nx ( (3) (5) (6) (7) (8) (9) Dfferentatng expresson (9) wth respect to,, and 3 and solvng a system of three equatons n three unnowns,, and 3, we have AIV 3V5 VVV 3 5+ IVV 3 5+ I3VV 5+ I5VV 3 AI3VV 5 VVV + I VV + I VV + I VV and (0) () 87

5 Secton on Survey Research Methods JSM 008 AI VV VVV 3 5+ IVV 3 5+ I3VV 5+ I5VV 3 6 In ths case, A Nx I I I6.. () In general, when p cells are combned wth another p cells, we have the followng: and p p p j DΠ V + I ΠV p Π j AI V,,, 3,..., p, D where, p. A N x I p [NOTE: Ths MSE analyss was conducted n two ways, usng orgnal PSFs and truncatng PSFs wth a mnmum value of 0.8 and a maxmum value of.0. See Tables -3.] 5. Results Table shows the rato of the RMSE of estmates applyng the condtonal global mnmum MSE approach to the correspondng RMSE for estmates applyng the conventonal collapsng approach. [NOTE: Only domans where there was a dfference n the RMSE are shown n Tables and.] A rato less than one ndcates that the global mnmum approach performed better than the conventonal collapsng approach. A rato greater than one ndcates the opposte relatonshp. Table s smlar to Table, except that the PSFs were truncated wth a mnmum value of 0.8 and a maxmum value of.0. Table 3 summarzes the results of Tables -. In general, the conventonal collapsng approach performed better n terms of RMSE than the proposed new method. 6. Conclusons A.) A lmtaton of the new method: analyss s condtonal on estmates usng orgnal PSFs, nstead of parameter values. B.) Another lmtaton of the new approach s that t s varable dependent,.e., t depends on the rato of cell means for a specfc varable. For ths paper, analyss was done by optmzng wth respect to the varable percent havng health nsurance. C.) The approach we adopted here s to try to optmze globally n terms of mean square error. However, global optmzaton does not necessarly optmze at the local level and the statstcs we compared were local ones, or at the doman level. Thus, ths approach does not do as well as the conventonal approach. References Gonzalez, Joe F.; Town, Machell; Km, Jay J. (005) Mean Square Error Analyss of Health Estmates from the Behavoral Rs Factor Survellance System for Countes along the Unted States-Mexco Border Regon, Proceedngs of the Amercan Statstcal Assocaton, Survey Research Methods Secton. Gonzalez, Joe F.; Town, Machell; Km, Jay J. (006) Estmaton and Relablty Issues of Health Estmates from the Behavoral Rs Factor Survellance System for U.S. Countes Contguous to the Unted States-Mexco Border, Proceedngs of the Amercan Statstcal Assocaton, Survey Research Methods Secton. 87

6 Secton on Survey Research Methods JSM 008 Gonzalez, Joe F.; Town, Machell; Km, Jay J. (007) Mnmzng Condtonal Local Bas for Health Estmates from the Behavoral Rs Factor Survellance System for U.S. Countes Contguous to the Unted States-Mexco Border, Proceedngs of the Amercan Statstcal Assocaton, Survey Research Methods Secton. Ja, Haomao; Muenng Peter; Boraws, Elane. (00) Comparson of Small-Area Analyss Technques for Estmatng County-Level Outcomes, Amercan Journal of Preventve Medcne; 6 (5): Ja, Haomao; Ln, Mchael; Holt, James.; Modad, Al H.; L, Lee; Levy, Paul S. (006) Montorng County-Level Vaccnaton Coverage Durng the Influenza Season, Amercan Journal of Preventve Medcne; 3 (): Km, Jay J. (00) Effect of Collapsng Rows/Columns of Weghtng Matrx on Weghts, Proceedngs of the ASA Survey Research Methods Secton. Km, Jay J.; Vallant, Rchard; Zha, Wenxng, (006) Cell Collapsng Strateges based on Collapsng Adjustment Factor. Proceedngs of the Amercan Statstcal Assocaton, Survey Research Methods Secton. Km, Jay J. (007) Alternatve Approach for Collapsng Usng a Collapsng Adjustment Factor, NCHS Internal Memorandum. Fgure. Map of Unted States-Mexco Border Showng Major Sster Ctes

7 Secton on Survey Research Methods JSM 008 Fgure. U.S. Countes along Unted States-Mexco Border. U.S. Countes Included n Border Regon 000 Populaton 55. mllon 6.6 mllon 8 Table. Rato of (RMSE Global Mnmum, Usng Orgnal PSF) / (RMSE Conventonal Collapsng) by Race-Sex-Age and Seven Health Condtons, 00 BRFFS. Race-Sex- Age Asthma Hgh BP Hgh CHOL Dabetes Insurance Current Smoer Any Exercse NH-WM NH-BM NH-BF HM HF [NOTE: Only domans where there was a dfference n the RMSE are shown n Table.] 87

8 Secton on Survey Research Methods JSM 008 Table. Rato of (RMSE Global Mnmum, usng Truncated PSF) / (RMSE Conventonal Collapsng) by Race-Sex-Age and Seven Health Condtons, 00 BRFSS. Race-Sex- Age Asthma Hgh BP Hgh CHOL Dabetes Insurance Current Smoer Any Exercse NH-WM NH-BM NH-BF HM HF [NOTE: Only domans where there was a dfference n the RMSE are shown n Table.] Table 3. Performance of Global Mnmum MSE Approach vs. Conventonal Collapsng for Seven Health Condtons for Several Age-Sex-Ethncty/Race Domans, 00 BRFSS. Health Condton Usng Orgnal PSF Usng Truncated PSF Global Better Conventonal Better Global Better Conventonal Better Asthma H-BP H-CHOL Dabetes Health Insurance Current Smoer Any Exercse