Introduction. The Journal of Nutrition Methodology and Mathematical Modeling

Transcription

1 The Joural of Nutritio Methodology ad Mathematical Modelig The Populatio Distributio of Ratios of Usual Itakes of Dietary Compoets That Are Cosumed Every Day Ca Be Estimated from Repeated 24-Hour Recalls 1 3 Laurece S. Freedma, 4 * Patricia M. Guether, 5 Kevi W. Dodd, 6 Susa M. Krebs-Smith, 6 ad Douglas Midthue 6 4 Gerter Istitute for Epidemiology ad Health Policy Research, Tel Hashomer 52161, Israel; 5 Ceter for Nutritio Policy ad Promotio, USDA, Alexadria, VA 22302; ad 6 Natioal Cacer Istitute, Bethesda, MD Abstract Estimatig the populatio distributio of the usual itake of a utriet relative to that of aother utriet requires determiatio of idividual-level ratios. If itake data are available o a per-day basis, as with 24-h dietary recalls, those ratios ca be determied i 1 of 2 ways: as the usual ratio of itakes or the ratio of usual itakes. Each of these ratios has its ow meaig ad determiatio; the ratio of usual itakes is coceptually cosistet with determiatios obtaied from FFQ data. We preset a method for estimatig the ratio of usual itakes that uses bivariate modelig of the 2 utriet itakes i questio. Applicatio of the method to the NHANES data for the years yielded estimated distributios for percet of usual eergy itake from total fat, percet of usual eergy itake from saturated fat, ad usual sodium itake per 1000 kcal (4184 kj) of usual eergy itake. Distributios for both the total populatio ad for age-geder subgroups were estimated. Approximately 60% of adults (.19 y) had a usual total fat itake that was withi the recommeded rage of 20 35% of total eergy, but oly ~34% had a usual saturated fat itake,10% of total eergy. The results chaged oly miimally whe the other defiitio of usual itake, the usual ratio of itakes, was adopted. J. Nutr. 140: , Itroductio 1 L.S.F. was supported through a cotract held by Iformatio Maagemet Systems Ic with the US Natioal Cacer Istitute; the remaiig authors were supported by their respective istitutios: USDA ad the Natioal Cacer Istitute. 2 Author disclosures: L. S. Freedma, P. M. Guether, K. W. Dodd, S. M. Krebs-Smith, ad D. Midthue, o coflicts of iterest. 3 A Supplemetal Appedix describig the statistical method used is available with the olie postig of this paper at j.utritio.org. * To whom correspodece should be addressed. lsf@actcom.co.il. A major purpose of dietary surveillace or moitorig is to evaluate dietary itakes relative to some stadard. Stadards may be averages, aroud which the populatio s itakes should be distributed, or thresholds, above or below which the populatio s itake should fall, but they are all established with regard to usual itake, geerally defied as the log-ru average daily itake over a period of time (1,2). This is importat because diets vary cosiderably from day to day. Noetheless, the primary assessmet method used i dietary surveillace is the 24-h dietary recall (3), a method that iheretly captures itake oe day at a time ad thus yields a large amout of withi-perso variatio. I previous work o estimatig the proportios of the populatio meetig recommeded dietary itake levels, ivestigators have either preseted the distributios of the reported values (4) or have adjusted the variace of the distributio to exclude withi-perso variatio (5 8). Oly the latter methods successfully remove the withi-perso variatio ad produce distributios of usual itake that have approximately the correct spread or variace. However, these methods have heretofore bee available oly for itakes of sigle dietary compoets that are cosumed early every day by early everyoe [see Dodd et al. (9) for a review]. I dietary surveillace, it is ofte of iterest to examie the populatio distributio of usual itake for a ratio of 2 dietary compoets. Examples iclude the distributio of itakes of saturated fat, total fat, or sodium, each expressed as a ratio of total eergy itake. Estimatig such distributios from atioal survey data that are based upo dietary itake reports from 24-h recalls is ot trivial. It has bee oted previously (10,11) that there are 2 ways of describig the distributio of ratios of itakes. Likewise, 2 defiitios of a idividual s usual itake ratio are available. First, oe could take the log-term mea of the daily ratio of itakes, which we will call the usual ratio (of itakes). Secod, oe could take the ratio of the log-term meas of the daily itakes, which we will call the ratio of usual itakes. A simple (but rather extreme) example shows that these are differet /08 $8.00 ã 2010 America Society for Nutritio. Mauscript received May 18, Iitial review completed August 3, Revisio accepted November 1, First published olie November 18, 2009; doi: /j

2 TABLE 1 Summary of the distributio of percet of usual eergy itake from total fat i the total US populatio ad selected age-geder subgroups, ,2 Percetile Mea 6 SE ad females % % 1 3 y y y y y y y $71 y $19 y y y y y y $71 y $19 y $1 y 17, Percet of usual eergy itake from fat = [usual itake of fat (kj)] / [usual itake of eergy (kj)]. Suppose that a perso cosumes o alterate days 10,000 kj, of which 4000 kj are from fat, ad 6000 kj, of which oly 600 kj are from fat. Usig the usual ratio, the usual percet eergy from fat is the average of 40 ad 10%, i.e. 25%. Usig the ratio of usual itakes, the usual fat itake is 2300 kj, the usual eergy itake is 8000 kj, ad their ratio is 29%. The questio of which defiitio is the more appropriate for purposes of dietary surveillace is ot a easy matter to resolve, TABLE 2 Summary of the distributio of percet of usual eergy itake from saturated fat i the total US populatio ad selected age-geder subgroups, ,2 Percetile Mea 6 SE ad females % % 1 3 y y y y y y y $71 y $19 y y y y y y $71 y $19 y $1 y 17, Percet of usual eergy itake from fat = [usual itake of fat (kj)] / [usual itake of eergy (kj)]. 112 Freedma et al.

3 because the decisio may deped o biological kowledge that is ofte lackig. The usual ratio is simpler to calculate, but the ratio of usual itakes is coceptually cosistet with the ratio that would be determied from FFQ, because they query logterm itake. For this reaso aloe, it is desirable to have a statistical method for estimatig the ratio of usual itakes ad derivig its distributio i the populatio from 24-h recall data. Therefore, our purposes i this article are to describe the methodology for estimatig the populatio distributio of the ratio of usual itakes ad to apply the method to estimate the distributios of several ratios. A feature of the method is the ability to estimate distributios i subpopulatios. Accordigly, we also preset distributios accordig to selected age ad geder groups. Fially, we compare the results of estimatig the populatio distributio of the ratio of usual itakes with those for the usual ratio ad shows that the differece was small i the examples. Methods Data. The data for this study were obtaied from 17,889 participats i the NHANES. All recalls obtaied from idividuals aged $1 y were icluded except those deemed ureliable by survey staff (297 idividuals), those reportig breast milk cosumptio (39 idividuals) because breast milk itake was ot quatified, ad 1 idividual who reported fastig o the survey day. Dietary itakes were assessed via computer-assisted, itervieweradmiistered 24-h recalls. I 2001, a sigle recall was requested from all idividuals. I , 2 recalls were requested of all participats. The first dietary iterview was coducted i a mobile examiatio ceter ad the secod was coducted 3 10 d later via telephoe. The NHANES has a complex, multistage, probability desig. For this study, oe of the authors (K.W.D.) created replicate weight sets suitable for the balaced repeated replicatio method of variace estimatio. The replicate weights were based o the dietary survey weights accompayig the NHANES data files, which adjust for survey desig, orespose, day of week, ad ay sequece effect i the secod recall. The NHANES surveys were approved by the NHANES Istitutioal Review Board uder protocol o Further iformatio about the NHANES is available elsewhere (12). Estimatig the populatio distributio of the ratio of usual itakes. The method, described briefly here, is based o a joit bivariate model for the 2 utriets (the umerator ad the deomiator of the ratio) i questio. A more precise ad techical descriptio is provided i the Supplemetal Appedix. Each reported utriet itake was first mathematically trasformed to approximate ormality usig a Box-Cox (power) trasformatio. The trasformatio was chose to miimize the mea squared error aroud a straight lie fit to a weighted QQ plot usig the samplig survey weights of each participat. The data were the aalyzed usig a bivariate liear mixed effects model, icludig the followig terms for each utriet: a itercept (fixed effect), a idicator for whether the reported day was a weekday or a weeked (fixed effect), a idicator for the sequece umber (first vs. secod) of the report (fixed effect), idicators for age group (fixed effects), a subject-specific term (radom effect), ad a withi-subject error term (radom error). For the aalysis of childre s itakes, a extra covariate for geder (fixed effect) was icluded. For adults, me ad wome were aalyzed separately. The covariate weekday/weeked was icluded to accommodate the differece i itake that ofte occurs betwee the weeked (Friday to Suday) ad the rest of the week. The covariate sequece umber was icluded to accommodate the possibility that participats report less fully o the secod recall tha o the first. The first recall was take to be the ubiased report. The covariate age group, which is a factor with several levels, was icluded to allow estimatio of the distributio withi specific age groups. TABLE 3 Summary of the distributio of usual sodium itake relative to usual eergy itake i the total U.S. populatio ad selected age-geder subgroups, ,2 Percetile Mea 6 SE ad females mg/1000 kcal 3 mg/1000 kcal 1 3 y y y y y y y $71 y $19 y y y y y y $71 y $19 y $1 y 17, Usual itake of sodium (mg) per 1000 kcal of usual eergy itake = [usual itake of sodium (mg)] / [usual itake of eergy (kcal)]. 3 1 kcal = kj. Distributio of ratios of usual itakes 113

4 TABLE 4 Proportios i the total U.S. populatio ad selected age-geder subgroups with usual itake of total fat equal to 20 35% of usual eergy itake ad proportios with usual itake of saturated fat less tha 10% of usual eergy itake, Proportio with total fat = 20 35% of eergy 6 SE Proportio with saturated fat,10% of eergy 6 SE ad females 1 3 y y y y y y y $71 y $19 y y y y y y $71 y $19 y $1 y 17, Icludig a covariate i the model allows estimatio of distributios i subpopulatios ad results i much greater precisio tha aalyzig the model o oly the subset of data from that subpopulatio (13). The subject-specific terms of the 2 utriets were assumed to have a bivariate ormal distributio, with 2 variaces ad a covariace estimated from the data. Likewise, the withi-subject terms were assumed to be bivariate ormal ad idepedet of the subject-specific terms ad required aother 2 variaces ad a covariace to be estimated. The model parameters could be estimated, because may participats completed more tha oe 24-h recall. If there are o repeated determiatios, the withi-subject variace parameters could ot be estimated. I the data from NHANES , 69% of the participats completed 2 24-h recalls. The model was fitted to the data usig the NLMIXED procedure i the statistical software package SAS ad the samplig weights of each participat were icorporated ito the aalysis. The output yielded estimates of the fixed-effect ad radom-effect model parameters, icludig the withi-subject covariaces. Three rus of the NLMIXED procedure for each type of ratio were performed o childre aged 1 8 y, males aged $9 y, ad females $9 y. Mote Carlo simulatios were the ru usig the parameter values estimated from the model. These simulatios geerated usual itakes of each utriet for a large umber of pseudo-idividuals (the details of these simulatios are described i the Supplemetal Appedix). The ratio of usual itakes was calculated for each pseudo-idividual ad, usig the samplig weights, the percetiles of the distributio of ratios of usual itakes were estimated. SE were estimated usig balaced repeated replicatio. These procedures were used to estimate distributios for 10 age-geder subgroups. The distributios for me ad wome $19 y were estimated by combiig the distributios of 4 fier age groupigs accordig to the populatio proportio i each subgroup. Results are show for the followig ratios: total fat:eergy, saturated fat:eergy, ad sodium:eergy. Values i the text are meas or proportios 6 1 SE, or estimated percetiles. The SAS code for performig these aalyses is available at cacer.gov/diet/usualitakes/. Estimatig the populatio distributio of the usual ratio. The method for estimatig the populatio distributio of the usual ratio is simpler tha for the ratio of usual itakes, because it is based o the uivariate distributio of the ratio of daily itakes rather tha o the bivariate distributio of the umerator ad deomiator. Several methods ca be applied directly to idividuals 24-h recall reported daily ratios (5,6,13) ad would be expected to give very similar results. For this report, the oe-part versio of a method developed at the Natioal Cacer Istitute (13) was used. Results The estimated mea percetage of usual eergy itake from total fat i the total populatio was % ad the media 33.3% (Table 1). The 5th ad 95th percetiles were 25.1 ad 42.9%, respectively. There was modest variatio with age, with older persos tedig to have a higher percetage itake ad very little differece betwee me ad wome. The estimated mea percetage of usual eergy itake from saturated fat i the total populatio was % ad the media 11.0% (Table 2). The 5th ad 95th percetiles were 7.8 ad 15.0%, respectively. The yougest childre (1 3 y) had the highest percetage; the percetage was lower i childre aged 4 18 y ad lowest i adults. 19 y, with little variatio amog adults by age group or betwee me ad wome. The estimated mea usual itake of sodium per 1000 kcal (4184 kj) of usual eergy itake i the total populatio was mg ad the media was 1538 mg (Table 3). Itakes were lower amog youg childre (1 3 y). Itakes were also slightly lower amog youger adults (31 50 y) tha older adults (.50 y). Differeces betwee me ad wome were mior. Supplemetal Tables providig SE for the idividual percetile TABLE 5 Compariso of the mea ratio of usual itakes to the mea usual ratio for percet eergy from total fat i the total U.S. populatio ad selected age-geder subgroups, Ratio of usual itakes Usual ratio Differece ad females % 1 3 y y y y y y y $71 y $19 y y y y y y $71 y $19 y $1 y 17, Values are meas 6 SE, estimated from data o 17,889 participats i NHANES. 114 Freedma et al.

5 TABLE 6 Compariso of the mea ratio of usual itakes to the mea usual ratio for percet eergy from saturated fat i the total U.S. populatio ad selected age-geder subgroups, Ratio of usual itakes Usual ratio Differece ad females % 1 3 y y y y y y y $71 y $19 y y y y y y $71 y $19 y $1 y 17, Values are meas 6 SE, estimated from data o 17,889 participats i NHANES. For the 3 examples give, differeces betwee me ad wome were mior. Thus, although absolute itakes of these utriets differed substatially betwee me ad wome, after adjustmet for eergy itake, the itakes were very similar. Because there are 2 differet defiitios of usual itake of a ratio, ivestigators may ask which to use ad whether it matters which is used. The followig formula provides the ivestigator with a method of judgig whether the 2 defiitios will lead to similar results. Deote a idividual s ratio o a give day by x/y. If CV y is the withi-perso CV of the deomiator (expressed as a proportio, ot as a percetage) ad CV x is that of the umerator, ad if r xy is the withi-perso correlatio betwee the umerator ad deomiator, the: idividual 0 s usual ratio ffi ð1 þ CV 2 2r y xycv x CV y Þ 3 idividual 0 s ratio of usual itakes: This approximate result is obtaied usig Taylor s expasio ad should provide reasoable accuracy for CV,0.75. It is similar to ad mathematically cosistet with the expressio give by Krebs-Smith et al. (10), although those authors were cocered with ratios at the populatio level rather tha at the idividual level. The closer the bracketed expressio is to 1.0, the closer the usual ratio will be to the ratio of usual itakes ad, cosequetly, the closer the 2 methods of estimatig the populatio distributio of usual itake will be for the ratio of utriets i questio. Data from repeat 24-h recalls i the Eatig at America s Table Study (15) idicate that the withi-perso CV for eergy is ~0.32, for saturated fat is 0.37, ad for sodium 0.43 [Supplemetal Table 1 i (11)]. The withi-perso correlatios with eergy were 0.78 for saturated fat ad 0.71 for estimates for these ratios ad the estimated distributios for other ratios are available. 7 The methodology described also allows estimatio of the proportio of the populatio whose ratio of usual itakes falls withi a chose iterval. A estimated % of the populatio had a usual total fat cosumptio that was withi the acceptable macroutriet distributio rage for total fat (20 35% of eergy) as set by the Istitute of Medicie (14) (Table 4). The proportio meetig this recommedatio was lowest i the 51- to 70-y age group, where oly % did so. Approximately 34% of the adult populatio s usual saturated fat cosumptio was,10% of eergy, as recommeded by the Dietary Guidelies for Americas (2). The proportio of childre meetig that recommedatio was smaller. The differece betwee the estimated distributio of the ratio of usual itakes ad the distributio of the usual ratio of itakes for the same 3 ratios was small (Tables 5 7). The differeces were i both directios but very small compared with the quatity estimated. All differeces were,3% of the estimated value. Discussio The method described i this article has provided for the first time, to our kowledge, estimates of the distributio of ratios of usual itakes of utriets to usual eergy itake for the U. S. populatio ad age-geder subgroups. Ratios give more direct iformatio o the quality of the compositio of the diet cosumed tha is provided by absolute itakes of utriets ad distributios of such ratios have heretofore bee uavailable. TABLE 7 Compariso of the mea ratio of usual itakes to the mea usual ratio for sodium relative to eergy itake i the total U.S. populatio ad selected age-geder subgroups, Ratio of usual itakes Usual ratio Differece ad females mg/1000 kcal y y y y y y y $71 y $19 y y y y y y $71 y $19 y $1 y 17, Values are meas 6 SE, estimated from data o 17,889 participats i NHANES. 2 1 kcal = kj. Distributio of ratios of usual itakes 115

6 sodium [Supplemetal Table 1 i (11)]. Thus, the bracketed expressio above for the saturated fat:eergy ratio is equal to ad for the sodium:eergy ratio is 1.004, values that are close eough to 1 that oe would expect very little differece betwee the methods. That the values are so close to 1 is due to the relatively high correlatio betwee umerator ad deomiator, together with the similarity i their CV. As predicted by the above formula, the results preseted i Tables 6 ad 7 show very little differece betwee the 2 methods for the saturated fat:eergy ratio ad the sodium: eergy ratio. Table 5 shows that the differece was also small for the total fat:eergy ratio. The formula predicts, however, that differeces could be more importat i other situatios. For example, i a case where the deomiator has a high CV ad the umerator has little or o correlatio with the deomiator, oe might expect larger differeces. Thus, ratios of microutriets, such as vitami C, to eergy may display larger differeces. I view of the possibility of larger differeces beig foud betwee the 2 methods, it would seem appropriate to idetify if ad whe oe of the defiitios is more appropriate. As metioed i the Itroductio, this choice is difficult i the absece of relevat biological iformatio. For example, high itakes of saturated fat are cosidered deleterious ad it is recommeded that Americas cosume,10% of eergy from such fatty acids. What is less clear is whether this ratio of 10% of eergy should ot be exceeded o a diural basis or over time. If each day s ratio has some relevace, the the usual ratio may be more appropriate. If, however, the relevat ratio is the proportio of all eergy cosumed over a log period of time derived from saturated fat, the the ratio of usual itakes may be more appropriate. For most ratios of iterest i utritio, biological iformatio to guide choosig the most relevat ratio is ot yet available. It may be that oe or the other method will be foud to be more appropriate for some ratios tha others. Most utritioists we have questioed have stated a preferece for the ratio of usual itakes, perhaps reflectig a ituitio that this term better reflects the steady state of a idividual. As metioed earlier, the ratio of usual itakes has the added advatage of beig coceptually cosistet with determiatios based o food frequecy data. The method described ca be applied to data gathered by repeated 24-h recalls o utriets or other dietary costituets that are cosumed early every day by early everyoe i the populatio. The method is iteded for use o quite large datasets with sample sizes of at least 1000 or more, especially if distributios i populatio subgroups are to be estimated. If oe is iterested i the distributio of a total populatio oly, the a sample of several hudred may suffice. O occasio there is a eed to examie the populatio distributio of the ratio of a episodically cosumed food or utriet (oe that is ot typically cosumed every day) to aother food or eergy. For example, oe may be iterested i cholesterol itake from eggs as a proportio of total cholesterol itake. I such cases, the required statistical modelig becomes more complex. Methods usig a extesio of the 2-part model described by Kipis et al. (16) are ow beig developed to allow the estimatio of these types of distributios. Ackowledgmets L.S.F., P.M.G., ad S.M.K-S. desiged research; D.M. ad K.W.D. performed statistical aalysis; ad L.S.F., P.M.G., ad S.M.K-S. wrote the paper. L.S.F. had primary resposibility for fial cotet. All authors read ad approved the fial mauscript. Literature Cited 1. Istitute of Medicie, Food ad Nutritio Board. Dietary referece itakes: applicatios i dietary assessmet. Washigto, DC: Natioal Academy Press; U.S. Departmet of Health ad Huma Services ad USDA. Dietary guidelies for Americas th ed. Washigto, DC: US Govermet Pritig Office; Moshfegh AJ, Raper N, Igwerse I, Clevelad L, Aad J, Goldma J, LaComb R. A improved approach to 24-hour dietary recall methodology. A Nutr Metab. 2001;45 Suppl 1: Moshfegh AJ. Food ad utriet itakes by idividuals i the Uited States, by sex ad age, Natiowide Food Surveys Report No Washigto, DC: USDA; NRC, Subcommittee o Criteria for Dietary Evaluatio, Coordiatig Committee o Evaluatio of Food Cosumptio Surveys, Food ad Nutritio Board. Nutriet adequacy: assessmet usig food cosumptio surveys. Washigto, DC: Natioal Academy Press; Nusser SM, Carriquiry AL, Dodd KW, Fuller WA. A semiparametric trasformatio approach to estimatig usual daily itake distributios. J Am Stat Assoc. 1996;91: Guether PM, Kott PK, Carriquiry AL. Developmet of a approach for estimatig usual utriet itake distributios at the populatio level. J Nutr. 1997;127: Moshfegh A, Goldma J, Clevelad L What We Eat i America, NHANES : usual utriet itakes from food compared to dietary referece itakes. USDA, Agricultural Research Service [cited 2009 Apr 27]. Available from: Place/ /pdf/usualitaketable s pdf. 9. Dodd KW, Guether PM, Freedma LS, Subar AF, Kipis V, Midthue D, Tooze JA, Krebs-Smith SM. Statistical methods for estimatig usual itake of utriets ad foods: a review of the theory. J Am Diet Assoc. 2006;106: Krebs-Smith SM, Kott PS, Guether PM. Mea proportio ad populatio proportio: two aswers to the same questio? J Am Diet Assoc. 1989;89: Freedma LS, Guether PM, Krebs-Smith SM, Kott PS. A populatio s mea Healthy Eatig Idex-2005 scores are best estimated by the populatio ratio whe oe 24-hour recall is available. J Nutr. 2008;138: NHANES. [Website o the Iteret]. [cited Oct]. Available from: Tooze JA, Midthue D, Dodd KW, Freedma LS, Krebs-Smith SM, Subar AF, Guether PM, Carroll RJ, Kipis V. A ew statistical method for estimatig the usual itake of episodically cosumed foods with applicatio to their distributio. J Am Diet Assoc. 2006;106: Istitute of Medicie, Food ad Nutritio Board. Dietary referece itakes for eergy, carbohydrate, fiber, fat, fatty acids, cholesterol, protei, ad amio acids. Washigto, DC: Natioal Academies Press; Subar AF, Thompso FE, Kipis V, Midthue D, Hurwitz P, McNutt S, McItosh A, Rosefeld S. Comparative validatio of the Block, Willett, ad Natioal Cacer Istitute food frequecy questioaires: The Eatig at America s Table Study. Am J Epidemiol. 2001;154: Kipis V, Midthue D, Buckma DW, Dodd KW, Guether PM, Krebs- Smith SM, Subar AF, Tooze JA, Carroll RJ, et al. Modelig data with excess zeros ad measuremet error: applicatio to evaluatig relatioships betwee episodically cosumed foods ad health outcomes. Biometrics. Epub 2009 Feb Freedma et al.