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MODEL IMPLEMENTATION: DATA USED AND MODEL SPECIFICATION
The exceptions to this approach were alcohol and percentage of energy from alcohol, where the model was run for only two groups: males nineteen years and over and females nineteen years and over. This is because there were not enough nonzero alcohol intakes to run the model for the NRV age groups 23, 48, 913, and 1418 years. MODEL SPECIFICATION Model types In general, the NCI method models usual daily intake as: probability of consumption x amount consumed ^{9} Based on this premise, there are three types of the NCI method models for the purpose of estimating group usual intakes. All three model types have been implemented in the Australian Health Survey: Usual Nutrient Intakes, 201112, using both of the NCI method macros mixtran and distrib.^{9}
2. Correlated twopart: A feature of nutrition data is that there is often a correlation between the probability of consuming a food/nutrient and the amount consumed. For example, people who are more likely to drink coffee/tea, i.e.consume caffeine on any day (higher probability) are often also more likely to consume more than one cup (higher amount). The NCI method allows for this correlation between probability and amount in the correlated twopart model.^{10} 3. Uncorrelated twopart: A simpler, uncorrelated form of the twopart model, which fits the probability and amount parts independently, is also available.^{9} For the usual nutrient intakes publication, the twopart model was used when more than 5% of intakes had zero amounts of the nutrient. It was therefore used for folic acid, caffeine, alcohol, and percentage of energy from alcohol. The correlated (rather than uncorrelated) twopart model was used for these nutrients (with one exception noted below) because there was evidence of correlation between probability and amount for these nutrients in the 201112 NNPAS. The exception to this was alcohol intakes of females nineteen years and over. For this group and nutrient, the simpler uncorrelated form of the twopart model was used. This is because when calculating errors using group jackknife, the correlated form could not run (failed to converge) for certain replicate weight groups. The effect of this on the estimates for alcohol intake in females is discussed in Data Quality. All other nutrients were consumed nearly every day by nearly every respondent, and so the onepart model was used. For these nutrients, the NCI model assigns any zero intakes a value equal to half the minimum nonzero value from the input dataset.^{1} Covariates In the NCI method, covariates are data items or variables that describe characteristics of the individuals within a group, which are relevant to their nutrient intake. Four covariates were used in this publication for all models: sex, NRV age group, weekend vs weekday, and sequence effect.^{11} The purpose of each of each of these covariates is outlined below. Age and sex An advantage of the NCI method is that covariates can be used to output results for subgroups, when running the model on the pooled intakes of a larger group.^{12}^{,13} For example, when running the model for all children under nine, including covariates describing each individual’s age group (23 years vs 48 years) and sex (male vs female) means that it is possible to output results for the NRV age and sex groups males 23 years, females 23 years, males 48 years, and females 48 years. For this reason, sex^{14} and the NRV age groups were used as covariates in the usual nutrient intakes publication. Weekend vs weekday A covariate describing whether the intake occurred on a weekend or a weekday was also included to allow the method to adjust or weight the usual intake distribution to represent a typical day. In this publication, a weekend record was defined as an intake that occurred on a Saturday or a Sunday.^{15} Sequence effect The NCI method can make an adjustment for the fact that the second day of intake data is often consistently different (e.g. lower reported food consumption and energy intake) to the first day of intake data. This may occur in nutrition data sets because of respondent fatigue, or because of differences in the collection of the second day of intake data (e.g. telephone interview rather than a facetoface interview, as is the case for the 201112 NNPAS). This option was used in the usual nutrient intakes publication. MODELLING RATIOS Modelling ratios is a special case. Two different approaches can be taken, and the results should be interpreted slightly differently in light of the approach chosen.^{16} The approach used in the usual nutrient intakes publication was to find the distribution of the ‘usual ratio of intakes’, as opposed to the distribution of the ‘ratio of usual intakes’. Ratios are variables which are calculated as one variable divided by another variable. Four usual intake distributions in the usual nutrient intakes publication, usual percentage of energy from carbohydrate, protein, fat, and alcohol, are distributions of usual ratios. In this publication, these ratios have first been calculated on an individual daily basis as the total percentage of energy coming from the macronutrient on the intake day (e.g. energy consumed as fat), divided by the total energy intake for the day. This was done for both Day 1 and Day 2 for each respondent. The NCI method was then run on these ratios in a similar way to other nutrients (using the same macros). The group usual distributions of these ratios, output from the NCI method, are therefore usual ratios of intakes, that is, the usual daily intake ratio.^{16} This differs from the alternative approach of finding the usual intake of energy from the macronutrient, and usual energy intake in the NCI method, and then finding the ratio of the two usual intakes.^{17,18 }This alternative approach would require the use of different macros.^{17} ENDNOTES 1 Tooze, JA et al. 2010, ‘A mixedeffects model approach for estimating the distribution of usual intake of nutrients: The NCI method’, Statistics in Medicine, vol. 140, pp.111116, <http://jn.nutrition.org>, last accessed 09/02/2015. 2 VerkaikKloosterman, J et al. 2011, ‘A threepart, mixedeffects model to estimate the habitual total vitamin D intake distribution from food and dietary supplements in Dutch young children’, The Journal of Nutrition Methodology and Mathematical Modeling, vol 141, pp. 20552011, <http://jn.nutrition.org>, last accessed 09/02/2015. 3 Garriguet, D 2010. ‘Combining nutrient intake from food/beverages and vitamin/mineral supplements’, Statistics Canada Health Reports, vol. 21, no. 4. 4 Bailey, RL et al. 2010, ‘Total folate and folic acid intakes from foods and dietary supplements of US children aged 113 y’ American Journal of Clinical Nutrition, vol. 92, pp. 353358. <http://ajcn.nutrition.org/>, last accessed 09/02/2015. 5 Barr, SI, DiFrancesco, L & Fulgoni, VL III, 2012. ‘Consumption of breakfast and the type of breakfast consumed are positively associated with nutrient intakes and adequacy of Canadian adults’, The Journal of Nutrition Nutritional Epidemiology, vol. 143, pp.8692, <http://jn.nutrition.org/>, last accessed 09/02/2015. 6 Fulgoni, VL III et al. 2012, ‘Foods, fortificants, and supplements : where do Americans get their nutrients ?’, The Journal of Nutrition Nutrient Requirements and Optimal Nutrition, vol. 141, pp.18471854, <http://jn.nutrition.org/>, last accessed 09/02/2015. 7 Bailey et al. 2010. ‘Estimation of total usual calcium and vitamin D intakes in the United States’, The Journal of Nutrition Nutritional Epidemiology, vol. 140, pp. 817822, <http://jn.nutrition.org/>, last accessed 09/02/2015. 8 Based on discussions with the NCI, threeway stratification was selected as a balance between the specificity of full stratification (separately fitting a model for every age and sex group) and the stability and parsimony of no stratification (fitting a single model for all age and sex groups). Splitting at nine years grouped those expected to have similar intakes together, and produced results within plausible ranges. Using stratification meant that models for each of the three groups were independently fitted, therefore allowing for some interaction effects between sex and age, including allowing for independent estimation of within and betweenperson variation. 9 National Cancer Institute, 2013, Usual dietary intakes: details of the method, <http://appliedresearch.cancer.gov/diet/usualintakes/details.html>, last accessed 16/02/2015. 10 Tooze, JA et al. 2006, ‘A new statistical method for estimating the usual intake of episodically consumed foods with application to their distribution’, Journal of the American Dietetic Association, vol. 106, pp. 15751587. 11 Base groups used for categorical covariates were the largest group. 12 Using covariates to output results by subgroups offers stability in the estimates of certain model parameters (within and betweenperson variation), over separately running the model for each individual subgroup. This is because the modelling process is able to draw on the strength of the full pooled intakes in the ingoing dataset for these parameters. 13 Dodd, KW et al. 2006, ‘Statistical methods for estimating usual intake of nutrients and foods : a review of the theory’, Journal of the American Dietetic Association, vol. 106, pp. 16401650, <http://www.andjrnl.org/>, last accessed 09/02/2015. 14 When running the model for males nine years of age and over, all individuals in the ingoing data were of the same sex. Similarly when running the model for females nine years of age and over, all individuals in the ingoing data were of the same sex. Therefore, sex was omitted as a covariate in these runs. 15 Note that the default in the NCI macros is a threeday weekend (Friday/Saturday/Sunday). A twoday weekend was specified to for comparability with other Australian nutrition data sets. 16 Freedman, LS et al. 2010, ‘The population distribution of ratios of usual intakes of dietary components that are consumed every day can be estimated from repeated 24hour recalls’, The Journal of Nutrition Methodology and Mathematical Modeling, vol. 140, pp.111116, <http://jn.nutrition.org/>, last accessed 9/2/2015. 17 National Cancer Institute, 2013, Usual dietary intakes: the NCI method, <http://appliedresearch.cancer.gov/diet/usualintakes/method.html>, last accessed 16/02/2015. 18 Carriquiry, AL et al. 1995, ‘Estimation of the usual intake distributions of ratios of dietary components’, Dietary Assessment Research Series Report 5, <http://www.card.iastate.edu/publications/dbs/pdffiles/95sr79.pdf>, last accessed 09/02/2015.

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