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One of the main interests in the nutrition field is to estimate the distribution of usual nutrient in-take. Data from vitamin intake generally present high asymmetry mainly to the presence of outliers. This can occur due to the variability of the diet and, in this case, robust estimation to get the distribution of the data can be required. Then, the aim of paper is to propose an alternative approach for estimating usual intake through asymmetric distributions with random effects applied to data set 10 vitamins obtained from a dietetic survey for 368 older people from Botucatu city, S?o Paulo, Brazil. In general, these asymmetric distributions include parameters related to mean, median, dispersion measures and such parameters provide good estimates for the intake distribution. In order to make some comparisons, a model fitted by National Cancer Institute (NCI) method with only for amount of nutrient intake was established using Akaike Information Criteria (AIC). NCI method is based on a Box-Cox transformation coupled with normal distribution but in case of asymmetric data, this transformation can be not useful. It was observed that, in the presence of outliers, the asymmetric models provided a better fit than the NCI method in the major of the cases. Then, these models can be an alternative method to estimate the distribution of nutrient intake mainly because a transformation for the data is no necessary and all the information can be obtained directly from the parameters.

One of the main interests of the researchers in the nutrition area is to estimate the distribution of usual nutrient intakes of a population group.

The statistical modelling to measure the distribution of usual nutrient intake of a population presents a challenge, since different individuals tend to have different dietary habits from each other (between-person variability), and the individual himself does not necessarily have a constant consumption (within-person variability) [

In the literature, it is common to use a Box & Cox transformation [

Normal distribution is one of the most used distributions in the analysis of continuous data due to its properties, especially in the context of linear models. However, the presence of outliers affects relevantly the inference based on the normal distribution, encouraging the development of robust procedures, which are defined as less sensitive to deviations from the assumptions which they are based on [

Thus, the aim of this paper is to obtain an estimate for the usual consumption of vitamins for older people through the application of asymmetric models, and some of them may contemplate a robust estimation procedure (in case of strong presence of aberrant points). Furthermore, a comparison with the NCI method was made considering only the amount consumed [

The analyzed data came from a representative sample of 368 individuals belonging to an epidemiological study that aimed to assess the adequacy of nutrient intake for older people from Botucatu city, São Paulo, Brazil.

The sample was collected in the year of 2011 through the application of the 24-hour recall (R24h). The study included elders who do not have cognitive deficits and agreed to participate into the research. In order to estimate the usual intake of the subject, more than one R24h is needed, due to the variability in consumption on different days of the week. Thus, up to three R24h were obtained from each subject on nonconsecutive days of the week, one of them being obtained necessarily on the weekend.

The data collected by the recalls were transformed into micronutrient consumption data using the NDSR program (Nutrition Data System for Research).

Nutrient intakes are different for men and women. Thus, the analyses were performed by gender.

The data were also collected considering age, marital status, education and morbidities as well as anthropometry measures and information about the Activities of Daily Living (ADL) and the Instrumental Activities of Daily Living (IADL).

A descriptive analysis of ten vitamin consumptions were presented as: mean, standard deviation (SD), median and coefficient of variation (CV*) based on the median of the data distribution [

The data modeling was performed by means of a random intercept model, which characterizes different measurements on the same subject. The idea of the used model is that the between-person variability is absorbed by a random effect, and the within-person variability is absorbed by the nature of the chosen distribution for the response variable that is similar to the NCI method [

Asymmetric distributions were proposed for the response variable and it was used a normal distribution with zero mean and variance κ2 for the random effect. In order to select such asymmetric distributions, the fitdist and histdist functions from Gamlss (Generalized Additive Models for Location, Scale and Shape) routine at R software, v.3.0.1, were used [

The NCI method for amount-only model presents in SAS version 9.3 software implemented by macro MIXTRAN was used for comparison with the proposed models, since it has a similar structure with the asymmetric models in this study. The average usual intake consumption estimated by the NCI method using the macro DISTRIB, is also shown for the comparison purpose with the parameters estimated by asymmetric models.

The sample of 368 older people presented mean age of 71.20 ± 7.11 years old for men and 71.79 ± 7.21 years old for women.

Gama distribution, generalized Gamma, Weibull, Lognormal and Box-Cox t were adjusted to the response variable. The adjusted distributions may have an asymmetric shape and leptokurtic, depending on the values assigned to their parameters. These distributions were selected through fitdist and histdist functions, which selected the best distribution from the raw data. On the features of these distributions, the generalized gamma distribution is a specific parameterization of the gamma distribution proposed by Lopatatzidis and Green, in which it has an additional parameter ν [

Variable | Category | Men (%) (n = 136) | Women (%) (n = 232) | p-value |
---|---|---|---|---|

Marital status | Not married | 18.1 | 54.0 | 0.0001 |

Married | 81.9 | 46.0 | ||

Education | Until primary school | 66.1 | 81.6 | 0.0003 |

Above primary school | 33.9 | 18.4 | ||

Hypertension | Yes | 51.7 | 58.9 | 0.2644 |

No | 48.3 | 41.1 | ||

Diabetes | Yes | 29.1 | 27.8 | 0.4447 |

No | 70.9 | 72.2 | ||

Cholesterol | Yes | 12.5 | 16.8 | 0.2665 |

No | 87.5 | 83.2 | ||

Cardiovascular disease | Yes | 6.9 | 8.1 | 0.6722 |

No | 91.9 | 93.1 | ||

BMI^{1} | Underweight | 20.6 | 17.7 | 0.4487 |

Normal | 32.3 | 28.4 | ||

Overweight | 47.1 | 53.9 | ||

ADL^{2} | Independent | 86.7 | 80.3 | 0.1194 |

Dependent | 6.8 | 10.3 | ||

IADL^{3} | Independent | 70.0 | 59.1 | 0.5285 |

Dependent | 23.5 | 31.5 |

^{1}Body mass index; ^{2}Activities of daily living; ^{3}Instrumental activities of daily living.

Vitamins | Men (n = 136) | Women (n = 232) | p-value | ||||||
---|---|---|---|---|---|---|---|---|---|

Mean | SD | Median | CV* | Mean | SD | Median | CV* | ||

A (mcg) | 1249.71 | 3163.41 | 713.22 | 0.91 | 1135.33 | 1712.59 | 756.86 | 0.97 | 0.0001 |

D (mcg) | 4.33 | 3.42 | 3.64 | 0.71 | 3.94 | 2.83 | 3.40 | 0.70 | 0.0001 |

E (mg) | 7.55 | 12.61 | 6.13 | 0.4 | 6.13 | 3.57 | 5.48 | 0.48 | 0.0001 |

K (mcg) | 241.11 | 1656.86 | 103.37 | 0.96 | 196.00 | 1145.12 | 101.77 | 0.85 | 0.0001 |

C (mg) | 209.41 | 856.62 | 54.72 | 1.53 | 104.98 | 269.25 | 54.08 | 1.19 | 0.0001 |

B1 (mg) | 1.78 | 1.23 | 1.53 | 0.40 | 1.48 | 0.74 | 1.34 | 0.44 | 0.0001 |

B2 (mg) | 1.69 | 0.91 | 1.55 | 0.48 | 1.52 | 0.72 | 1.41 | 0.41 | 0.0001 |

B3 (mg) | 24.23 | 18.22 | 20.60 | 0.53 | 19.83 | 11.37 | 17.50 | 0.55 | 0.0001 |

B6 (mg) | 2.08 | 2.09 | 1.77 | 0.49 | 1.67 | 0.82 | 1.52 | 0.52 | 0.0620 |

B12 (mcg) | 6.25 | 10.73 | 3.47 | 0.77 | 7.54 | 18.20 | 2.93 | 0.79 | 0.0001 |

^{*}p-value from mann-whitney test.

infinity, it results in a truncated normal distribution [

In

The Akaike criterion value was used to compare the NCI method for vitamin intakes and the asymmetric distributions. By this criterion, it was observed that there was no difference between the models, although most of the asymmetrical models had a lower value. It was not considered the adjustment of energy for the evaluated nutrients, since the Akaike values were not very different from those without adjustments. The results are shown in

It is important to notice that the NCI method presented limitations for the adjustment of some vitamins as it uses a Box-Cox transformation type. When this transformation is not found, the result in MIXTRAN macro uses a logarithmic transformation to solve the problem, but this does not guarantee that this assumption can lead data to normal distribution. Asymmetric models also showed problems in the estimation of some models by the gamlss routine. When this problem happened, alternative distributions were selected through histdist and fitdistfunctions.

Several methods to estimate the usual intake have been proposed in literature such as National Cancer Institute (NCI―considered as a standard method in this work), Multiple Source Method (MSM), Iowa State University (ISU) and Statistical Program for Age-adjusted Dietary Assessment (SPADE) [

The use of asymmetric distributions was already proposed but without taking in to account the between and

Gender | Vitamins | Fitted model | Parameter estimates |
---|---|---|---|

Male | A (mcg) | Box-Cox t | |

D (mcg) | Gama | ||

E (mg) | Box-Cox t | ||

K (mcg) | Box-Cox t | ||

C (mg) | Box-Cox t | ||

B1 (mg) | Gama | ||

B2 (mg) | Lognormal | ||

B3 (mg) | Box-Cox t | ||

B6 (mg) | Generalized Gama | ||

B12 (mcg) | Generalized Gama | ||

Female | A (mcg) | Box-Cox t | |

D (mcg) | Weibull | ||

E (mg) | Lognormal | ||

K (mcg) | Box-Cox t | ||

C (mg) | Box-Cox t | ||

B1 (mg) | Generalized Gama | ||

B2 (mg) | Lognormal | ||

B3 (mg) | Lognormal | ||

B6 (mg) | Gama | ||

B12 (mcg) | Gama |

Gender | Male | Female | ||
---|---|---|---|---|

Vitamins | NCI | Asymmetric models | NCI | Asymmetric models |

A (mcg) | 5641.90 | 5614.30 | 9403.40 | 9426.02 |

D (mcg) | 1637.30 | 1593.65 | 2630.90 | 2586.15 |

E (mg) | 1861.90 | 1812.65 | 2879.90 | 2821.25 |

K (mcg) | 4244.20 | 4167.70 | 6951.60 | 6943.42 |

C (mg) | 4011.20 | 3974.29 | 6535.30 | 6500.84 |

B1 (mg) | 783.70 | 743.53 | 1062.40 | 1022.61 |

B2 (mg) | 719.70 | 660.30 | 1042.20 | 952.31 |

B3 (mg) | 2747.50 | 2730.01 | 4330.40 | 4300.48 |

B6 (mg) | 967.00 | 913.07 | 1310.40 | 1272.12 |

B12 (mcg) | 1871.00 | 1823.47 | 3209.00 | 3229.78 |

within-person variability [

Another class of functions, called Box-Cox symmetric class [

In both methods (NCI and asymmetric models), it was observed that, due to the presence of high asymmetry and outliers, the variability of the random effect is high with or without energy adjustment. This means that the between-person variability exists and shows that there is not a nutrient pattern of consumption.

Therefore, this work shows that the adjustment of asymmetric models for nutritional intake data are effective and have, as an advantage, the direct calculation of the mean and median intake using fitted distribution without the need of a transformation, as made in the NCI method. Another advantage is the practicality of application, due to the tools presented in the gamlss routine. However, for future studies, it is intended to implement such asymmetric distributions to improve the issue of parameter estimation, and eliminate the problems related to the lack of convergence found in the used routine. Moreover, with such models implemented, it is possible to estimate the prevalence of inadequacy of nutrient intakes based on a cutoff point fixed a priori.

In this work, the use of asymmetric distribution to fit the nutrient intake distribution was proposed based on a random effect model in case of outliers and models with robust estimation procedure. An advantage of this new approach is that no data transformation is needed and the results can be interpreted directly from the estimated parameters. In addition, the inclusion of outliers is possible by means of robust procedures providing more plausible estimates.

The authors would like to thank the São Paulo Research Foundation (FAPESP-Process no. 2008/10261-8) and the National Council for Scientific and Technological Development (CNPq-Process no. 301197/2011-3) for the financial support for this research.

José Eduardo Corrente,Giovana Fumes, (2016) Use of Asymmetric Models to Adjust the Vitamin Intake Distribution Data for Older People. Health,08,887-893. doi: 10.4236/health.2016.89092