Step 0: Initial data adjustment |
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Subject the R24h data to Power or
log transformation until the data approach
the normal distribution. |
Adjust the observed R24h to no individual bias such
as seasons of the year, days of the week, and effect of
sampling. Build a two-stage transformation so that the modified
R24h data approach the normal distribution. |
Adjust the observed R24h to no individual bias such
as seasons of the year, days of the week, and effect of
sampling. Subject the R24h data to Power or
log transformation until the data approach
the normal distribution. |
Estimate the distribution of the probability of
intake for a given day on the basis of the relative frequency of
R24h values that are different from zero. Place the R24h zero
values aside and adjust the observed R24h to no individual bias
such as seasons of the year, days of the week, and effect of
sampling. Build a two-stage transformation so that the modified
R24h data approach the normal distribution. |
Apply Box-Cox transformation so that data approach
the normal distribution. |
Apply Box-Cox transformation so that data approach
the normal distribution. |
Step 1: Description of the relationship between individual
R24h data and usual food intake |
There is no bias in the estimation of transformed
usual intake on the basis of R24h data (assumption A). |
There is no bias in the estimation of usual intake
in the no transformed scale on the basis of R24h data
(assumption B). |
There is no bias in the estimation of usual intake
in the no transformed scale on the basis of R24h data
(assumption B). |
Usual intake corresponds to the probability of
consumption in a given day multiplied by the total usual intake
for a given day. One R24h measures the intake exactly equal to
zero. There is no bias in the estimation of usual intake in the
no transformed scale on the basis of R24h data (assumption
B). |
Estimate the probability of intake using logistic
regression and the total daily intake using linear
regression. |
Assemble a fractional polynomial model for no
transformed data. |
Step 2: Separation of the total variation of the R24h data
into intra- and inter-individual variations |
The intra-individual variation is the same for all
individuals. |
The intra-individual variation may vary among
individuals. |
The intra-individual variation is the same for all
individuals. |
The intra-individual variation may vary among
individuals. |
Transformed remains are used to estimate the inter-
and intra-individual variations, which are then used to convert
the mean intake of an individual to an overall mean. |
Obtain a mixed-effects fractional polynomial model
to separate the inter- and intra-individual variability on the
basis of age. |
Step 3: Estimation of the distribution of usual intake
taking intra-individual variation into account |
Assemble a group of intermediate values, which
retain the variability of transformed R24h data among
individuals. Inverse transformation: apply the inverse function
of the initial value to each intermediate value. The inverse of
the empirical distribution corresponds to the distribution of
usual intake. |
Assemble a group of intermediate values, which
retain the variability of the transformed R24h data among
individuals. Inverse transformation: apply the inverse function
of the two-stage transformation, in parallel to adjusting
biases, and correct each intermediate value in a normal scale to
obtain the original scale. The inverse of the empirical
distribution corresponds to the distribution of usual
intake. |
Assemble a group of intermediate values, which
retain the variability of the transformed R24h data among
individuals. Inverse transformation: use the inverse function of
the initial Power or log
transformation in parallel to adjusting for bias, and correct
each intermediate value in a normal scale to obtain the original
scale. The inverse of the empirical distribution corresponds to
the distribution of usual intake. |
Inverse transformation: apply the inverse function
of the two-stage transformation, in parallel to adjusting
biases; concomitant to bias adjustment, mathematically describe
the original distribution of the usual daily intake.
Mathematically combine the distribution of the daily intake with
the estimated distribution of the probability of intake to
obtain the group of intermediate values that represent usual
intake, while assuming that usual intake and daily intake are
statistically independent variables. The inverse of the
empirical distribution corresponds to the distribution of usual
intake. |
Inverse transformation: integrate nonnegative whole
values of the Box-Cox parameters. The estimation of usual intake
is obtained by multiplying the probability of intake and the
total daily intake estimated by regression models. |
Identify discrepant values using the Grubbs method.
Test residual normality and data distribution by the
Kolmogorov-Smirnov test using the statistical model S-plus.
Check λ distribution. Identified discrepant values are
eliminated, and previous steps are repeated. Inverse
transformation: apply inverse transformation with a quadratic
Gaussian function (Monte Carlo Simulations). |