The timing of carbohydrates intake

# The timing of carbohydrates intake
## the National Diet and Nutrition Survey Rolling Programme (2008-<del>2014</del>2016)
### Chaochen Wang
### <del>2018/4/23-Project Talk (LG6)</del> 2019/03/12 Seminar in the Department of Public Health, Nagoya City University

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# Background

.medium["Temporal eating patterns"--the **timing**, **frequency**, and **regularity** of food intake or eating occasions across the day may play a role in health outcomes:]

- Interplay between timing of food intake and circadian rhythms, physiology, and metabolism. (Asher *et al* 2015, Cell)

- Skipping breakfast is associated with higher risk of type 2 diabetes. (Uemura *et al* 2015, J Epidemiol)

- Shift workers have a higher risk of metabolic syndrome (De Bacquer *et al*, 2009 Int J Epidemiol) and type 2 diabetes (Pan *et al* 2011, PLoS Med).

- Evening energy intake is positively associated with overweight/obesity. (Almoosawi *et al* 2016, Proc Nutr Soc)

- Three distinct temporal eating patterns were identified (next 2 slides) in both Australian poulation (Leech *et al* 2017, Int J Behav Nutr Phys Act) and general population in the UK (Mansukhani, R. & Palla, L. 2018 Proc Nutr Soc).

???

- There is evidence indicating that "temporal eating patterns" is potentially associated with health outcomes.

- Here are some examples in the literature.

- However, currently very few studies have investigated when/the timing people consume food throughout the day.

- Some initial work based on eating occasions at hourly time intervals throughout the day from survey data, revealed the presence of 3 groups of eaters. These analyses were based on total energy consumption.

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# Australian (NNPAS)
.footnote[Leech *et al* 2017, Int J Behav Nutr Phys Act]

???

- Australian National Nutrition and Physical Activity Survey found that in both men and women, Australian adults have three distinct eating patterns:

- "Conventiional": about 40% in both men and women, had a high conditional probability (> 0.7) for having meals at 12:00 and 18:00.

- "Later lunch": about 30% in both men and women, had a more than 0.9 of probability of having lunch at 13:00.

- "Grazing": about 20%-30% in both men and women, had frequent but no obvious peak in probability of eating, and had higher probability of eating after 20:00 compared with the other two patterns.

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???

Similarly, three types of meal time classes were identified in the UK National Nutrion survey:

- a standard meal class (the red line)

- a later meal class (the green line)

- an irregular meal time class (the blue line).

28% of Men and 31% of women fell into the standard class 
35% of Men and 27% of women fell into the later class 
37% of Men and 42% of women fell into the irregular meal time class.

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# Objectives

- .medium[Investigate the timing of eating within the day and specific nutrients -- carbohydrates.]

- .medium[~~Potentially we will also look at the temporal patterns of carbohydrates quality, more specifically intrinsic milk sugar, extrinsic milk sugar, starch and non-starch polysaccharide.~~]
 
- .medium[Additionally, depending on the findings of preceding analysis, the association between carbohydrates eating patterns and diabetes and/or obesity will be explored.]

???

In this project, we aimed to

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# Chrononutrition and NDNS data

- First hurdle is represented by the need (for collection) of **suitable** data that record the timing of food consumption.

- National Diet and Nutrition Survey 2008-2016 presents an opportunity: 
    - Collects 3 or 4 consecutive days' diet diaries from about 1000 people yearly; 
    - Reprensentative sample of the British population;
    - Records information on the time of eating for each eating occasion.

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# NDNS RP data

- .medium[[The NDNS RP](https://www.gov.uk/government/collections/national-diet-and-nutrition-survey) is an ongoing programme funded by the UK government on the purpose of surveillance of the food consumption, nutrient intake, and nutritional status of the general UK population.]

- .medium[Data can be downloaded from [the UK data service](https://www.ukdataservice.ac.uk/)] after application (within 30 min).

- .medium[Collection of dietary data: the four-day food diary.]

???
Let's briefly explain the data source,

(on the slides)

The food diary contains 4 consecutive days of dietary records. Participants were provided with a diary and asked to keep a record of everything they ate and drank over these four days, both in and outside the home.

The example of the food diary is shown in the next few slides.

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# Challenges

- Timing of food intake may vary depending on 
  - different classification of time (temporal intervals); 
  - Use of nutrients or foods or perhaps energy intake.

- Which kind of statistical methods are suitable for conducting **unsupervised learning** about temporal eating patterns in a more synthetic and interpretable way?

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### How can we account for the data collected **over the 4 days and nested** within the same person ?

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# Latent class analysis (1)

- Latent Class Analysis (LCA): to separate people into several eating pattern groups and also to calculate the probability of an Eating Occasion (EO) occurring for each class for every hour of the day.

- Let `$L$` be the categorical latent variable with `$c = 1,\cdots, C$` latent classes. `$r_c$` represents the **prevalence/the probability** of latent variable.

- The latent classes are defined to be **mutually exclusive and exhaustive**. Therefore, `$$\sum_{c=1}^Cr_c = 1$$`

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# Latent class analysis (2)

- The item response probability `$\rho_{j, r_j | c}$` represents the probability of the response `$r_j$` to observed variable `$j$`, given (conditional on) membership in latent class `$c$`.

`$$\sum_{r_j = 1}^{R_j}\rho_{j,r_j|c} = 1$$`

- Because `$$P(\overrightarrow{Y} = \overrightarrow{y} | L = c) = \prod_{j = 1}^J\prod_{r_j = 1}^{R_j}\rho_{j,r_j|c}$$`

- Also because the [definition of conditional probability](https://wangcc.me/seminar_2019/#8): `$P(A \cap B) = P(A)P(A|B)$`:

`$$P(\overrightarrow{Y} = \overrightarrow{y}  \cap L = c) = P(L = c)P(\overrightarrow{Y} = \overrightarrow{y} | L = c)$$`

???
because each individual provides one response to variable `$j$`, the vector of item-response probabilities for a pariticular variable conditional on a particular latent class sums to 1.

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# Latent class analysis (3)

$$
`\begin{aligned}
P(\overrightarrow{Y} = \overrightarrow{y}  \cap L = c) &= P(L = c)P(\overrightarrow{Y} = \overrightarrow{y} | L = c) \\
                                 &= r_c \prod_{j = 1}^J\prod_{r_j = 1}^{R_j}\rho_{j,r_j|c}
\end{aligned}`
$$

- Also because

`$$P(\overrightarrow{Y} = \overrightarrow{y} ) = \sum_{c = 1}^CP(\overrightarrow{Y} = \overrightarrow{y}  \cap L = c)$$`

- Therefore,

`$$P(\overrightarrow{Y} = \overrightarrow{y} ) = \sum_{c = 1}^Cr_c \prod_{j = 1}^J\prod_{r_j = 1}^{R_j}\rho_{j,r_j|c}$$`

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# Multilevel LCA (1)

We already know that (if we know the distribution of `$r_{ck}$`) multilevel logistic regression can be defined as:
$$
`\begin{aligned}
\text{logit}[P(C_{ik}) = r_{ck}] & = \beta_{0k} + \beta_{1}x_{ik} \;\;\;\;\;\;\;\;\; \textbf{(day-level)}  \\
\beta_{0k} & = \gamma_0 + \gamma_1 w_k + u_{0k} \; \textbf{(individual-level)} \\ 
\Rightarrow P(C_{ik}) & = \frac{\exp{(\gamma_0 + \beta_{1}x_{ik} + \gamma_1 w_k + u_{0k})}}{1 + \exp{(\gamma_0 + \beta_{1}x_{ik} + \gamma_1 w_k + u_{0k})}} \\
\end{aligned}`
$$

- `$P(C_{ik}) = r_{ck}$` Represents the randomly selected `$i$`th observation **day** of the `$k$`th individual is **a particular carbohydrate eating day `$c$`**.

- `$\beta_{0k}$` is the random intercept;

- `$u_{0k} \sim N(0, \sigma^2_{u_0})$` where `$\sigma^2_{u_0}$` indicates the influence of the **individuals**.

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# Multilevel LCA (2)

So, we can extend the LCA model with random intercepts that allows the same person to have different probabilities across several days of data:

`$$P(\overrightarrow{Y_k} = \overrightarrow{y_k}) = \sum_{c = 1}^Cr_{ck} \prod_{j = 1}^J\prod_{r_j = 1}^{R_j}\rho_{j,r_j|c,k}$$`

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## Data description and choices made for modelling:

- 24483 days observed on 6155 adults (2537 men and 3618 women);

- Seven time slots as in NDNS classification;

- Categorization of caborhydrate (CH) consumption:

- no intake;
 - CH contributed >= 50% of total energy intake; 
 - CH contributed < 50% of total energy intake.

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# Discussion

- Low-CH eaters cunsumed the highest amount of total energy intake (7985.5 kJ), and had higher percentages of energy contributed by fat and alcohol, especially after 8 pm.

- Moderate-CH eaters consumed the lowest amount of total energy (7341.8 kJ) while they had the tendency of eating later in the day.

- Hig-CH eaters consumed most of their CH and energy within time slots of 6-9 am, 12-2 pm, and 5-8 pm.

- The high-CH eaters' profile seemed to be the healthiest.

- Low-CH eaters may have resulted from health/weight concerns, leading to fat or alcohol as replacements for CH.

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# Thanks!

Slides address: [wangcc.me/NDNS5slides](http://wangcc.me/NDNSslides5/)