Add time trend in risk factors

[jzhu20]

We are adding an underlying time trend in risk factors from consuming UPF (ultra-processed food). The plan is to add time (or year) as an additional variable into risk factor equations.

• [x] The parameters need to be estimated.
• [x] It needs to be confirmed how this time trend will affect other equations in Health-GPS.
• [x] #492
• [x] #493

[jzhu20]

Details on estimating time trend parameters from Jingmin:

• With time trend parameters provided for each individual in Maxime's data, time trend parameters will be estimated on gender, age, sector, income, baseline nutrients before time trend (carbohydrate, fat, protein, sodium) to add to HealthGPS.

Steps from James:

1. update base nutrients as before
2. compute and add a delta for the time trend, based on base nutrients and income, sector, etcetera
3. do clipped expected value adjustment as before
4. do clipped policy update as before

Jingmin needs to confirm:

• [x] Whether factors mean of nutrients needs to be updated or not
• [x] Whether policy parameters need to be updated or not, since baseline nutrients are adjusted with time trend now

[jzhu20]

Update on applying time factor:

Everyone in the virtual population is assigned a time factor for each nutrient based on age, gender, income, sector and nutrient levels. This individual-specific time factor remains constant over life course. At each year step, nutrient intake needs to multiply the individual-specific time factor.

Time trend also needs to be added to factors mean of nutrients. Mean weight needs to be adjusted based on steady state equations, and nutrients with time trend.

[jzhu20]

Estimating time factor as a function of age, sex, income, sector, and baseline nutrient intake.

• 0.01 filter
• No smoothing on time factors
• X: sex, age1, age2, age3, sector, income tertile, log_carb, log_fat, log_protein, log_sodium

In Health-GPS, individual time factor is calculated at initialisation or at birth. It remains fixed over life course until death.

Time coefficient f is a function of time factor r and years since initialisation T, i.e., f = r^T.

Time-trend-adjusted nutrient intake = nutrient intake f = nutrient intake r^T

[jzhu20]

Factors mean is adjusted with a fixed time factor r, i.e., Adjusted mean = mean * r^T.

Time factor is

• 1.00425 for Carbohydrate;
• 1.0122 for Fat;
• 1.00452 for Protein;
• 1.00392 for Sodium.

Mean weight adjustment happens after nutrients intake is adjusted with time trend.

For a certain age, gender group, mean weight = 0.06256 mean time-trend-adjusted-Energy Intake - 0.6256 mean height + 0.4925 age - 16.6166 gender + 16.1161

where mean time-trend-adjusted-Energy Intake = 4 mean time-trend-adjusted-carb + 9 mean time-trend-adjusted-fat + 4 mean time-trend-adjusted-protein + 0 mean time-trend-adjusted-sodium