The Economic Impact of Lower Protein Infant Formula for the Children of Overweight and Obese Mothers

The global prevalence of obesity is rising rapidly, highlighting the importance of understanding risk factors related to the condition. Childhood obesity, which has itself become increasingly prevalent, is an important predictor of adulthood obesity. Studies suggest that the protein content consumed in infanthood is an important predictor of weight gain in childhood, which may contribute to higher body mass index (BMI). For instance, there is evidence that a lower protein infant formula (lpIF) for infants of overweight or obese mothers can offer advantages over currently-used infant formulas with regard to preventing excessive weight gain. The current study used health economic modelling to predict the long-term clinical and economic outcomes in Mexico associated with lpIF compared to a currently-used formula. A discrete event simulation was constructed to extrapolate the outcomes of trials on the use of formula in infanthood to changes in lifetime BMI, the health outcomes due to the changes in BMI and the healthcare system costs, productivity and quality of life impact associated with these outcomes. The model predicts that individuals who receive lpIF in infancy go on to have lower BMI levels throughout their lives, are less likely to be obese or develop obesity-related disease, live longer, incur fewer health system costs and have improved productivity. Simulation-based economic modelling suggests that the benefits seen in the short term, with the use of lpIF over a currently-used formula, could translate into considerable health and economic benefits in the long term. Modelling over such long timeframes is inevitably subject to uncertainty. Further research should be undertaken to improve the certainty of the model.

BMI (17 years) = α + b1 × weight gain in infancy + b2 × birth weight + b3 × gender (female) + b4 × gestational age + b5 × maternal socioeconomic status + b6 × maternal BMI The Stockholm Weight Development Study (SWEDES) study is based on a sample of 2342 mothers invited to participate between 1984 and 1985 and who were followed during and after their pregnancies. A total of 1423 of these mothers completed the study at the one-year follow-up, and 481 mothers and their children participated in the follow-up study (SWEDES) after 17 years.
A meta-analysis of 10 studies suggested that the analysis of SWEDES may underestimate the impact of weight gain in infancy on BMI at age 17 years [1]. To account for this underestimate, the coefficient on the weight gain variable in the original model was inflated by the difference between the odds ratio from the SWEDES cohort and that from the Philadelphia Blood Pressure Project (PBPP) cohort. The PBPP study was selected as it estimated the relationship between infant weight gain and BMI at 20 years old, the closest age of the studies included in the meta-analysis to that in the model. PBPP is a cohort of 300 African Americans born between 1962 and 1966 in the United States (U.S.) and followed up to 20 years of age.  Table S4. In the discrete event simulation (DES), individuals are categorised into one of these subgroups based on their BMI at 17 years old, and the relevant function is selected to estimate the change in their BMI over time until the age of 48 years old. Individuals' BMI from age 49 years onwards is predicted based on a function derived from fitting a polynomial equation (Equation (S-E6)) to WHO data on the cross-sectional average BMI, by gender, for 10-year age groups between 49 and 79 years and the average BMI between 80 and 100 years [3]. BMI = (BMI at age 49) + linear term × age + quadratic term × (age^2) (S-E6) An individual's BMI at age 49 years is predicted by the model (see section BMI between the ages of 18 and 48 years above). The estimates of the linear and quadratic terms for the equation above are provided in Table S5. Table S5. Linear and quadratic terms used in the projection of BMI for ages 49 years and above [4].

Primary Events
Equation (S-E7) and Table S6 report the function used to determine the probability that an individual would experience diabetes over a period of 7. If the individual is not expected to experience a disease-related event in the next 7.5 years, their risk would be re-assessed after this period for the following 7.5 years, and so on, until their death. S4 of S13 CHD Risk Table S7 describes the function (Equation (S-E8)) used to estimate the probability of an initial CHD event.  Table S8 shows the probability that an initial CHD is either an MI, an angina or a cardiac death. * These do not add up to 100% since the remaining probability is associated with the initial CHD event being cardiac death.

Stroke Risk
Equation (S-E9) provides the function used to estimate the probability that an individual experiences a stroke. S5 of S13 The estimates of the coefficients for the equation above are provided in Table S9.

Secondary Events
The sources used to estimate the risk of secondary events, contingent upon the nature of the primary event and the time since the primary event, are described in Table S10.

Mortality
There are two sources of mortality in the model. First, background mortality, which is assigned to each individual at birth, is the time of death provided the person does not die from any of the modelled disease events. Table S11 shows the functions used to estimate background mortality. These are generated by fitting a Gompertz function (parameters λ and γ) piece-wise to the different age brackets in the all-cause mortality life tables for Mexico [4]. S6 of S13 Second, experiencing disease events is associated with a mortality risk. The background mortality is adjusted for death associated with the cardiovascular events predicted separately in the model in order to avoid double counting. The data used to do this are reported in Table S12. Since diseases occur in the model only after the age of 18 years, background mortality was not adjusted prior to that age. 25.9% These disease-specific mortality risks comprises two elements. First, the probability that an initial CHD event is fatal is reported in Table S13. Table S13. Proportion of initial CHD events that are cardiac death [7].

Healthcare Costs
Table S15 reports the data used to calculate the costs of diseases. Costs are inflated to 2014 values using the national Mexican price index [15]. S7 of S13  [18] * The standard error is calculated based on the assumption that this variable is normally distributed with 95% of the area within 1.96 standard deviations of the mean. Table S16 reports the parameter values, dispersion parameters, descriptions and sources for the utility decrements.

Productivity Impacts
Productivity impacts are incorporated into the model in two ways. First, before the age of 13 years, an individuals' BMI will impact their probability of missing school, with a knock-on impact on their parents' ability to attend work. Second, after the age of 18 years, employment status and productivity are impacted by the experience of health events.

School Absenteeism
Table S17 describes the function used to estimate the number of days individuals miss from school between the ages of 4 years and 12 years. Geier et al. (2007) [21] estimated the function from data collected from a cohort of 1069 fourth to sixth graders in the U.S. BMI was estimated by assuming a linear relationship between BMI at 2 years old and 17 years old.
The impact of school absence on productivity is estimated by assuming that a day off school would cause one parent to miss work for the 20.7% of children in Mexico for whom both parents work [22]. S8 of S13

Disease-Related Productivity Impacts
After the age of 18 years, for those individuals who are employed (Table S18), productivity loss is estimated based on days missed from work due to disease events. In a small proportion of instances, disease events will lead to individuals being permanently out of employment. In most instances, disease events are associated with a period off work. Table S19 summarises the data used to estimate these productivity impacts. Productivity losses are accrued until the individual retires at 65 years old [21] and assuming 257 working days per year.
For chronic conditions, such as diabetes and angina, a certain number of days is expected to be missed from work every year [23,24]. If, for example, diabetes causes 40 days off work per year, the patient is assumed to be off work 10 days at each quarter of the year.
If two disease events are experienced simultaneously, the highest number of days off work associated with these events is applied. The value of the productivity impact is estimated using the capital approach in the base case and with the friction approach in a scenario analysis. The capital approach assumes that an absent employee will never be replaced at work by another individual and is estimated using Equation (S-E10): Productivity cost loss = total days of work loss × (elasticity of productivity × mean daily salary) (S-E10) where the elasticity of productivity is 0.8, the proportion of the day during which the individual is actually productive [30] and the average daily salary is MXN 268.10 [31].
The friction approach assumes that absent employees will be replaced after a "friction" period, the time required to replace a person at work. If an individual is absent from work for a period less than the friction period, the friction method reduces to the capital method. If, however, the period of absence is greater than the friction period, the friction method estimates productivity costs using Equation (S-E11).
Productivity cost loss = (friction days × (elasticity of productivity × mean daily salary) + friction costs (S-E11) where the friction period is 68.32 days (assumed to be the same in Mexico as in the U.K. [31]), and the friction cost (one-off cost of replacing an employee: vacancy cover, redundancy cost, recruitment and selection, training and induction cost) is MXN 26,266 [30]. Figure S1 shows the outcome of the PSA. Each blue diamond point on the figure is the outcome of a model run, undertaken to capture the parameter uncertainty in the model by randomly sampling from parameter distributions of the input parameters. The red square indicates the point at which the mean cost and mean QALY values intersect. Figure S1. Cost-effectiveness plane for the outcome of the probabilistic sensitivity analysis (discounted). Table S20 shows the PSA outcomes by quadrant. Southeast is the quadrant with the most model runs, where lpIF is less expensive and more effective. S10 of S13 Table S20. Allocation of PSA outcomes by quadrants of the cost-effectiveness plane.

Quadrant
Allocation Northeast quadrant: lpIF is more expensive and more effective 20.1% Northwest quadrant: lpIF is more expensive and less effective 16.0% Southeast quadrant: lpIF is less expensive and more effective 32.7% Southwest quadrant: lpIF is less expensive and less effective 31.2%

Validation
In order to assess the validity of the predictions of the model, Table S21 compares the result of the model specified for the current situation in Mexico (individual characteristics based on descriptive statistics for the Mexican population and using standard high-protein formula) with the observed outcomes for the Mexican population. It demonstrates that the model fairly accurately predicts the current life expectancy in Mexico and is the same ballpark for the other BMI and disease risk outcomes.  Table S22 provides the individual characteristics considered in the model, broken down by age groups. Values for ages 18 to 20 were unavailable and, thus, assumed to be the same as those for the age range of 20 to 29. The standard error is calculated based on the assumption that this variable is normally distributed with 95% of the area within 1.96 standard deviations of the mean.