The reporting of this study followed the 2013 Consolidated Health Economic Evaluation Reporting Standards guidelines .
SPHR diabetes prevention model
The School for Public Health Research (SPHR) Diabetes prevention model has been used to assess the cost-effectiveness of diabetes prevention interventions [14,15,16]. For this study we use version 3.3 of the model and full detail of the model background, methods, assumptions and parameters is in the Additional files 2 and 3.
The SPHR models is an individual patient level model in which the baseline characteristics of an individual are used to estimate annual changes in metabolic risk factors and the risk of related diseases. This model was used because it enables change in BMI to be modelled, trajectories of BMI and other metabolic factors to vary among individuals and estimates of the impact of weight loss and weight loss maintenance on a range of health conditions including CVD, type 2 diabetes, osteoarthritis, and depression. The model structure is shown in Additional file 2, Fig. 1. Each year changes in metabolic factors, namely BMI, HbA1c, SBP and total cholesterol, occur depending on the individual baseline characteristics including age, sex, ethnicity, smoking, family history of CVD, and family history of type 2 diabetes. Associations between the trajectories of the metabolic risk factors were based on latent growth curve modelling analysis conducted on the Whitehall II prospective cohort study . Change in glycaemia, SBP and total cholesterol are all conditional on change in BMI.
These metabolic factors then contribute to the risk of an individual patient experiencing a disease or related complications. At GP visits, an individual in the model may be diagnosed with diabetes, hypertension, and dyslipidaemia. GP attendance is conditional on age, sex, BMI, ethnicity and health outcomes (heart disease, depression, osteoarthritis, diabetes, stroke, cancer) based on the South Yorkshire Cohort study . Individuals can also experience cancer (breast or colon), osteoarthritis and depression, CVD events (angina, myocardial infarction (MI), stroke, or transient ischemic attack (TIA) and diabetes related complications (renal failure, amputation, foot ulcer, and blindness) based on risk equations described in section 7 of Additional file 2. Many of the diagnoses and events in the model are conditional on BMI. It contributes to the risk of the first cardiovascular events as part of the QRISK2 prediction model . This is a validated algorithm to identify individuals at high risk of cardiovascular disease. Subsequent cardiovascular events are conditional on the nature of the first event. Incidence of breast and colorectal cancer were estimated from the European prospective investigation of cancer (EPIC) cohort  and based on a large meta-analysis including 221 prospective observational studies , a risk adjustment was included such that individuals with a high BMI have a higher probability of the cancer diagnosis. Osteoarthritis was also conditional on BMI; this was based on a stakeholder discussion and a longitudinal analysis based in Italy as there were no appropriate UK studies available . A diagnosis of diabetes was dependent on blood glucose (HbA1c), the trajectory of which is associated with BMI and, of the diabetes-related complications, neuropathy (ulcer and amputation) was conditional on BMI based on the UKPDS outcomes model v2 . Depression was not conditional on BMI however it was assumed that a diagnosis of diabetes and/or cardiovascular disease increased the incidence of depression for individuals who did not have depression at baseline based on two US cohort studies [24, 25]. Depression was not a causal factor for any health outcomes in the model.
The consequences of interventions are measured in Quality Adjusted Life Years (QALYs), as recommend by the National Institute for Health and Care Excellence (NICE) , based on the EQ-5D-3L, and costs/savings in pounds sterling. The model has an annual cycle length and a lifetime horizon as weight loss and maintenance have the potential to impact long-term health outcomes. The setting is primary care in England, UK and a healthcare perspective (National Health Service (NHS) in England) was used. This includes cost healthcare costs incurred by the NHS and excludes any costs incurred by the patient such as travel and time costs associated with the intervention. Both costs and QALYs were discounted at an annual rate of 3.5% as recommended by NICE .
The analyses were conducted for two separate populations; i) individuals with a BMI of 28 kg/m2 or above without diabetes and ii) individuals with a diagnosis of type 2 diabetes prescribed one non-insulin diabetes medication. These populations were chosen as they are at high risk of negative health impacts, have the potential to respond to early intervention (i.e. before developing diabetes, or diabetes dependent on insulin or several medications) and were likely target populations for this type of intervention . The baseline characteristics of both populations can be found in Supplementary Table 1.
For population (i), the baseline data on individuals was obtained from Health survey for England (HSE) 2014 , which is representative of the population of England and includes clinical risk factors including HbA1c, SBP, BMI and cholesterol and health outcomes. The population of interest was defined as adults with a BMI of 28 kg/m2 and over (prior to initial weight-loss), based on previous studies in which this was a criteria for referral to a weight management programme by a GP , and with a HbA1c below 6.5% (the criteria used for a diabetes diagnosis). Children aged under 18 and adults with a diagnosis of diabetes were excluded. Within the final sample (n = 2738), a subgroup of individuals with an HbA1c of 6–6.49% were examined separately (n = 322) as this criteria is used to identify individuals at higher risk of diabetes .
For population (ii), HSE only included a small number (approximately 400) of individuals with diabetes and thus would be unlikely to represent the diabetic population well and has little information about the diabetes diagnosis such as time of diagnosis and treatment. For this population, the THIN (The Health Improvement Network) 2014 dataset  was used which has a large number of individuals with diabetes. Of the 3.7 million individuals from 427 GP practices, 131,000 had type 2 diabetes. The time since diagnosis and treatment prescribed was also available for this dataset alongside BMI, HbA1c, cholesterol, and SBP and demographic factors such as age, gender, and ethnicity. A baseline population was created by sampling from the summary statistics of this data by using a multivariate distribution using the mean estimates and covariances between these variables. Individual patient level data was not available due to restrictions on the use of this at the time of analysis. Although individual data is preferable, this method enabled the use of a baseline population that was representative of individuals with diabetes. The sample was not restricted by time spent on this medication but those on more than one anti-diabetic mediation or on insulin were excluded. A subgroup analysis for those with a BMI of 28 or above was also included based on previous studies in which this was a criteria for GP referral to a weight management programme .
The structure and assumptions in the model remained the same for both baseline populations. The model enabled different health trajectories for those with and without diabetes which enables the model to be flexible to both populations. For example, for individuals without diabetes, the trajectory of HbA1c was estimated based on an analysis of the Whitehall II dataset  however for those with diabetes, the trajectory is estimated using the UKPDS outcomes model , a population of individuals newly diagnosed with diabetes. Similarly, individuals with a diagnoses of diabetes are eligible for antihypertensive treatment at the threshold of a SBP of 140 mmHg compared to a threshold of 160 mmHg for participants without diabetes based on National Institute for Health and Care Excellence (NICE) guidelines (11).
The estimated effect of the intervention on weight has been obtained by examination of the literature. We conducted a random-effects meta-analysis of behavioural weight loss maintenance studies to estimate the expected effect of a weight loss maintenance intervention compared to no intervention (current standard care in the UK) after weight loss resulting from a behavioural intervention. Following the PRISMA process, relevant studies were screened from two previous systematic review and meta-analysis studies of weight loss maintenance interventions [4, 33] to identify those studies that met our pre-specified inclusion criteria. The inclusion criteria were chosen to reflect likely commissioning of services in the UK NHS and were informed by current practice and discussions with our stakeholder group comprising health economists, clinicians and researchers and lay members. Studies had to include adult participants with a BMI ≥ 25 kg/m2, who had lost ≥5% of their weight before starting the weight loss maintenance programme. Studies that required ≥10% initial weight loss to join the study or which solely recruited participants with a specific health condition were excluded as this population was deemed highly selective and not representative of the intended population. The intervention had to be a behavioural intervention including advice on diet and physical activity for the primary purpose of weight management. Interventions that used meal replacements and financial incentives were excluded as these interventions are unlikely to be widely commissioned in the UK NHS. Studies had to report weight outcomes ≥12 months from the start of the weight maintenance intervention. Only randomised controlled trials were included. We applied these inclusion and exclusion criteria to the two systematic reviews, which reported data from a total of 32 behavioural intervention arms from 20 studies [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. Nine studies were excluded from our analyses for the following reasons: (a) inclusion criteria did not reflect the target population, [35, 42, 49, 53] (b) intervention included meal replacement or financial incentives [38, 46, 52] (c) primary purpose of the intervention was not weight management  or (d) did not report weight outcomes ≥12 months from the start of the weight maintenance intervention [37, 41].
Three analyses of the studies were undertaken. Firstly, fourteen intervention arms from nine studies [34, 39, 40, 43,44,45, 47, 48, 50] were included in a meta-analysis to estimate initial weight loss of participants that were eligible for a weight loss maintenance intervention. Second, fifteen intervention arms from ten studies [34, 36, 39, 40, 43,44,45, 47, 48, 50] contributed to the meta-analysis to estimate weight loss maintenance intervention effects at 12-month post-weight loss. Supplementary Fig. 1 in shows the nature of the control arm, and type of weight loss maintenance intervention for the studies included in this meta-analysis. All interventions targeted weight management through dietary and exercise advice but were varied in the method and duration of delivery, and control groups varied from no contact to in-person support. Third, two intervention arms from one study contributed to the estimates at 2-year post-weight loss  as this was the only eligible study that included a 2 year follow-up. The two interventions were unlimited access to an interactive technology–based intervention, and an intervention in which participants had monthly individual contact with an interventionist. Participants in the control group received printed diet and physical activity recommendations.
Table 1 shows the results of the random-effects meta-analysis; the initial weight loss before the weight maintenance intervention is estimated at 8.93 kg from an average initial weight of 89.76 kg, and individuals partaking in a weight loss maintenance intervention had an average regain of 1.33 kg by year 1 and 4.38 kg by year 2 compared to a regain of 2.84 kg by year 1 and 5.6 kg by year 2 in a control group. Forest plots comparing the active intervention with control group at 12- and 24-month follow-up are shown Supplementary Figs. 2 and 3. There was no evidence of an influence of individual studies on the overall estimates at 12 months (Supplementary Fig. 4). Influence plots were not generated for 24 months follow-up as only one study provided data at this time point. The revised Cochrane risk of bias tool for randomised trials  was used to assess the studies; four were low risk of bias [39, 40, 47, 50], 3 were high risk [34, 45, 48] and there were some concerns regarding the remaining three studies [36, 43, 44]. A sensitivity analysis in which the meta-analysis excluded the studies with a high risk of bias did not significantly impact the outcomes (Supplementary Table 2) There was moderate heterogeneity across studies in weight maintenance at 12 months (I2 = 59%, P = 0.002).
Effect on weight trajectory beyond follow-up
In the absence of data on the longer-term weight trajectories, we made the conservative assumption that participants would return to baseline weight trajectory at some point. To determine when this point would be, the regain between years 1 and 2 was extrapolated linearly (assuming the same regain as between years 1 and 2 for each subsequent year), until the trajectory reached that of the simulated individual’s weight if they had never had the initial weight-loss intervention.). Both the control and treatment group returned to this original trajectory by 5 years (to the nearest full year) after the initial weight loss (Fig. 1). This aligns with research that indicates that on average participants regain weight loss after approximately 5 years . Simulated individuals do not return to their baseline weight but the weight that they would have reached after 5 years in the SPHR model without the intervention. The initial weight-loss was simulated in year 0 at the start of the model, and then regained in subsequent years.
The trajectory of BMI is estimated in the health economic model but the weight change from the meta-analysis is in kg because it was the outcome measured in all studies. Therefore, the weight change in kg was converted to BMI change using the height of the simulated individual. In the absence of any data about the direct effects of the weight loss and weight regain on other metabolic factors, an indirect effect of the BMI change on HbA1c, SBP and cholesterol was modelled. Specifically, covariates from the analysis conducted on the Whitehall dataset were used to predict the change in the metabolic factors from changes in BMI in the population simulated  (detail in Additional file 2, page 18).
This analysis was conducted with the assumption that the proposed intervention would be funded for patient through primary care (i.e., the payer would be the NHS). This is already the case for some commercial weight loss and diabetes prevention programmes in the UK . There is no fee charged to the individual receiving the interventions and patient borne costs (e.g., travel etc. are not included). Justifiable costs will be calculated for each person who has the intervention based on the assumption that all eligible individuals will participate in the intervention. It is assumed that all intervention costs will be incurred at time zero and so no discount rate is applied.
Health economic modelling
For each run of the model, 20,000 eligible individuals were randomly sampled from the two baseline populations with replacement. As the aim of this analysis was to estimate a justifiable cost for a proposed intervention, the cost of the weight loss maintenance intervention was set to £0 within the model and the amount that could be spent on this intervention while remaining cost-effective was calculated using increasing maximum ICERs. For NICE, this is estimated to be between £20,000 and £30,000 per QALY  and therefore the cost per person at these ICER values were the targets for the analysis. Public health interventions often have a lower threshold because the benefits are further in the future, therefore the maximum cost of the intervention while being cost saving was also calculated. At this cost or lower, the cost savings as a result of the intervention is greater than the cost of the intervention.
Sensitivity analysis was conducted on the duration of effect, the initial weight-loss and the rate of regain (Table 2). By duration of effect, we are referring to the amount of time between year 0 and the point at which the weight trajectories reach the trajectory they would have followed without any weight loss. Because the duration was estimated by extrapolating the regain from the first two years, in sensitivity analysis the impact of different durations (4–6 years) were examined (scenarios 1–3). A linear regain was assumed between the 2-year estimate of weight and the duration of effect (i.e., 4, 5 or 6 years). The rate of regain, the amount regained at year 1 and year 2, was varied using the 95% confidence intervals (CIs; scenarios 4 and 5). The weight loss that both groups achieved before entering either a weight loss maintenance intervention or control condition (no intervention) was also examined. The figure of 8.93 kg obtained from the meta-analysis is based on a target population of people who have lost ≥5% weight, which reflects the likely implementation of a weight loss maintenance programme in practice. We also examined a scenario in which there was not a minimum weight loss required to take part in the weight loss maintenance programme and examined the impact of a lower initial weight loss of 2.84 kg (scenario 6), based on average weight loss from a previous meta-analysis  of weight loss interventions that were applicable to UK primary care. An initial weight loss of 6.12 kg (scenario 7), which was the midpoint between the lower value of 2.84 kg and the base case value of 8.93 kg, was also tested. The regain was adjusted proportionally. These are represented graphically in Supplementary Fig. 5. Probabilistic sensitivity analyses were conducted to assess uncertainty within the model inputs using probabilistic sensitivity analysis with 5000 Monte Carlo simulations. The model parameters and uncertainty distributions are shown in Additional file 3.