Methodology

Research articles · Dec 31, 2018

Global sensitivity analysis of a model simulating an individual’s health state through their lifetime

Abbygail Jaccard, Lise Retat, Martin Brown, Laura Webber, Zaid Chalabi

UK Health Forum, United Kingdom; Department of Public Health, Environments and Society, London School of Hygiene and Tropical Medicine, United Kingdom

Volume 11(3) Winter 2018

Cite as: A. Jaccard, L. Retat, M. Brown, L. Webber, Z. Chalabi; 2018; Global sensitivity analysis of a model simulating an individual’s health state through their lifetime; International Journal of Microsimulation; 11(3); 100–121. doi: 10.34196/ijm.00190

Abstract

In public health, model predictions are used by decision-makers to minimise health burdens and monetary costs of non-communicable diseases. Fully understanding the uncertainty underlying those predictions is thus crucial. One-parameter-at-a-time methods are typically used for model uncertainty analysis but are often impractical for large-scale nonlinear models containing a very large number of parameters and cannot be used to examine the uncertainty associated with parameter interaction. An individual-based chronic disease model was developed to model the impact of Body Mass Index (BMI) trends on the rates of non-communicable diseases. The model was simulated for overweight and obese male case studies and used to predict their life expectancy, disease-free life expectancy and quality-adjusted life years. Uncertainty was estimated by carrying out a global sensitivity analysis by assessing the contribution to the overall uncertainty from a selection of parameters individually and from their interactions. Results show that the uncertainty of the BMI input parameter had the greatest impact on the disease-free life expectancy and quality- adjusted life year uncertainty compared to the relative risks of colorectal cancer and stroke. Life expectancy uncertainty was influenced by BMI and colorectal cancer relative risks. Global sensitivity analysis enables the assessment of the parametric uncertainty for individual parameters and their interaction. This allows the communication of the uncertainty of different policy options. A strategy for scaling-up uncertainty analysis from an individual to a population level is discussed.

This article contains 6 figures and 8 tables.

Figures

Figure 1. Schematic of the individual-based chronic disease model used to simulate individuals through time.
Figure 2. A graphical illustration of the first-order Sobol indices for each model input parameter: BMI, relative risk of stroke and relative risk of colorectal cancer for disease-free life expectancy.
Figure 3. A graphical illustration of the first-order Sobol indices for each model input parameter: BMI, relative risk of stroke and relative risk of colorectal cancer for life expectancy.
Figure 4. A graphical illustration of the first-order Sobol indices for each model input parameter: BMI, relative risk of stroke and relative risk of colorectal cancer for quality-adjusted life year.
Figure B.1. A graph illustrating the relationship between the RR for stroke and BMI for males for two different age groups.
Figure B.2. A graph illustrating the relationship between the RR for colorectal cancer and BMI for males for two different age groups.

Tables

Table 1. Summary of the BMI model parameters and their variances used in the sensitivity analysis.
Model parameter Mean Standard deviation Lower bound Upper bound
Healthy weight BMI probability (BMI < 25 kg/m2) 0.252 0.078 0.117 0.387
Overweight BMI probability (25 ≤ BMI < 30 kg/m2) 0.314 0.083 0.170 0.459
Obese BMI probability (BMI ≥ 30 kg/m2) 0.434 0.107 0.248 0.619
Mean BMI category probability 0.333 0.090 0.177 0.490
Mean BMI1 level 25.192 20.591 27.028
Case study 1 BMI level 27.5 22.899 29.336
Case study 2 BMI level 37.5 35.207 41.644
Table 2. Summary of the relative risk model parameters and their variances used in the sensitivity analysis.
Model parameter Mean Standard deviation Lower bound Upper bound
Relative risk stroke for overweight 1.213 0.056 1.116 1.310
Relative risk stroke for obese 1.758 0.107 1.573 1.944
Relative risk colorectal cancer overweight for 1.231 0.082 1.089 1.373
Relative risk colorectal cancer obese for 1.823 0.224 1.435 2.211
Table 3. Scalar additives z1, z2 and z3 sampled by PSUADE.
PSUADE parameter Lower bound for overweight Upper bound for overweight Lower bound for obese Upper bound for obese
z1 22.899 29.336 35.207 41.644
z2 1.116 1.310 1.573 1.944
z3 1.089 1.373 1.435 2.211
Table 4. Summary of the mean, standard deviation and variance for the disease-free life expectancy for the two case studies.
Case study Mean (years) Standard deviation (years) Variance (years2)
Overweight male 63.47 3.41 11.59
Obese male 48.32 3.14 9.87
Table 5. Summary of the mean, standard deviation and variance for the life expectancy for the two case studies.
Case study Mean (years) Standard deviation (years) Variance (years2)
Overweight male 79.76 0.11 0.01
Obese male 79.17 0.31 0.09
Table 6.
Case study Mean (years) Standard deviation (years) Variance (years2)
Overweight male 75.09 1.01 1.02
Obese male 70.06 1.06 1.12
Table C.1. Description of the categories used for the RF BMI.
Risk factor (RF) Number of categories (N) Categories
BMI 3 BMI < 25 kg/m2 (normal weight)
BMI from 25 to 29.99 kg/m-2 (overweight)
BMI ≥ 30 kg/m2 (obesity)
Disease epidemiological data sources.
Disease Incidence Prevalence Mortality Survival Relative Risk Utility Weight
CHD Smolina et al 2012. Corrected data on incidence and mortality in 2013 (Smolina, Wright, Rayner, & Goldacre, 2012) BHF, Cardiovascular Disease Statistics 2014 (British Heart Foundation, 2015) ONS, Deaths Registrations Summary Statistics, England and Wales, 2014 (Office for National Statistics, 2014) Computed from prevalence and mortality World Obesity Federation (DYNAMO project) (World Obesity Federation) Laires et al. 2015 (Laires, Ejzykowicz, Hsu, Ambegaonkar, & Davies, 2015)
Stroke BHF, stroke statistics 2009 (British Heart Foundation, 2009) BHF, Cardiovascular Disease Statistics 2014 (British Heart Foundation, 2015) ONS, Deaths Registrations Summary Statistics, England and Wales, 2014 (Office for National Statistics, 2014) Computed from prevalence and mortality World Obesity Federation (DYNAMO project) (World Obesity Federation) Rivero-Arias et al. 2010 (Rivero-Arias et al., 2010)
Hypertension Derived from prevalence Health Survey for England 2012 (Health and Social Care Information Centre, 2012) non terminal non terminal World Obesity Federation (DYNAMO project) (World Obesity Federation) Sullivan et al. 2011 (Sullivan, Slejko, Sculpher, & Ghushchyan, 2011)
Diabetes Personal communication Dr. Craig Currie at Cardiff University National Diabetes Audit 2015–2016(NHS Digital, 2017) non terminal non terminal World Obesity Federation (DYNAMO project) (World Obesity Federation) Sullivan et al. 2011 (Sullivan et al., 2011)
Colorectal cancer CRUK, 2013 Statistics by cancer type (Cancer Research UK, 2016b) NA CRUK Mortality by cancer type(Cancer Research UK, 2016a) ONS Cancer Survival in England: adults diagnosed between 2009 and 2013 and followed up to 2014 (Office for National Statistics, 2015) & ONS Cancer Survival in England: 10 year survival rates adults diagnosed between 2010–2011 and followed up to 2012 (Office for National Statistics, 2013) World Obesity Federation (DYNAMO project) (World Obesity Federation) Sullivan et al. 2011 (Sullivan et al., 2011)