Variance-based sensitivity analysis of tuberculosis transmission models

Abstract

Mathematical models are widely used to provide evidence to inform policies for tuberculosis (TB) control. These models contain many sources of input uncertainty including the choice of model structure, parameter values and input data. Quantifying the role of these different sources of input uncertainty on the model outputs is important for understanding model dynamics and improving evidence for policy making. In this paper, we applied the Sobol sensitivity analysis method to a TB transmission model used to simulate the effects of a hypothetical population-wide screening strategy. We demonstrated how the method can be used to quantify the importance of both model parameters and model structure and how the analysis can be conducted on groups of inputs. Uncertainty in the model outputs was dominated by uncertainty in the intervention parameters. The important inputs were context dependent, depending on the setting, time horizon and outcome measure considered. In particular, the choice of model structure had an increasing effect on output uncertainty in high TB incidence settings. Grouping inputs identified the same influential inputs. Wider use of the Sobol method could inform ongoing development of infectious disease models and improve the use of modelling evidence in decision making.

Keywords: modelling; sensitivity analysis; tuberculosis.

Figure 1.

Model structure. (a) Core model structure with serial exposed states. (b) Core model structure with parallel exposed states. In both (a) and (b), dashed arrows represent births and natural mortality. (c) Preventive treatment care cascade. Values on the left-hand side indicate the proportion completing the step (median (95% range)); values on the right-hand side indicate the cumulative proportion retained at each stage (based on median proportions at each step). S = susceptible, L_F = recently exposed, L_S = remotely exposed, L_R = recently re-exposed, I = active TB, TST = tuberculin skin test, PT = preventive treatment. See table 1 for parameter definitions.

Figure 2.

Model estimates of percentage reduction in TB incidence and mortality. Blue: global TB incidence setting; pink: high TB incidence (Philippines) setting. Boxes show the first and third quartiles (the 25th and 75th percentiles), horizontal lines the median. Whiskers extend to 1.5 times the interquartile range and points indicate outliers.

Figure 3.

Results of individual Sobol analysis. Panels show results for different outputs. (a,b) Reduction in TB incidence; (c,d) reduction in TB mortality; (a,c) 1 year time horizon; (b,d) 10 year time horizon. Blue bars show the individual indices (S_i), red bars the total effects (T_i). Error bars show 95% confidence intervals based on bootstrapping. Lighter shading indicates inputs that are non-influential based on comparison with the dummy indices. Dashed vertical lines divide the individual inputs into the groups used in the grouped analysis.

Figure 4.

Results of grouped Sobol analysis. Panels show results for different outputs. (a,b) Reduction in TB incidence; (c,d) reduction in TB mortality; (a,c) 1 year time horizon; (b,d) 10 year time horizon. Blue bars show the individual indices (S_i), red bars the total effects (T_i). Error bars show 95% confidence intervals based on bootstrapping. Lighter shading indicates inputs that are non-influential based on comparison with the dummy indices.

Figure 5.

Comparison of sensitivity indices for different incidence settings. (a) Global TB incidence; (b) example of high TB incidence country. Blue bars show the individual indices (S_i), pink bars the total effects (T_i). Error bars show 95% confidence intervals based on bootstrapping. Lighter shading indicates inputs that are non-influential based on comparison with the dummy indices.