TABLE 1.
Comparison of sensitivity analysis methods
| Category | Methods | Assumptions | Advantages | Disadvantages | Approximate computational expense |
|---|---|---|---|---|---|
| LSA | Derivative‐based; analytic calculations, automatic differentiation, finite differences, or complex‐step approximation | Model is smooth; also, model is either linear or additive, or is well‐calibrated with no interactions between parameters | Computationally inexpensive, easy to implement | Due to its local nature, results may not be representative of sensitivities in other parts of parameter space when assumptions do not hold |
P+1 model evaluations, where P is the number of parameters under investigation e.g., 11 evaluations for P = 10 |
| GSA | Derivative‐based: Morris method and others (cf. Kucherenko and Iooss 61 ) | Generally applicable | Least computationally‐expensive GSA method; easy to implement; Morris method is applicable to nonlinear and non‐monotonic model outputs, and when parameters have interactions 56 , 59 | Although these methods globally sample parameter space, the calculations at each point are still one‐at‐a‐time; thus variance of sensitivities can be either due to interactions or nonlinearity in model parameters (see Saltelli et al., 56 p. 111) |
> N*(P+1) model evaluations, where N is number of samples, with N often 10 to 100 e.g., ~500 evaluations for P = 10, N = 50 |
| Correlation‐based: PRCC | Output is monotonic in each of the input parameters | Easy to implement; robust for nonlinear models, and for parameters with correlations | Computationally expensive even if only 2 values sampled per parameter |
> 2^P (Base number of 2 explores only the corners of parameter space) e.g., >1024 evaluations for P = 10 |
|
| Variance‐based: Sobol indices, FAST, eFAST | Variance is a good statistic to represent model output distribution (cf. Pianosi and Wagener 94 for a GSA method for non‐normal output distributions); some methods work even when parameters are correlated or otherwise dependent 60 | Few assumptions; generally suitable for QSP models; applicable to nonlinear and non‐monotonic outputs, and when parameters have interactions (see Saltelli et al., 95 p. 384); quantify the relative influence of parameters | Very computationally expensive; most methods do not perform well on models with correlated parameters 95 |
The larger of: >(2^P)*(P+2) or > N*(P+2) model evaluations e.g., > max (12000, 12288) evaluations for P = 10, N = 1000 (Base = 2 only explores the corners of parameter space) |
Abbreviations: eFAST, extended Fourier amplitude sensitivity test, FAST, Fourier amplitude sensitivity test; GSA, global sensitivity analysis; LSA, local sensitivity analysis; PRCC, partial rank correlation coefficient; QSP, quantitative systems pharmacology.