Incorporating calibrated model parameters into sensitivity analyses: deterministic and probabilistic approaches.

OBJECTIVE: The aim of this study was to examine how calibration uncertainty affects the overall uncertainty of a mathematical model and to evaluate potential drivers of calibration uncertainty.
METHODS: A lifetime Markov model of the natural history of human papillomavirus (HPV) infection and cervical disease was developed to assess the cost effectiveness of a hypothetical HPV vaccine. Published data on cervical cancer incidence and mortality and prevalence of pre-cursor lesions were used as endpoints to calibrate the age- and HPV-type-specific transition probabilities between health states using the Nelder-Mead simplex method of calibration. A conventional probabilistic sensitivity analysis (PSA) was performed to assess uncertainty in vaccine efficacy, cost and utility estimates. To quantify the uncertainty around calibrated transition probabilities, a second PSA (calibration PSA) was performed using 25 distinct combinations of objective functions and starting simplexes.
RESULTS: The initial calibration produced an incremental cost-effectiveness ratio (ICER) of $US 4300 per QALY for vaccination compared with no vaccination, and the conventional PSA gave a 95% credible interval of dominant to $US 9800 around this estimate (2005 values). The 95% credible interval for the ICERs in the calibration PSA ranged from $US 1000 to $US 37,700.
CONCLUSIONS: Compared with a conventional PSA, the calibration PSA results reveal a greater level of uncertainty in cost-effectiveness results. Sensitivity analyses around model calibration should be performed to account for uncertainty arising from the calibration process.