PROBABILISTIC ONE-WAY SENSITIVITY ANALYSIS: A MODIFIED TORNADO DIAGRAM
Conventional tornado diagram has several challenges: it is based on deterministic one-way sensitivity analysis (1-way SA) which produces biased results when parameters are correlated. Moreover, it uses the incremental cost effectiveness ratio (ICER) which has a number of problems such as non-uniqueness. Our purpose is to generate a modified tornado diagram that addresses the above problems to improve decision-making.
We develop a modified tornado diagram that allows the result of probabilistic 1-way SA to be presented clearly to decision-makers through these processes: (a) for each of three parameters (probability, utility and cost), we fixed several (outer loop) values. For each outer loop value, we allowed the other parameters to undergo simulation so that when simulation is complete we observe the costs and effects for two strategies (21 gene assay versus ROR used in genomic tests for early-stage breast cancer) under comparison. (b)We proceeded to calculate the incremental net monetary benefit (INMB) of gene assay against ROR, corresponding to each outer loop value. (c) Next, we plotted the probability density function (PDF) for each parameter with INMB on the x-axis and probability on the y-axis; a vertical line is then drawn at the point where the INMB is zero (decision-switching point). (d) Finally, we calculated the Expected Value of Perfect Parameter Information (EVPPI) for each parameter and arranged the PDF graphs with highest-EVPPI parameter on top and lowest-EVPPI parameter at the bottom.
The modified tornado diagram we have developed is shown below:
The graph shows PDF for the two willingness-to-pay (WTP) values we used in calculating INMB. The EVPPI for each curve and the proportion of each curve that lies above 0 on the x-axis (thus, the probability that gene assay is cost-effective) are reported on the graph. For WTP of £20,000, only the probability parameter contributes towards decision uncertainty. For WTP of £30,000 the order of importance of parameters to decision-makers is probability, utility, and cost.
We have executed a probabilistic 1-way SA which, while examining the sensitivity of model conclusions to changes in only one parameter's value, simultaneously takes into consideration its correlation with other parameters. We have also used INMB as model output instead of the ICER. Our approach yields a more reliable decision-making tool.