### PSM (Probabilistic Simulation Method)

#### 1. Description

PSM (Probabilistic Simulation Method) is a statistical technique for exploring the impact of uncertainty in data on a model's results.[1][2] In applying PSM to benefit-risk assessment, statistical summaries of data in a quantitative model are replaced with probability distributions related to the patient-level data. The overall benefit-risk balance is then calculated a large number of times with different input data drawn from the probability distributions in proportion to their likelihood of being chosen. This generates a probability distribution over the difference between benefits and risks for the drug, and another distribution for the comparator. The same process can then be applied to determine the probability that the benefit-risk balance of the drug is more than that of the comparator.

#### 2. Evaluation

##### 2.1 Principle

- PSM is not a method specific to benefit-risk assessment.

- It is a mathematically sound technique of estimation and inference.

- Under probabilistic simulations, many different possible scenarios of benefit-risk assessments can be explored.

##### 2.2 Features

- PSM provides a good means to quantify and explore the uncertainty of the benefit-risk balance.

- There is no restriction in the number of criteria a PSM model can accommodate.

- PSM can accommodate any type of metric.

- PSM can accommodate correlations between favourable and unfavourable effects, if it is known.

##### 2.3 Visualisation

- PSM can be presented as scatter plots or box plots.

##### 2.4 Assessability and accessibility

- Many statistical software packages can perform probabilistic simulations.

- Specialised software packages for PSM include:
##### Analytica (http://www.lumina.com/why-analytica)

##### @Risk (http://www.palisade.com/risk)

##### Crystal Ball (http://www.oracle.com/us/products/applications/crystalball/overview/index.html)

- The acceptability and interpretability of the results depend on the specific models, which may depend on the metric index used to characterise benefit-risk balance.

This method was tested in the Natalizumab, Rimonabant, Rosiglitazone, Telithromycin and Warfarin case studies.

#### 3. References

[1] Lynd LD, O'Brien BJ. Advances in risk-benefit evaluation using probabilistic simulation methods: an application to the prophylaxis of deep vein thrombosis. J Clin Epidemiol 2004 Aug;57(8):795-803.[2] van Staa TP, Smeeth L, Persson I, Parkinson J, Leufkens HG. What is the harm-benefit ratio of Cox-2 inhibitors? Int J Epidemiol 2008 Apr;37(2):405-13.