### Introduction

In healthcare decision making, a number of attributes can affect whether or not an intervention is deemed appropriate for use. Aside from effectiveness and safety consideration, attention is also placed on the likely cost-effectiveness of the technology. This is reported as its ‘most plausible’ (or ‘base case’) incremental cost-effectiveness ratio (ICER), as well as an estimate of the likely confidence around that measure. Usually, this is demonstrated by producing a cost-effectiveness scatter plot and accompanying cost-effectiveness acceptability curve (CEAC).

In probabilistic sensitivity analysis (PSA), it is typical to see distributions assigned to all (relevant) parameters in a model. In most cases, it is assumed that input parameters vary independantly, little or no attention given to estimating and accounting for correlation between input parameters. This model explores the impact of input correlation on the outcomes of PSA.

### Aims

This model does not set out to recommend statistical approaches towards input parameter correlation. Instead, it aims to explore the potential consequences of choosing whether to account for input parameter correlation.

### Scenarios

In the model, PSA can be run under 3 main scenarios:

- No correlation: All parameters are allowed to vary independently. Costs are generated as independent observations from the gamma distribution, while utility values and transition probabilities are generated as independent observations from the beta distribution.
- Part correlation: Within each type of input (costs, utilities, transition probabilities for the treatment, transition probabilities for the comparator) parameters are varied using a single multiplier, based on a lognormal distribution with mean 1. Probabilities that worsen the patient’s health state are generated by multiplying their mean by the multiplier, whilst probabilities that improve the patient’s health state are generated by dividing their mean by the multiplier (no change is estimated using the residual probability).
- Full correlation: Similar to part correlation, except that a single multiplier is used to estimate all parameters in the model. Costs, the probability of worsening under the treatment and the probability of improvement under the comparator are generated by multiplying their mean by the multiplier while utilities, the probability of improvement under the treatment and the probability of worsening under the multiplier are generated by dividing their mean by the multiplier. This represents the "worst case scenario", where accounting for parameter correlation will result in substantially more extreme values than not doing so.

Two additional scenarios are available:

- Costs and utilities correlated: Similar to part correlation, except that the multiplier used to generate utility inputs is constrained to be the reciprocal of the multiplier used to generate costs inputs. This forces a negative correlation between costs and utility values for each health state.
- Base case: Deterministic analysis with no random elements.