Devin Incerti does not blog much; only about 7 times in 4 years. When he does, however, it’s worth paying attention. For instance, he has put together a super helpful blog post describing how to do probabilistic sensitivity analysis (PSA) in R. A key feature of any PSA is determining the distribution from which one makes draws for different parameter values. Dr. Incerti–my colleague at PHE–gives some helpful pointers of how to use the following distributions:
- Normal distribution: The standard ‘bell curve’ is often used for most continuous variables. Note that the normal distribution is especially helpful since the central limit theorem establishes that in relative large samples, the sample mean is approximately normally distributed even if the underlying probability distribution is not.
- Multivariate normal. This distribution generalizes the univariate normal distribution and can be used to approximate parameters from regression models due to the multivariate central limit theorem.
- Beta distribution. This distribution is useful for the distribution of a probability or proportion. One of the few Bayesian approaches that can be analytically derived, the beta distribution is a conjugate prior for the binomial distribution.
- Dirichlet distribution. A multivariate generalization of the beta distribution, that is frequently used as the conjugate prior to the multinomial distribution. This distribution is helpful when there are multiple discrete health states (e.g., healthy, moderately sick, very sick), or outcomes (high cost, moderate cost, low cost).
- Gamma and lognormal distributions. When you have right-skewed data–like most health care cost or utilization data–the gamma and lognormal distributions are often used. The gamma distribution contains a shape and scale parameters which define the distribution’s mean and variance (among other moments), whereas the lognormal distribution is fully parameterized by the mean and variance.
- Uniform distribution. This distribution is often useful when there is little data on the parameter of interest but the parameter range is known. The distribution assigns an equal probability to all values within the distribution’s domain.
Dr. Incerti’s blog post also describes how to preform a PSA, and has R code describing how to create these distributions. There are also a lot of helpful graphs as well.