## Archive for April, 2013

### An algebra guy’s take on the meta-analysis posts

April 29, 2013

As I was reading through the meta-analysis posts in order to correct various typos, the forgotten non-probability me woke up and raised the following question:

What if one were to treat the reported RR ($t$), 95% confidence interval ($t_L, t_U$) and p-value ($p_v$) as the true values of the non-reported quantities, in essence ignoring the round-off error?

Could this lead to a (?simpler) solution bypassing the need for Monte Carlo? What this solution would look like and how it differs (implementationally) from the Bayesian one ? More importantly how does it hold up against the Bayesian solution?

After a very long leave of absence I return to the issue of extracting the effect estimate ($T$) and standard error ($se$) from reported and (rounded to a fixed number of decimal points) relative risk ($t$), limits of 95% confidence intervals ($t_L$ and $t_U$) and p-value ($p_v$) figures found in scientific publications. This solution is a Bayesian one, requiring nothing more than a straightforward application of the Bayes theorem for the posterior distribution of the A straightforward application of Bayes theorem for the quantities $T, se$ given the $t, t_L, t_U, p_v$:
$P(T,se|t, t_L, t_U, p_v) \propto P(t|T,se,t_L, t_U, p_v) \times P(T,se|t_L, t_U, p_v)$