## Meta-analytic Death Match : dumb algebra guy v.s. the Bayesian King Kong

May 2, 2013

Maybe I overdid it with the title, but I think the data speak for themselves in the (?much) anticipated,  pre-announced comparison between a naive, algebra based solution and the Bayesian, Monte Carlo based one.

To carry out this comparison, I assumed: Read the rest of this entry »

## 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?

## Extracting standard errors and effect estimates for meta-analysis: paging Rev Bayes

April 14, 2013

After a very long leave of absence I return to the issue of extracting the effect estimate ($t T$) 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 $t, t_L, t_U, p_v$:

$P(T,se|t, t_L, t_U, p_v) \propto P(t|T,se,t_L, t_U, p_v) \times P(T,se|t_L, t_U, p_v)$

## Extracting standard errors (cont’d) : critique

February 1, 2013

In a previous post I presented a possible solution to the extraction of standard errors and hazard ratios from publications in which only rounded approximations to the risk ratios and the associated 95% confidence interval are considered.

This solution, is subject to a criticism that I will now discuss : it suffers from an internal contradiction. Specifically, while one can use two of the three pieces of data (the actual risk ratio and the two limits of the 95% CI) simultaneously, one will arrive at different and conflicting probability estimates which is clearly not what one wants!.

## Extracting standard errors from 95%CI for meta-analysis (or weird uses for measurement error models)

December 29, 2012

I was recently confronted with the task of running a meta-analysis of a subject in which the various studies had reported (adjusted) measures of treatment efficacy on various continuous outcomes. This is one of the areas in which the data for meta-analysis comes not in the usual form of #events and #patients(N) , but as treatment effects and their associated standard errors. Not too uncommon examples include the effects of a given intervention on Blood Pressure, Cholesterol levels, Psychometric scales, Cox regression Hazard Ratios or Logistic Regression Odds Ratios etc. And then it hit me: for almost all of the studies I wanted to pool, I did have access at all to the actual data that I had to process!! For sure, there were treatment effects (actually hazard ratios,HRs, for my project) in the papers but the standard errors were not reported; furthermore, the information that was actually contained in the manuscripts (HRs, 95%CI and the p-value) was not the “real thing” but its approximation, rounded down to one (and sometimes two) significant digits.

I’m sure that others have run into this issue previously, but I have never seen a formal, discussion for handling this missing data problem. Read the rest of this entry »

## Intro to Bayesian methods

October 20, 2012

http://www.r-bloggers.com/introduction-to-bayesian-methods-guest-lecture/ Nice, gentle and viewable!

October 14, 2012

## Optimizing Survival Likelihoods With Poisson Models for Rate and Exposure

October 13, 2012

In a previous post I mentioned that Poisson models can be used to carry out survival analysis tasks e.g. estimation of survival curves or even relative risk modelling. Yet, I never showed how this can be done. So I will close the gap today and highlight how this works from a purely mathematical vantage point.

## The Normalizing Constant Paradox | Normal Deviate

October 7, 2012

An interesting question and an excellent discussion!