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

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:

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

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 (), 95% confidence interval () and p-value () 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

After a very long leave of absence I return to the issue of extracting the effect estimate () and standard error () from reported and (rounded to a fixed number of decimal points) relative risk (), limits of 95% confidence intervals ( and ) and p-value () 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 given the :

Extracting standard errors (cont’d) : critique

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)

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.

Intro to Bayesian methods

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

In continuation of the Normalizing Constant Paradox: The Harmonic Mean of the Likelihood: Worst Monte Carlo Method Ever | Radford Neal’s blog

http://radfordneal.wordpress.com/2008/08/17/the-harmonic-mean-of-the-likelihood-worst-monte-carlo-method-ever/

Optimizing Survival Likelihoods With Poisson Models for Rate and Exposure

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

An interesting question and an excellent discussion!

http://normaldeviate.wordpress.com/2012/10/05/the-normalizing-constant-paradox/

Any takers?

Survival Analysis via Hazard Based Modeling and Generalized Linear Models

The connection between survival analysis via hazard based modelling and generalized linear models had been made very early even since the description of the proportional hazard (PHM) Cox (1972) and generalized linear models (GLM) Nelder and Wedderburn (1972). For example,

– Breslow (1974) considers the proportional hazard model as a discrete time logistic regression in which discrete probability masses are put on the (ordered) set of observed failure times