## Posts Tagged ‘statistics’

### In the absence of real world data the effectiveness of a clinical intervention is half its efficacy (in a randomized trial)

August 14, 2013

Suppose one is approached by one’s partner with the results of a new intervention that helped X% of N carefully chosen participants in a Randomized Controlled Trial (RCT), with only minimal adverse events (seen in Y% of the N patients). The colleague, a TRUE BELIEVER – champion of innovation and defender of progress against the medical luddites of this world, wants to convince you to implement this new therapy as part of the standard protocol in your common practice. He is thinking that it should be offered to all newcomers, including patients who would not have been eligible to participate in the aforementioned trial. What would a healthy sceptic do? Champion innovation and adopt the new therapy on the spot, or defend tradition and wait? Is it possible to ground the answer in the cold, objective language of math and warm up to/cool down your partner accordingly? (more…)

### The probability that one random variable is smaller or larger than a Beta random variable

August 14, 2013

This super wonkish post will serve as convenient basket case for all the inglorious math that will be required for a series of more Evindence Based Medicine oriented posts. A result that will be repeatedly required in these posts is an expression for the probability that one random variable is smaller (or larger) than a Beta random variable. The necessity for this result is due to the ability of the Beta distribution to quantitate beliefs about the percentages or proportions of dichotomous outcomes , having observed $\alpha$ “successes” and $\beta$ “failures”.  So if one had just read about the efficacy  ($E$) of an intervention in a Randomized Controlled Trial (RCT), the Beta distribution would be a readily available candidate to summarize the uncertainty about the efficacy as $B(E|p\,N,(1-p)\,N)$ where $p$ is the proportion of responders and $N$ the number of study participants. (more…)

### The expectation of the ratio of two random variables

August 4, 2013

I was recently revising a paper concerning statistical simulations of hemodialysis trials, in which I examine the effects of different technical aspects of the dialysis prescription at the population level. I had used the reported figures from a number of recent high profile papers, when I noticed that while the results were right on average, there was a substantial number of outliers, i.e. “digital patients” who would actually not be among the living if they were to be dialyzed with these parameters in the real world. (more…)

### On the futility of discourse between two people of different degrees of conviction : Reflections on the Lindley Paradox

July 6, 2013

In an exchange between two people, it is the one with the stronger conviction,not the better grasp of reality, who will win.

The phrase above snapped into my head when I watched an honest and very extensive dialog between two business partners who were examining an issue. Partner A had come into the table with a very strong conviction about the issue and what needed to be done, while partner B was not so sure and was open to entertain a number of possible courses of action. Over a course of 45 min, they examined the data available to them and decided to proceed with A’s opinion. What is surprising is not the decision per se , but the fact that before the meeting A had confided to me that the available information contradicted his belief; B had also said that A’s position was rather implausible given the same data. Yet, when they sat down and considered what was in front of them they reached a rather different conclusion!

### 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?

### 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.