“While nothing is more uncertain than a single life, nothing is more certain than the average duration of a thousand lives” -Elizur Wright By: Gail Larsen MS4 2011

 Part of the statistical analysis for my MPH Thesis project  Implantable cardioverter-defibrillators (ICD) decrease mortality in appropriately selected patients  However, ICD shocks have been associated with increased risk of death

Are shocks detrimental per se, or are shocks a marker of a sicker patient population?

 Two examples: Research Question#1: Do patients that receive shocks do worse than patients that do not receive shocks? Research Question #2: Do patients that only receive ATP (antitachycardia pacing) do worse than patients that receive shocks or patients that receive no therapy?  ATP has not been found to increase mortality **Note…the following survival curves are unadjusted comparisons and do not control for covariates, which was of course done in adjusted analysis.

 Results seem to indicate that shocks are protective?  That’s fine but this completely opposite of the expected result  Let’s take a second look at the analysis

 Study endpoint = time to death or last follow-up Follow-up time = Implant date – status date  Each patient = one observation Shock yes/no Dead yes/no

 Shock should be modeled as a time- dependent covariate. In other words, a person is not as risk from shocks until they have had their first shock.  Risk changes after the occurrence of first shock **Note…this was the way this was modeled in other studies so prior analyses were appropriate.

 Results now consistent with what has been previously found  Patients receiving shocks do worse than patients receiving no shocks

**Note…ATP only = 2 = Shock. Sorry I didn’t make nicer graphs.

 Results seem to indicate that ATP is harmful (even more so than shocks)…which has never been found before?  Again, let’s take a second look at the analysis

 Patients stratified as no therapy, ATP only, or shock in initial analysis  Many patients in the shock group received ≥1 ATP episodes before their first shock episode and should be included in that group before becoming part of the shock group

 Results now consistent with what has been previously found  ATP not associated with an increased risk of death

TimeContributorTheory Ancient GreecePhilosophersTheoretical- no quantitative 16 th CenturyCardanoAttempts to calculate probabilities of dice (game theory) 17th Century Graunt, Petty, Pascal, Bernoulli, Halley Vital statistics of populations; Studied probability through games of chance; First mortality tables- relates death to age; Law of large numbers 18th CenturyLaplace, Gauss, Bayes Normal curve, Regression through study of astronomy, Bayes Theorem 19th CenturyQuetelet, Galton First application of statistical analyses to human biology studied genetic variation in humans(used regression and correlation). The Average Person. 20 th CenturyLots of peopleContributing to statistical analysis as we know it -Wilcoxon, Cox, Fisher, ANOVA, Logistic/ Multiple regression, etc.

 Probability deals with predicting the likelihood of future events Probability theory- the variables and the initial state are known  Statistics involves the analysis of the frequency of past events Statistics- the outcome is known, but the past causes are uncertain

BayesianFrequentist Probability is subjective- can be applied to single events based on degree of confidence or prior belief Probability is objective- relative frequency of an event in a large number of trials (ex. coin flip) Parameters are random variables that has a given distribution, and probability statements can be made about them Parameters are fixes and unknown constants Probability has a distribution over the parameters, and point estimates are usually done by either taking the mode or the mean of the distribution Statistical process only has interpretation based on certain frequencies (ex. 95% CI of a parameter will contain the true value 95% of the time)

 Relies on drawing random samples from a population  Assigns probability to a repeatable event in which the uncertainty is due to randomness  Basis for hypothesis testing and confidence intervals The type of statistics we are used to seeing  Does not condition on the observed data

 Chooses a probability distribution as the prior, which represents beliefs about the parameters of interest  Chooses a probability distribution for the likelihood, which represents beliefs about the data  Computes the posterior, which represents an update of our beliefs about the parameters after having observed the data

 This exercise was not to illustrate that findings should be the same as the findings that came before In fact, it would have been great if shocks weren’t associated with increased risk of death in our study.  This exercise was to illustrate that drastically (polar opposite) conclusions can be reached depending on how the data is set up and modeled

 Just like medicine, statistical analysis is an evolving science  Just like medicine, there is controversy as to what are the best (most appropriate) methods to use

 It is not necessary to completely understand & critique the methods section of every study I only pretend to understand the underlying math and concepts  It is worth knowing a little bit about this stuff or at the very least trying to elucidate the underlying assumptions, population included, etc.  It is worth knowing somebody who does understand this stuff

Education is the path from cocky ignorance to miserable uncertainty. - Mark Twain Uncertainty and mystery are energies of life. Don’t let them scare you unduly, for they keep boredom at bay and spark creativity. - R.I. Fitzhenry The Black Swan: The Impact of the HIGHLY IMPROBABLE. Nassim Nicholas Taleb