Its All Time Dependent

Why Statistics are Scary: a personal journey

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 2011BackgroundPart 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

The QuestionAre shocks detrimental per se, or are shocks a marker of a sicker patient population?Why statistics are scaryTwo 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

**Notethe following survival curves are unadjusted comparisons and do not control for covariates, which was of course done in adjusted analysis. Research Question# 1: Data analysis take one

???Results seem to indicate that shocks are protective?

Thats fine but this completely opposite of the expected result

Lets take a second look at the analysis

Analysis AssumptionsStudy endpoint = time to death or last follow-upFollow-up time = Implant date status date

Each patient = one observationShock yes/noDead yes/noButits all time dependentShock 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**Notethis was the way this was modeled in other studies so prior analyses were appropriate.Research Question #1:Data analysis take two

Thats betterResults now consistent with what has been previously found

Patients receiving shocks do worse than patients receiving no shocksResearch Question #2: Data analysis take one

**NoteATP only = 2 = Shock. Sorry I didnt make nicer graphs.???Results seem to indicate that ATP is harmful (even more so than shocks)which has never been found before?

Again, lets take a second look at the analysis

Againits all Time DependentPatients 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 groupResearch Question #2: Data Analysis Take Two

Thats betterResults now consistent with what has been previously found

ATP not associated with an increased risk of deathStatistics: A brief historyTimeContributorTheoryAncient GreecePhilosophersTheoretical- no quantitative16th 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 numbers18th Century Laplace, Gauss, BayesNormal curve, Regression through study of astronomy, Bayes Theorem19th Century Quetelet, Galton First application of statistical analyses to human biology studied genetic variation in humans(used regression and correlation). The Average Person.20th CenturyLots of peopleContributing to statistical analysis as we know it-Wilcoxon, Cox, Fisher, ANOVA, Logistic/ Multiple regression, etc.Quick noteProbability deals with predicting the likelihood of future eventsProbability theory- the variables and the initial state are known

Statistics involves the analysis of the frequency of past eventsStatistics- the outcome is known, but the past causes are uncertainSchools of Statistical ThoughtBayesianFrequentistProbability is subjective- can be applied to single events based on degree of confidence or prior beliefProbability 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 themParameters are fixes and unknown constantsProbability has a distribution over the parameters, and point estimates are usually done by either taking the mode or the mean of the distributionStatistical process only has interpretation based on certain frequencies (ex. 95% CI of a parameter will contain the true value 95% of the time)Frequentist InferenceRelies 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 intervalsThe type of statistics we are used to seeing

Does not condition on the observed data

Baysian InferenceChooses 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

Take Home Point #1This exercise was not to illustrate that findings should be the same as the findings that came beforeIn fact, it would have been great if shocks werent 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

Take Home Point #2Just like medicine, statistical analysis is an evolving science

Just like medicine, there is controversy as to what are the best (most appropriate) methods to useTake Home Point #3It 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 TwainUncertainty and mystery are energies of life. Dont 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