Common sense statistics

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30-05-2020

Raja Selvaraj

Introduction

Why this topic ?

One of the best tools in the statistical detective’s toolkit is common sense

Sainani, K. L. (2019). How to Be a Statistical Detective. PM&R. 10.1002/pmrj.12305

Why me ?

Statistics: A subject which most statisticians find difficult but in which nearly all physicians are expert.

Anon

Treatment of MI

Treatment - Streptokinase ? Aspirin ?

  • 45 year old male
  • Chest pain since 4 hours
  • 2 mm ST elevation in anterior leads
  • Raised Trop T

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ISIS - 2

  • Large study - 17,187 patients
  • Acute MI < 24 hours
  • 2 x 2 design
  • Streptokinase vs placebo infusion and Aspirin vs placebo tablets
  • Significant separate benefit, benefit also additive

ISIS-2 collaborative group. Randomised Trial of Intravenous Streptokinase, Oral Aspirin, Both, or Neither Among 17,187 Cases of Suspected Acute Myocardial Infarction: ISIS-2. Lancet. 1988 Aug 13;2(8607):349-60.

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Additional piece of information

  • Date of birth - October 01
  • Does it change treatment ?

Subgroup analysis

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Subgroup analysis

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Subgroup analysis - Aspirin

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"All these subgroup analyses should, perhaps, be taken less as evidence about who benefits than as evidence that such analyses are potentially misleading."

XKCD

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https://xkcd.com/552/

Jelly beans

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https://xkcd.com/882/

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So what is the problem here ?

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  • Multiple comparisons / multiple testing
  • p-hacking
  • publishing bias

Multiple comparisons

Thresholds for significance based on one comparison or test. Thus 5% chance of the finding being random gives 95% confidence its real

p value

  • What is the chance that the difference we are seeing is due to purely random variation ?

A simple experiment

  • 400 patient attenders in Cardiology OPD
  • BP measured
  • 50 found to have systolic BP > 130 mm Hg
  • Advised to drink one extra glass of water each day for one week
  • Significant fall in BP after one week !

A thought experiment

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Regression toward the mean

  • In any series with complex phenomena that are dependent on many variables, where chance is involved, extreme outcomes tend to be followed by more moderate ones.
  • Confounder in many trials - eg. Renal artery denervation

Texas sharpshooter

Prediction of BMV efficacy

  • Ratio of PA diastolic pressure / RA pressure predicts increase in MVA during BMV
  • What question do you want to ask ?

The Texas Sharpshooter

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Fananapazir and pacing for HOCM

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Visualize your results

Anscombe's quartet - Correlation 0.816

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Anscombe, Francis J. (1973) Graphs in statistical analysis. American Statistician, 27, 17–21.

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https://xkcd.com/1725/

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Sainani, K.L. (2020), How to Be a Statistical Detective. Journal of Injury, Function and Rehabilitation, 12: 211-215. 10.1002/pmrj.12305

A very important concept to understand

Homeopathic cure for cobra envenomation

  • A cure is prepared according to homeopathic principles
  • In a study the adverse outcomes are reduced compared to controls
  • Significantly lesser, p = 0.03 !

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https://xkcd.com/1132/

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Summary

  • Subgroup analysis
  • Multiple testing and comparisons
  • Regression towards the mean
  • Placebo effect
  • Bayesian and frequentist approaches