# Understanding Medical Research: course notes pt. 2

## 06 - Averages by other names

Shakespeare paraphrased: would an average by any other name give an accurate representation of your data? Blackjack winnings histogram: relative frequency of relative outcomes of repeated $10 rounds. Mean: -$3, SD= +-$85 (Spread ~200). Studies almost never show historgrams.

Abnormal data: mean and SD misleading. Enter the median. Mean US Income 2014 $72k, Median income $53k. Measure of dispersion: Standard Deviation for normal data, interquertile range for non-normal.

If authors use means and SD, implies normal data. Medians and IQR? Non-normal data.

## 07 - Secret Sauce

Two burlap sacks - 10k one with gold, and one with chocolate and one minute. Sample ten coins? Sac A: 9/10 gold coins, Sac B: 1/10 choco coins. Or 6/10 ration? Confidence falls.

Sampling is at the root of all medical studies. Sampling is uncertain. Margin of Error? As single study may miss the reality a bit. 0.98 / square of sample size. We can't repeat 1000 times, though. 10 flips: margin of error 31%, 1000 flips, 3,1%.

Hot tea and esophageal cancer - findings may not matter, even if true. Non-random sampling. BMI from Salt Lake City. Is this a random sample? Criteria may reduce study group into a non-random sample population.

## 08 - Statistics as an onion 🧅

Lot of layers. Walk from "counts" to "risk ratios". Deno🧅minators make all the difference in medical studies. Some jargon. Link.

## 06 - Averages by other names

Shakespeare paraphrased: would an average by any other name give an accurate representation of your data? Blackjack winnings histogram: relative frequency of relative outcomes of repeated $10 rounds. Mean: -$3, SD= +-$85 (Spread ~200). Studies almost never show historgrams.

Abnormal data: mean and SD misleading. Enter the median. Mean US Income 2014 $72k, Median income $53k. Measure of dispersion: Standard Deviation for normal data, interquertile range for non-normal.

If authors use means and SD, implies normal data. Medians and IQR? Non-normal data.

## 07 - Secret Sauce

Two burlap sacks - 10k one with gold, and one with chocolate and one minute. Sample ten coins? Sac A: 9/10 gold coins, Sac B: 1/10 choco coins. Or 6/10 ration? Confidence falls.

Sampling is at the root of all medical studies. Sampling is uncertain. Margin of Error? As single study may miss the reality a bit. 0.98 / square of sample size. We can't repeat 1000 times, though. 10 flips: margin of error 31%, 1000 flips, 3,1%.

Hot tea and esophageal cancer - findings may not matter, even if true. Non-random sampling. BMI from Salt Lake City. Is this a random sample? Criteria may reduce study group into a non-random sample population.

## 08 - Statistics as an onion 🧅

Lot of layers. Walk from "counts" to "risk ratios". Deno🧅minators make all the difference in medical studies. Some jargon.

Coffee machine user sampling, for 1000 cups. Men 600, women 400. But what is the userbase size? A count, a ratio, to ratio of ratios - layers.

Homicide rate in 2016, by count: California 1930, Texas 1459, Illinois 941. Is California the most dangerous? - Whats the denominator, which percentage? Rate: per 100k? Louisiana 11.8, Missouri 8.8, Alabama 8.4. Contextualizeed ratio.

Comparison of Hospital Mortality .., Tsugawa 2017, JAMA IM. Female vs Male physicians: 2029 vs 4549 deaths. Negative outcomes table: 10.82 vs 11.49. Risk Difference: -0.67 less deaths for female physicians. Note: non-randomized trial.

Jargon check. Relative risk: Risk in group A/Risk in group B. Hazard ratio: rate in group A/rate in group B. Odds Ratio: odds in group A/odds in group B. Risk vs Odds? Risk: i out of N, a / a+b. Odds: N out of N, a/b. (sic? proportion of likelihood that event won't occur).

If 10/1000 get flu, risk is 1%. Odds of flu is then 10:990, 1.01%.

Effects measured as ratios of ratios. From counts. Know your denominator.

## 09 - Biggest Secret in Medicine

The difference between relative risk and absolute risk difference. Number Needed To Treat - NNT: application and the ethical implications.

Casino with $10000 dollar slot machine pull. 1,1 M€/100 pulls VS 1,1 M€/200 pulls (average chance). The Lipitor marketing bullshit claims +30% reduction in risk. Relative Risk: lipitor group: 2 heart attacks, placebo group 3 heart attacks = 2/3 = 0.66. Absolute risk difference: 3% - 2% = 1%.

Expressing Absolute Risk: 1/Absolute Risk Reduction. The number of people you need to treat with a drug so that one heart attack is prevented. For lipitor 1/0.01 = 100 people.

What's a good NNT? 42 people after a major heart attack for aspirin. 30 people after heart attack with mediterranean diet. 217 smokers with a CT scan to prevent death.

So, the Secret? If I'm treating 100 people to save 1 life - unknown which one is treated, 99 people treated unnecessary. Doctors seek to save lives, treat disease. The big secret is that most medications may not help you - the chances may be slim, as NNT -number demonstrates.

Talk to your doctor. Look for NNT -number in medical articles.

Relative Risk is for dramatic effect in marketing. NNT is the inverse of the Absolute Risk Difference. NNT vary, fact is most people may not directly benefit from most interventions.

## 10 - P-value Power & Problems

How to decide if a study is somehow significant? Common p-value misinterpretations. And how to really decide on significance. Link.

The Mysterious Quarter? Heads, heads, heads, heads... suspicious? 12 heads of Washington in a row? 0.5 probability for one heads, 0.004 to get 8 heads in a row.

Statistical significance is arbitrarily defined as p-value < 0.05. Not the same as clinical significance or effect. Do you want a car with 160 or 161 mph top speed?

How weird are your results? F.ex. how low is the probability of similar random event? Coin flips? 10 flips, 6 heads = 0.75 p-value. If the coin is a "normal coin".

Null hypothesis. And the Alt Hypotheis: dice are loaded, the thing is weird. Average surgeon vs internal medicine body mass? Out of 100, internal medicine 175 pounds, surgeon 180 pounds. If average doctor assumed to weigh the same? t = X1-X2 / Sp SQR(2/n).

Be careful! If weird results are to only occur 3% of the time - not the same as 97% certain there will not be weird results.

Related: Lady Tasting Tea by math et al https://www.youtube.com/watch?v=I9KsLCc-eiQ

Related: H.B. Mann's book https://archive.org/details/B-001-002-167/page/n7/mode/2up

Related; A. Ramdas on Fishers experiment https://www.youtube.com/watch?v=mGFMbS45cj8