Effect Estimation

• Odds ration makes regression analysis easier, but relative ratio is more intuitive.
• Odds are defined as $$\frac{p}{1-p}$$ if $$p$$ is the probability of an event
  • if the probability is 50% then it's $$\frac{0.5}{1-0.5}$$ which is 50-50 or even odds.

• Or it can be a relative risk: the likelihood of responding if given

treatment would be $$\frac{a}{a+b}.$$ So the relative likelihood of responding if given the treatment would be $$\frac{c}{c+d}.$$ So the relative likelihood of responding if given the treatment would be $$\frac{\frac{a}{a+b}}{\frac{c}{c+d}}$$

• People use the term effect size to mean standardized effect size.
• The standardized effect size, called Cohen's d, is the actual effect size described above (such as a mean number) divided by the standard deviation (the measure of variability).
• Cohen's d makes a number between 0 to 1 or higher
• 0.4 or lower is small effect size
• 0.4 to 0.7 is medium effect size
• greater than 0.7 is large effect size
• Nonetheless, Cohen's d is especially useful in research using continuous measures of outcome (such as psychiatric rating scales) and is commonly employed in experimental psychology research.

• Number needed to treat or harm is 1 divided by the absolute risk reduction or risk increase.
• example: If 50% of people responded to a drug and 30% responded to placebo the absolute risk reduction would be 20%. The number needed to treat would be 1/0.2 which is 5.

• NNT of 5 or less is very large.
• NNT of 5-10 is large.
• NNT of 10-20 is medium.
• NNT of 20-50 is small.
• NNT of greater than 50 is very small.

• NNH is used to determine side effects.
• formula is the same as NNT.

• Jerzy Neyman who created hypothesis testing also advanced confidence intervals approach.
• Rather Neyman saw it as a conceptual construct that helped us appreciate how well our observations have approached reality. As Salsburg puts it: “the confdence interval has to be viewed not in terms of each conclusion but as a process. In the long run, the statistician who always computes 95 percent confdence intervals will fnd that the true value of the parameter lies within the computed interval 95 percent of the time. Note that, to Neyman, the probability associated with the confdence interval was not the probability that we are correct. It was the frequency of correct statements that a statistician who uses his method will make in the long run. It says nothing about how “accurate” the current estimate is.” (Salsburg, 2001; p. 123.)

• “The CI uses mathematical formulae similar to what are used to calculate p-values (each extreme is computed at 1.96 standard deviations from the mean in a normal distribution), and thus the 95% limit of a CI is equivalent to a p-value = 0.05. Tis is why CIs can give the same information as p-values, but CIs also give much more: the probability of the observed findings when compared to that computed normal distribution.”

• prospective is better. Framingham and STEP-BD are good prospective cohorts.
• STEP-BD cost 20 million dollars

• cheap and can be very useful, but has limitations.

1. Limitations

   1. Recall bias

      The researchers found that patients recalled 80% of treatments received in the prior year, which may not seem bad; but by 5 years, they only recalled 67% of treatments received (Posternak and Zimmerman, 2003).