Differences

This shows you the differences between two versions of the page.

--- ebm:effect_estimation [2020/07/20 01:07] – dhawann
+++ ebm:effect_estimation [2020/07/20 01:40] (current) – [Odds ratio] dhawann
@@ Line 1: / Line 1: @@
+<html><script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
+<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script></html>
 ====== Effect Estimation ======
 ===== Odds ratio =====
-  * Better for regression analysis, but relative ratio is more intuitive.
+  * 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
+  * Odds are defined as $$\frac{p}{1-p}$$ if $$p$$ is the probability of an event
-    * if the probability is 50% then it's $ which is 50-50.
+    * if the probability is 50% then it's $$\frac{0.5}{1-0.5}$$ which is 50-50 or even odds.
 ===== Relative ratio =====
@@ Line 11: / Line 14: @@
   * 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 (a/a+b) / (c/c+d).
+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 $$\frac{\frac{a}{a+b}}{\frac{c}{c+d}}$$
 ===== Effect size =====
   * People use the term effect size to mean standardized effect size.
-  * The standardized effect size, called Cohen¡¯s d, is the actual 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).
-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
+  * 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.
-===== NNT and NNH =====
+===== Number Needed to Treat and Number Needed to Harm =====
-==== Forumula ====
+==== Formula ====
   * 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
+  * 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.
-absolute risk reduction would be 20%. The number needed to treat would be 1/0.2 which is 5.
 ==== NNT ====
@@ Line 51: / Line 49: @@
   * 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
+  * 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." [[https://www.amazon.com/Lady-Tasting-Tea-Statistics-Revolutionized/dp/0805071342|(Salsburg, 2001; p. 123.)]]
-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."
@@ Line 70: / Line 66: @@
 <HTML><ol></HTML>
 <HTML><li></HTML><HTML><p></HTML>Recall bias<HTML></p></HTML>
-<HTML><p></HTML>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).<HTML></p></HTML><HTML></li></HTML><HTML></ol></HTML>
+<HTML><p></HTML>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 ([[https://www.sciencedirect.com/science/article/abs/pii/S0165032702000496|Posternak and Zimmerman, 2003]]).<HTML></p></HTML><HTML></li></HTML><HTML></ol></HTML>
 <HTML></li></HTML><HTML></ol></HTML>