{"id":225,"date":"2018-06-08T11:22:04","date_gmt":"2018-06-08T15:22:04","guid":{"rendered":"http:\/\/blog.uvm.edu\/tbplante\/?p=225"},"modified":"2020-09-16T09:48:07","modified_gmt":"2020-09-16T13:48:07","slug":"the-confusion-nomenclature-of-epidemiology-and-biostatistics","status":"publish","type":"post","link":"https:\/\/blog.uvm.edu\/tbplante\/2018\/06\/08\/the-confusion-nomenclature-of-epidemiology-and-biostatistics\/","title":{"rendered":"The confusion nomenclature of epidemiology and biostatistics"},"content":{"rendered":"\n

This should be more simple.<\/h2>\n\n\n\n

Epidemiology and biostatistics are awash with synonyms and each institution has its own preferred nomenclature to describe the same general concepts. I started this page as a central place to document the various terms by concept. I’ll plan on revisiting and updating over time.<\/p>\n\n\n\n

Regression<\/h2>\n\n\n\n

Fundamentals<\/h3>\n\n\n\n

You probably learned the fundamentals of regression in introductory algebra but may not realize it.  Remember drawing a graph from a slope-intercept equation? Draw a graph where Y is equal to 1\/4x plus 5<\/strong><\/em>. (Here is the relevant Khan Academy Algebra I video about this<\/a>.) You take the general equation:<\/p>\n\n\n\n

Y = mx + b<\/p>\n\n\n\n

…where Y is the y-axis, m is the slope of the line, and b is where the line crosses the y-axis. The equation you will write is:<\/p>\n\n\n\n

Y=1\/4x + 5<\/p>\n\n\n\n

…and you will draw:<\/p>\n\n\n\n

\"\"<\/figure>
\n

<\/p>\n<\/div><\/div>\n\n\n\n

This sounding familiar? When you do a linear regression, you do the same thing. Instead, you regress Y on X<\/strong><\/em>, or:<\/p>\n\n\n\n

Y = \u03b21<\/sub>x1<\/sub> + \u03b20<\/sub><\/p>\n\n\n\n

And fitting in the variables here, you want to figure out what a predicted cholesterol level will be for folks by a given age<\/em>. You would regress cholesterol level on age<\/strong><\/em>:<\/p>\n\n\n\n

Cholesterol level = \u03b21<\/sub>*Age + \u03b20<\/sub><\/p>\n\n\n\n

Here, x1<\/sub> is the slope of the line for age and \u03b20<\/sub> is the intercept on the Y-axis, essentially the same as the b in Y=mx+b. When you run a regression in Stata, you type<\/p>\n\n\n\n

regress y x<\/pre>\n\n\n\n
or here,<\/p>\n\n\n\n
regress cholesterol age<\/pre>\n\n\n\n
Let’s say that Stata spits out something like:<\/p>\n\n\n\n
      Source |  xxxxxxxxxxxxxxxxxxxxxxxxxxxx  \n-------------+------------------------------    \n       Model |  xxxxxxxxxxxxxxxxxxxxxxxxxxxx   \n    Residual |  xxxxxxxxxxxxxxxxxxxxxxxxxxxx    \n-------------+------------------------------    \n       Total |  xxxxxxxxxxxxxxxxxxxxxxxxxxxx   \n\n------------------------------------------------------------------------------\n  cholesterol|      coeff       se         t <\/b>    P>|t|    [95% Conf. Interval]\n-------------+----------------------------------------------------------------\n         age |     0.500     xxxxxxxx    xxxxx   0.000     0.4000      0.60000\n       _cons |     100       xxxxxxxx    xxxxx   0.000     90.000      110.000\n------------------------------------------------------------------------------<\/pre>\n\n\n\n
The \u03b21 <\/sub>coefficient for age is 0.5. The intercept, or \u03b20<\/sub> is 100. You would interpret this as cholesterol level = 0.5*age in years + 100<\/strong><\/em>. You could plot this using your Algebra 1 skills.<\/p>\n\n\n\n
Cholesterol = 0.5*age + 100<\/p>\n\n\n\n
Or you can substitute in actual numbers. What is the predicted cholesterol at age 50? Answer: 125.<\/p>\n\n\n\n
If you want to make it more complex and add more variables to explain cholesterol level, it’s no longer a straight line on a graph, but the concept is the same. A multiple linear regression<\/strong><\/em> adds more X variables. You can figure out what a predicted cholesterol level will be for folks by age, sex, and BMI.<\/em> You would regress cholesterol level on age, sex, and BMI. <\/strong><\/em>(You would code sex as 0 or 1, like female = 1 and male = 0.)<\/p>\n\n\n\n
Y =  \u03b21<\/sub>x1<\/sub> + \u03b22<\/sub>x2<\/sub> + \u03b23<\/sub>x3<\/sub> + \u03b20<\/sub><\/p>\n\n\n\n
Or,<\/p>\n\n\n\n
Y =  \u03b21<\/sub>*Age + \u03b22<\/sub>*Sex + \u03b23<\/sub>*BMI + \u03b20<\/sub><\/p>\n\n\n\n
You get the idea.<\/p>\n\n\n\n
Names of Y and X<\/h3>\n\n\n\n
This is what irks me. There are so many synonyms for Y and X variables. Here is a chart that I’ll update over time with synonyms seen in the wild.<\/p>\n\n\n\n
 Y<\/th>=<\/th>x<\/th><\/tr>
Dependent<\/td> <\/td>Independent<\/td><\/tr>
Outcome<\/td> <\/td>Predictor<\/td><\/tr>
 <\/td> <\/td>Covariate<\/td><\/tr>
 <\/td> <\/td>Factor<\/td><\/tr>
 <\/td> <\/td>Exposure variable<\/td><\/tr>
 <\/td> <\/td>Explanatory variable<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"
This should be more simple. Epidemiology and biostatistics are awash with synonyms and each institution has its own preferred nomenclature to describe the same general concepts. I started this page as a central place to document the various terms by concept. I’ll plan on revisiting and updating over time. Regression Fundamentals You probably learned the … Continue reading The confusion nomenclature of epidemiology and biostatistics<\/span><\/a><\/p>\n","protected":false},"author":4473,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[502558],"tags":[],"class_list":["post-225","post","type-post","status-publish","format-standard","hentry","category-epidemiology-and-biostatistics"],"_links":{"self":[{"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/posts\/225","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/users\/4473"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/comments?post=225"}],"version-history":[{"count":6,"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/posts\/225\/revisions"}],"predecessor-version":[{"id":578,"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/posts\/225\/revisions\/578"}],"wp:attachment":[{"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/media?parent=225"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/categories?post=225"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.uvm.edu\/tbplante\/wp-json\/wp\/v2\/tags?post=225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}