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  • 1.  Effect Size Measure for Single Proportion

    Posted 02-23-2021 08:57
    Dear Colleagues:

    Does anyone know of an effect size measure for a single proportion? I know of a metric to compare two proportions, but not a single proportion. Example, adding radiation treatment to a particular surgical procedure increases the cost by 30%. I am trying to find an effect size for 30% or .30.

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    Brandy Sinco, BS, MA, MS
    Statistician Senior
    Michigan Medicine
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  • 2.  RE: Effect Size Measure for Single Proportion

    Posted 02-24-2021 11:23
    A proportion is a count divided by another count, where the numerator is a subset of the denominator. What you have is a ratio of two means, the average cost after adding a treatment divided by the average cost before adding that treatment (minus one and then times 100%). You know it is not a proportion because it can be negative or greater than one hundred percent. There are several ways you can compute an effect size here, but any approach would require a standard deviation of something.

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    Stephen Simon, blog.pmean.com
    Independent Statistical Consultant
    P. Mean Consulting
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    Original Message


  • 3.  RE: Effect Size Measure for Single Proportion

    Posted 02-24-2021 13:39
    Is the effect size measure that you mention for comparing two proportions based on binomial proportions? If so, your cost example is something different. You may already have stated the measure of effect: the percentage increase in cost.

    To give more-detailed suggestions, I would like to know more about the context --- the analysis from which the effect arises. I could imagine a clinical trial in which one group of patients receives radiation and another does not, with cost as one of the outcome variables. A basic comparison of cost would yield an effect in dollars (say). If an analysis of cost in a logarithmic scale is more appropriate, the difference on the log scale translates into a ratio on the dollar scale, and hence into a percentage increase (or decrease).

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    David Hoaglin
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    Original Message


  • 4.  RE: Effect Size Measure for Single Proportion

    Posted 02-24-2021 17:15
    Brandy,
    In the example you present, it sounds like the proportion can easily be greater than 100%. If that's true, then maybe we shouldn't think of it as a proportion. Maybe instead, we should think of it as either a difference between two conditions that's been normalized to one of the conditions, or else as a "ratio minus one". Mathematically, those two possibilities are the same, but interpretationally, they could be different, and could lead to different effect-size measures.

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    Eric Siegel, MS
    Biostatistics Project Manager
    Department of Biostatistics
    Univ. Arkansas Medical Sciences
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    Original Message


  • 5.  RE: Effect Size Measure for Single Proportion

    Posted 02-25-2021 08:25
    Thanks to everyone who offered their insight on my effect size question.  I originally suggested Cohen's d to my co-workers to quantify the difference between mean surgical procedure costs.  When they asked me how to quantify the ratio between means, my response, as usual was that if they thought they needed something, then I would find a way to do it.  

    After reading the comments, I still think Cohen's d is the best solution, but also the % change in cost can be added as an additional measure.  There is no need for an effect size for the % change in cost, because describing the % change acts like an effect measure by quantifying the difference without being dependent on sample size.

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    Brandy Sinco, BS, MA, MS
    Statistician Senior
    Michigan Medicine
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    Original Message


  • 6.  RE: Effect Size Measure for Single Proportion

    Posted 02-25-2021 15:48
    Hey Brandy, 

    Are you looking for something like ROI? 

    You could probably look at "Cost of success" and calculate that by taking the cost of treatment times the probability the surgery was successful. 

    Admittedly, I'd probably use a regression method to find how effective radiation really is. Then use that to determine if it is cost effective. 

    Something else to keep in mind is, "Can the patient afford it?" When my mom was dying from cancer, we could have spent $50,000 to get her another 6 mos of life. We couldn't afford that. 


    BTW, this is giving me an idea for a problem to give my intro to stats students, compare ROI and real costs. Thanks!

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    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
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    Original Message


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