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  • 1.  Prevalence/Probbaility/Relative Frequency (Apologies for repeated posting)

    Posted 07-06-2017 09:13

    Dear Colleagues,

     

    I have always thought of a prevalence estimate, such as that obtained from a cross-sectional study that gathers data over a period of time, is a type of relative frequency and ,as such, can be regarded as a probability.  

     

    In teaching, I need to introduce some medical students to probability in epidemiology and have come across material that indicates that prevalence is NOT a probability.  I think this may apply if we a speaking  prevalence  estimated as the proportion of  individuals in a population that has disease at a single point in time (point) – such as mid-year prevalence estimate. 

     

    Is there "room" for accepting both views  - point prevalence is not a probability but period prevalence is - or is it that any prevalence estimate, regardless of how obtained is NOT a probability?   I would like your feedback.

     

    Regards

     

    Novie

     

     

    ************************************************

    Novie Younger-Coleman PhD

    Statistician/Senior Lecturer

    Caribbean Institute for Health Research

    (formerly Tropical Medicine Research Institute)

    University of the West Indies

    Kingston 7

    Jamaica

    Tel: 876 977 0746 or 927 2471 ext 227

    Fax: 876 927 2984

    e-mail: novie.younger@uwimona.edu.jm

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    THEME: Statistics for Success: Ethics, Data Security and Quality

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  • 2.  RE: Prevalence/Probbaility/Relative Frequency (Apologies for repeated posting)

    Posted 07-07-2017 11:19
    I have recently heard this (that prevalence is not random) stated by competent people, so it's not inherently ridiculous. However, I believe it is confused. 

    Probability is a statement about the future. A reported prevalence refers to the past, and is fixed -- as is an observed count of heads in a sequence of coin flips.  The reported prevalence in one area can tell us something about the prevalence in a different area, however, and that unknown future value should be stated with probabilistic confidence limits. The future prevalence in the same area is also random, but not in the same way:  next year's prevalence in the same location will be based mostly on the same individuals, different only due to deaths and incident cases, so the usual Poisson or binomial confidence limits are not appropriate.  It all depends on what future we wish to describe. 

       Peter Wollan



    Original Message


  • 3.  RE: Prevalence/Probbaility/Relative Frequency (Apologies for repeated posting)

    Posted 07-10-2017 11:51
    Should probabilistic reasoning only be used for the future? What about for instance phylogenetic trees in paleontology?

    ------------------------------
    Tore Wentzel-Larsen
    Norwegian Centre for Violence and Traumatic Stress Studies
    Regional Center for Child and Adolescent Mental Health, Eastern and Southern Norway



    Original Message


  • 4.  RE: Prevalence/Probbaility/Relative Frequency (Apologies for repeated posting)

    Posted 07-12-2017 09:34
    Tore brings up a good point. There is often confusion involving the words "prediction" and "future". The everyday meaning of the word "prediction" refers to the future, but the statistical meaning includes things like prediction to an out-of-sample case. This idea is used in cross-validation methods, where the data at hand are divided into a "modeling building" sample and a "validation" sample. Similarly, as Tore points out, statistical inference can be used to estimate things like phylogenetic trees that refer to "past events".

    ------------------------------
    Martha Smith
    University of Texas
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    Original Message


  • 5.  RE: Prevalence/Probbaility/Relative Frequency (Apologies for repeated posting)

    Posted 07-07-2017 11:19
    I went back to Fleiss, Statistical Methods for Rates and Proportions, 2nd ed. He said on page 1, "In this book, the terms probability, relative frequency, proportion, and rate are used synonymously." Point prevalence is a proportion, the number of subjects with the disease divided by the sample number.   It is standard practice to treat this as a probability.

    However I understand the other point of view-not to treat prevalence as a probability.  The word rate, and the term 'case rate' as a synonym for prevalence,  might refer to something that is greater than 1.  For example it might include multiple events per a person, which could lead to a rate that is not a proportion.  Or it could be used it the temporal sense, rate per hour,  So for the purposes of clarity, these newer books might want to make a distinction.

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    Georgette Asherman
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    Original Message


  • 6.  RE: Prevalence/Probbaility/Relative Frequency (Apologies for repeated posting)

    Posted 07-07-2017 17:12
    ​The prevalence is equivalent to the probability that a patient about whom you know absolutely nothing has the disease.   "Absolutely" would include not knowing age, ethnicity, sex, etc.

    ------------------------------
    Emil M Friedman, PhD
    emilfriedman@gmail.com
    http://www.statisticalconsulting.org
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    Original Message


  • 7.  RE: Prevalence/Probbaility/Relative Frequency (Apologies for repeated posting)

    Posted 07-07-2017 17:13
    ​The prevalence is equivalent to the probability that a patient about whom you know absolutely nothing has the disease.   "Absolutely" would include not knowing age, ethnicity, sex, etc.  We're also assuming that the prevalence has not changed since it was last measured and that its estimate was unbiased.

    ------------------------------
    Emil M Friedman, PhD
    emilfriedman@gmail.com
    http://www.statisticalconsulting.org
    ------------------------------

    Original Message


  • 8.  RE: Prevalence/Probbaility/Relative Frequency (Apologies for repeated posting)

    Posted 07-10-2017 09:31
    W. Edwards Deming would identify two distinct ways in which a prevalence estimate is not exact:

    1. Enumerative. There is doubt about what the current estimate is. This includes, but is not limited to, sampling error. Even a 100% census is subject to error. No two censuses will result in the same counts.

    Analytic. The processes underlying the estimates evolve dynamically over time. Current estimates represent reliable estimates of future results only if the underlying process is stable, i.e. If it's variation is approximately random. Prediction for nonstable processes requires an understanding of the underlying process dynamics.

    Jonathan Siegel
    Associate Director Clinical Statistics

    Sent from my iPhone


    Original Message


  • 9.  RE: Prevalence/Probbaility/Relative Frequency (Apologies for repeated posting)

    Posted 07-11-2017 13:32
    Nice points. I particularly like "This includes, but is not limited to, sampling error. Even a 100% census is subject to error". This is interestingly related to the article by Michael Höhle (Rank uncertainty) in Significance June 2017 where confidence intervals are computed for newborn first name frequencies even if the frequencies of names in the whole population are available. Actually I think the prefix "super" in "super-population models" is superfluous. A population model is not a larger population but, to cite Höhle's article, "a probabilistic model to describe our understanding of how the observed quantities in the specific population came about by random variables".

    ------------------------------
    Tore Wentzel-Larsen
    Norwegian Centre for Violence and Traumatic Stress Studies
    Regional Center for Child and Adolescent Mental Health, Eastern and Southern Norway]
    ------------------------------

    Original Message


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