Understanding the Role of Probability in Screening and Inference

This essay elucidates the role of probability in various contexts, primarily focusing on its application in screening tests and statistical inferences. It begins by defining probability and its fundamental characteristics, such as the sum of probabilities for an event and its complement equaling one. The essay then transitions to discussing screening tests, highlighting their importance in detecting disease markers and the significance of positive and negative predictive values, which are determined using conditional probabilities. The influence of specificity, sensitivity, and disease prevalence on positive predictive values is also examined. Furthermore, the essay emphasizes the use of probability models in statistical inferences, defining these models as mathematical representations of random phenomena and explaining how probabilities are assigned to different outcomes within a sample space. The essay concludes by underscoring the integral role probability plays in both medical testing and statistical analysis.

RUNNING HEADER: THE ROLE OF PROBABILTY 1
The Role of Probability
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The Role of Probability 2
Probability expresses the belief or knowledge than an event will happen or it has happened.
According to Fisz & Bartoszynski (2018), one of the characteristics of probability is that the sum
of the probabilities of an event and its complementary is one. On the other hand, the probability
of an impossible event is zero. Consequently, the probability of the union of two events is the
sum of their probabilities minus the probability of their intersection and if an event is a subset of
another event, then the probability is less than or equal to it.
Screening tests are laboratory tests which are used in detecting if a particular maker of a specific
disease is present or not. Such tests include routine EKGs, blood pressure tests, mammograms,
breast exams, routine blood, and urine tests, questionnaires regarding behaviors and risk factors
among others. According to Kollar et al., (2015) when conducting a screening test, the test needs
to provide an advantage in distinguishing between the presence or absence of a disease maker
under study. If it does exist, the screening test needs to demonstrate that early identification and
treatment of the disease will result in some improvement. After screening is done, the patient
would be interested in knowing the probability of actually having a disease if the test is positive
or the probability of not actually having the disease if the results are negative. Such questions are
the ones being referred to as positive predictive value if positive or negative predictive value of
the screening test if negative. Answering of the predictive values is done through the use of
conditional probabilities. The positive predictive values of screening tests are influenced by the
specificity, sensitivity and the prevalence of the disease in the population being screened. It can
be noted that positive and negative predictive values depend on a disease prevalence since they
cannot be estimated in control design cases.
Statistical inferences make the use of probability models. Probability models are mathematical
representations of phenomena which are random. A probability model is defined by its sample

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space, events within the sample space and the probabilities connected with each event. Hence, if
there are k possible outcomes (sample space) for a phenomenon with each equally likely to
happen (events within the sample space), then the individual outcome has a probability of 1/k
(probability connected with each event).

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Reference:
Fisz, M., & Bartoszyński, R. (2018). Probability theory and mathematical statistics (Vol. 3). J.
Wiley.
Kollár, D., McCartan, D. P., Bourke, M., Cross, K. S., & Dowdall, J. (2015). Predicting acute
appendicitis? A comparison of the Alvarado score, the Appendicitis Inflammatory
Response Score and clinical assessment. World journal of surgery, 39(1), 104-109.