Intro to Probabiltiy theory notes for Elements Class.pptx

Given a negative screening test or the absence of a

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Given a negative screening test (or the absence of a symptom), what is the probability that the subject doesn’t have the disease?
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44 Table-2 Sample of n subjects (where n is large) cross- classified according to disease status and screening test result. Test result Present (D) Absent (D´) Total Positive(T) a b a+b Negetive (T ´ ) c d c+d Total a+c b+d n
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45 Sensitivity of a Test (Probability of True positive) It is the probability of a positive test result ( or presence of the system) given the presence of the disease. Symbolically this is P(T|D) = a/(a+c) Specificity of a Test (Probability of True Negative) It is the probability of a negative test result (absence of the system) given the absence of the disease. Symbolically estimate of Specificity is given by the conditional probability P(T ´ |D ´ ) = d/(b+d)
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46 The Predictive Value of a Positive Test The predictive value positive of a screening test (or symptom) is the probability that a subject has the disease given that the subject has a positive screening result (or has the symptom). Symbolically, this is given by the conditional probability P(D|T) = a/(a+b) Predictive Value of a Negative test The predictive value negative of a screening test (or symptom) is the probability that a subject doesn’t have the disease given that the subject has a negative screening test result (or doesn’t have the symptom). Symbolically, this is given by the conditional probability P(D ´ |T ´ ) = d/(c+d)
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47 Probability of false negative : It is the probability that the screening test is negative given that the subject has disease. P(T´|D) = c/ (a + c). Probability of false positive : It is the probability that the screening test is positive given that the subject does not have disease. P(T|D´) = b/(b+d).
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48 Some Theoretical Probability Distribution The relationship between the values of a random variable and the probability of their occurrence summarized by means of a a probability distribution. It may be expressed in the form of a table, a graph or a formula. Knowledge of probability distribution of a random variable provides the researchers with a powerful tool for summarizing and describing a set of data and for reaching conclusion about a population on the basis of sample .
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49 Definition The probability distribution of a discrete random variable is a table, graph, formula, or other device used to specify all possible values of a discrete random variable along with their respective probabilities. Example: Prevalence of prescription and nonprescription drug use in pregnancy among women delivered at a large eastern hospital. N=4185 No of drugs 0 1 2 3 4 5 6 7 8 9 10 12 f 1425 1351 793 348 156 58 28 15 6 3 1 1
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50 Construct a probability distribution table. What is the probability that a randomly selected women who use 3 drugs?
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