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That is the proportion of people with a negative test who have disease and will be falsely reassured by a negative test result generic claritin 10 mg visa. In eighteenth-century English order claritin 10 mg with amex, it said: “The probability of an event is the ratio between the value at which an expec- tation depending on the happening of the event ought to be computed and the value of the thing expected upon its happening cheap generic claritin canada. In simple language purchase claritin online now, the theorem was an updated way to predict the odds of an event happening when confronted with new information. In making diagnoses Bayes’ theorem and predictive values 263 in clinical medicine, this new information is the likelihood ratio. Bayes’ theorem was put into mathematical form by Laplace, the discoverer of his famous law. Its use in statistics was supplanted at the start of the twentieth century by Sir Ronald Fisher’s ideas of statistical signiﬁcance, the use of P < 0. We won’t get into the actual formula in its usual and original form here because it only involves another very long and useless formula. A derivation and the full mathematical formula for Bayes’ theorem are given in Appendix 5, if interested. Odds describe the chance that something will happen against the chance it will not happen. Probability describes the chance that something will happen against the chance that it will or will not happen. The odds of an outcome are the number of people affected divided by the number of people not affected. In contrast, the probability of an outcome is the number of people affected divided by the number of people at risk or those affected plus those not affected. Probability is what we are estimat- ing when we select a pretest probability of disease for our patient. Let’s use a simple example to show the relationship between odds and proba- bility. If we have 5 white blocks and 5 black blocks in a jar, we can calculate the probability or odds of picking a black block at random and of course, without looking. For every one black block that is picked, on average, one white block will be picked. In horse racing or other games of chance, the odds are usually given backward by convention. This means that this horse is likely to lose 7 times for every eight races he enters. Here we answer the ques- tion of how many times will he have to race in order to win once? The probability of him winning any 264 Essential Evidence-Based Medicine Black and white blocks in a jar Odds Probability 9/1 = 9 9/10 = 0. Probability = Odds/(1 + Odds) To convert probability to odds: Odds = Probability/(1− Probability) one race is 1 in 8 or 1/8 or 0. If he were a better horse and the odds of him winning were 1 : 1, or one win for every loss, the odds could be expressed as 1/1 or 1. Odds are expressed as one number to another: for example, odds of 1 : 2 are expressed as “one to two” and equal the fraction 0. These two expressions and numbers are the same way of saying that for every three attempts, there will be one successful outcome. There are mathematical formulas for converting odds to probability and vice versa. This says post-test odds of Bayes’ theorem and predictive values 265 Fig. We get the pretest probability of disease from our differential diagnosis list and our estimate of the possibility of disease in our patient. The pretest probability is converted to pretest odds and multiplied by the likelihood ratio. This results in the post-test odds, which are converted back to a probability, the post-test probability. The end result of using Bayes’ theorem when a positive test occurs is the post- test probability of disease. For a negative test, Bayes’ theorem calculates the probability that the person still has disease even if a negative test occurs. In this case, a urine culture was done on all the children and therefore was the gold standard. In the study population, the probability of a urinary tract infection in the children being evaluated in that setting was 0. Clinical evaluation of a rapid screening test for urinary tract infections in children. In other words, a positive urine dipstick has increased the prob- ability of a urinary tract infection from 0. Using the same example for a negative test: (1) Pretest probability and odds of disease are unchanged. In other words, a negative urine dipstick has reduced the probability of uri- nary tract infection from 0. Of course, it is important to recognize that the pretest probabil- ity of not having a urinary tract infection before doing any test was estimated at 90%. Should we do the urine culture or gold standard test for all children who have a nega- tive dipstick test in order to pick up the 6% who actually have an infection? This conundrum must be accurately communicated to the patient, and in this case the parents, and plans made for all contingencies. Choosing to do the urine cul- ture on all children with a negative test will result in a huge number of unneces- sary cultures. They are expensive and will result in a large expenditure of effort and money for the health-care system. Whether or not to do the urine culture depends on the consequences of not diagnosing an infection at the time the child presents with their initial symptoms. In the ofﬁce, it is not known if these unde- tected children progress to kidney damage. The available evidence suggests that there is no signiﬁcant delayed damage, that the majority of these infections will spontaneously clear or the child will show up with persistent symptoms and be treated at a later time. Connect these two points, and continue the line until the post-test probability is reached. For our example of a child with signs and symptoms of a urinary tract infection, the plot of the post-test probability for this clinical situation is shown in Fig. Calculating post-test probabilities using sensitivity and speciﬁcity directly The other way of calculating post-test probabilities uses sensitivity and speci- ﬁcity directly to calculate the predictive values. Not only are positive and nega- tive predictive values of the test related to the sensitivity and speciﬁcity, but they are also dependent on the prevalence of disease. The prevalence of disease is the 268 Essential Evidence-Based Medicine. Simply knowing the sensitivity and speci- ﬁcity of a test without knowing the prevalence of the disease in the population from which the patient is drawn will not help to differentiate between disease and non-disease in your patient. Clinicians can use pretest probability for disease and non-disease respectively along with the test sensitivity and speciﬁcity to calculate the post-test probability that the patient has the disease (post-test probability = predictive value). Calculating predictive values step by step (1) Pick a likely pretest probability (P) of disease using the rules we discussed in Chapter 20. Moderate errors in the selection of this number will not signiﬁ- cantly affect the results or alter the interpretation of the result. Let’s go back to the 156 young children with diarrhea whom we met at the end of Chapter 23. We have already decided that this study population does not represent all children with diarrhea who present to a general pediatrician’s ofﬁce. In this setting, the pediatrician estimates the prevalence of bacterial diarrhea is closer to 0. For every seven children treated with antibiotics thinking they had bacterial diarrhea, only one really needed it.      