BIOSTATISTICS

Editor's Notes

• #15: Descriptive Statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. With descriptive statistics you are simply describing what is, what the data shows. Inferential Statistics investigate questions, models and hypotheses. In many cases, the conclusions from inferential statistics extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population thinks. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what's going on in our data.
• #17: Researchers focus on probabilities (often called p values) that fall lower end of continum. The reason for this is partly intuitive and partly historic.
• #18: Researchers focus on probabilities (often called p values) that fall lower end of continum. The reason for this is partly intuitive and partly historic.
• #19: Given a underlying theatrical structure, a representative sample, an appropriate research design, researcher. can test hypothesis. We test to see whether data support the hypothesis. Alterative hypothesis is called research hypothesis
• #20: Given a underlying theatrical structure, a representative sample, an appropriate research design, researcher. can test hypothesis. We test to see whether data support the hypothesis. Alterative hypothesis is called research hypothesis
• #21: Given a underlying theatrical structure, a representative sample, an appropriate research design, researcher. can test hypothesis. We test to see whether data support the hypothesis. Alterative hypothesis is called research hypothesis
• #39: As noted, calculation of sensitivity and specificity, and therefore calculation of predictive value, requires a way to determine authoritatively who has and does not have the condition of interest. This “gold standard” is typically the most definitive diagnostic procedure (for example, the definitive diagnosis of cancer is generally based on microscopic examination of a tissue specimen), the best available laboratory test (for example, a polymerase chain reaction (PCR) test for the actual virus, as opposed to a test for antibody to the virus), or a comprehensive clinical evaluation, where there is no definitive laboratory test. For example, the best diagnosis for arthritis might be obtained through an examination.
• #40: Data for estimating sensitivity and specificity are typically displayed in a 2 x 2 table that classifies people according to their disease status and test results. The above table has the True disease status along one dimension, with a column for cases and a column for non-cases, and the Test results on the other dimension, with a row for people who tested positive and a row for people who tested negative. In the top left-hand corner – the “a” cell – are the people who have the disease and whose test came up positive. They are “true positives”, cases who were correctly classified. In the lower right-hand corner – the “d” cell – are the people who do not have the disease and whose test came up negative. They are “true negatives”, non-cases who were correctly classified. The other two cells, b and c, contain people who were misclassified. Non-cases who nevertheless received a positive test are often called “false positives”, and cases who received a negative test are often called “false negatives”, but these terms are not always employed with these meanings. If cell “c” is in the lower left-hand corner of the table, then the left-hand column – the cases – has a total of (a + c) people, and we we can write the formula for sensitivity as a / (a+c): the number of cases correctly classified divided by the total number of cases. Similarly, the formula for specificity is d / (b+d): the number of correctly classified non-cases divided by the total number of non-cases.
• #41: If a population has a total of 200 cases, and the test correctly identifies 140 of them as cases, then a = 140, a+c = 200, and the sensitivity is: a / (a+c) = 140 / 200 = 70% If there are 20,000 people without the disease, and the test correctly classifies 19,000 of them as non-cases, then d = 19,000, b+d = 20,000, and the specificity is: d / (b+d) = 19,000 / 20,000 = 95%. As is often the case for a rare disease, even with what seems like a high specificity (95%), the number of false positives can easily exceed the number of true positives. This observation brings us to the concept of predictive value.
• #42: Sensitivity and specificity tell us what happens to cases and non-cases, respectively. However, appropriate interpretation of the results of a test – both screening tests and diagnostic tests – makes use of another concept that is very important for both the epidemiologic and the clinical perspectives, predictive value. Predictive value is also a probability of correct classification, but here the starting point, the denominator for the probability, is the way people have been classified by the test. There are two types of predictive value – predictive value of a positive test and predictive value of a negative test. Predictive value tells us the probability that the test was correct. This is obviously a key question for the clinician (and the patient), since we generally do not know whether someone is a case or not, but we do know whether the person tests positive or negative. In clinical epidemiology, the prevalence of a disease is referred to as the “prior probability” or “pretest probability”, since it is our initial estimate of the probability that the condition is present. Predictive values are referred to as posterior or posttest probabilities, since they provide estimates of probability that take into account the result of the screening or diagnostic test. The relation of the posttest and pretest probabilities indicates the informativeness of the test.
• #44: The table for examining predictive value is the same as that for sensitivity and specificity. Instead of using the total numbers of cases and non-cases, though, predictive value involves the total number of people with a positive test and the total number with a negative test. Positive predictive value, abbreviated PPV or PV+, is the proportion of all people with positive tests who truly have the condition – a / (a+b) in the above table. Negative predictive value (NPV or NP-) is the proportion of all people with negative tests who truly do not have the condition – d / (c+d) in the above table.
• #45: Using the same numbers as in our example for calculating sensitivity and specificity, we find that the predictive value of a positive test (PPV) is only 140 / 1,140 = 12.3%. The predictive value of a negative test (NPV) is 19,000 / 19,060 = 99.7%. Although the NPV is very high, that is not such an impressive result in this population, since the prevalence of the condition is only 200 / 20,200, which is not quite 1%. That means that if we select a person at random from the population, there is a 1% probability that the person will be a case (the pretest probability). The probability that a person who tests positive actually is a case is 12.3% (the posterior probability), so the test raises the probability substantially. On the other hand, the probability that a person randomly selected from the population does not actually have the condition is already 99%, so the additional information that a person tested negative cannot shift that estimate significantly. However, the PPV of 12.3% poses a dilemma. Of the 1,140 people who tested positive, the vast majority – 87.7% – are falsely positive. They do not have the disease. Thus, for every person whose disease is detected and who may therefore be helped, 7 people who do not have the disease and will therefore not derive any benefit will undergo a diagnostic workup that may be costly, uncomfortable, and possibly harmful. This tradeoff is the dilemma in population screening for a rare disease.
• #46: The above table illustrates the relation among positive predictive value (PPV), sensitivity, specificity, and prevalence of the condition. Note that sensitivity and specificity are being regarded as properties of the test, unaffected – in principle – by the rarity of the condition. In contrast, prevalence is a property of the population in which the test being screened, and PPV shows the result of applying a test with given sensitivity and specificity to a population with a given prevalence. For sensitivity held constant at 70% and specificity held constant at 95%, PPV is only 1.4% for a disease with a prevalence of 1 in 1,000, but rises to over 40% when the prevalence is 5%. This table illustrates the difference between using a test for screening and for diagnosis. Using the test in the general population, where the disease is rare (say, less than 1%), will result in a positive predictive value below 15% – the large majority of people who test positive will not have the condition. In contrast, people with symptoms are much more likely to have the condition. If the prevalence among them is above 5%, then the proportion of false positive tests is greatly reduced. The challenge in population screening is to try to target a population at sufficiently high risk that the number of false positives is acceptable and yet a sufficient proportion of the cases are included. A point often not mentioned in introductory presentations is that while sensitivity and specificity are in principle fixed properties of the test, in practice a test is not a fixed entity. Various factors can affect the sensitivity and specificity of a test when it is actually implemented, since there are often human factors involved in interpreting test results, equipment may require frequent calibration, etc.
• #48: Suggestions to the facilitator Ask participants why and when sampling is required and explain.