Statistics & graphics for the laboratory

Statistics & graphics for the laboratory
Diagnostic measures, with Bayesian statistics Dietmar Stöckl Linda Thienpont In cooperation with AQML: D Stöckl, L Thienpont & Kristian Linnet, MD, PhD Per Hyltoft Petersen, MSc Sverre Sandberg, MD, PhD

Prof Dr Linda M Thienpont University of Gent
Institute for Pharmaceutical Sciences Laboratory for Analytical Chemistry Harelbekestraat 72, B-9000 Gent, Belgium STT Consulting Dietmar Stöckl, PhD Abraham Hansstraat 11 B-9667 Horebeke, Belgium Tel + FAX: +32/ Copyright: STT Consulting 2007 Statistics & graphics for the laboratory

Content Content overview Sensitivity and specificity ROC curves Influence of analytical quality on sensitivity and specificity and ROC curves Predictive values Independent tests Bayesian statistics ”Double Bayes” Odds/Likelihood and likelihood ratios Influence of analytical quality on predictive values, Likelihood ratios The optimal study design Glossary EXCEL-files Diagnostic Measures Diagnostic Measures- Calculator Statistics & graphics for the laboratory

Introduction What is a disease? A disease is what the patient has. A diagnosis is what the physician thinks the patient has. The diagnosis can vary between physicians, and as time develops. There are often different valid methods to establish the diagnosis. Diagnosis – The Bimodal distribution Prerequisites The “gold-standard” The true status of each population has to be established by other means than the test being subject to evaluation, namely, a so-called “gold standard”, or reference standard. Defining a decision point (“cut-off” value) A decision point (sick/healthy) must be defined. Note that this point must not lie at the crossing of the two distributions. Dependent on the importance of false negatives or false positives, it can be moved towards increased sensitivity or specificity. Note: For monitoring, a medically significant change has to be defined. Classification of results With respect to the gold standard, test outcome is classified as “true positive”, “false positive”, “true negative”, or “false negative”. “Gold standard”: The best test available. Problems (a) new tests being “better” than the reference standard (b) the test is part of the reference standard The reference standard must be performed without knowledge to the results of the test that shall be examined. The test that shall be examined must be performed without knowledge of the result from the reference standard. Statistics & graphics for the laboratory

Bimodal situation Bimodal situation Classification of results True positive (TP): The number of diseased patients correctly classified by the test. True negative (TN): The number of non-diseased patients correctly classified by the test. False positive (FP): The number of non-diseased patients misclassified by the test. False negative (FN): The number of diseased patients misclassified by the test. The 2 x 2 Table Statistics & graphics for the laboratory

Sensitivity and specificity
= TP/(TP + FN) Specificity = TN/(TN + FP) A sensitivity of 80% means that 80 percent of the diseased people will have a positive test. For a quantitative test this is dependent on the cut-off point. The 2 x 2 table expanded Changing the cut-off point A change of the cut-off will change sensitivity and specificity! Statistics & graphics for the laboratory

Changing the cut-off point
Sensitivity and specificity Changing the cut-off point An EXCEL-template Sensitivity/Specificity & Prevalence In principle, both are independent of the prevalence. BUT - in a population with low prevalence, e.g. primary health care the disease (D+) is often in an earlier stage, shifting the mean of D+ to the left. Diagnostic Measures Statistics & graphics for the laboratory

Sensitivity/Specificity & Prevalence
Sensitivity and specificity Sensitivity/Specificity & Prevalence In a population with a disease where there are many differential diagnosis giving high values the mean value of the ”Non-Diseased” population is shifted to the right. Sensitivity/Specificity & analytical bias Bias changes sensitivity & specificity (same effect as moving the cut-off point!) Sensitivity/Specificity & imprecision Imprecision : Sensitivity  & Specificity  Statistics & graphics for the laboratory

Sensitivity/Specificity & analytical error
Sensitivity and specificity Sensitivity/Specificity & analytical error Summary Systematic error The introduction of a systematic error in the direction of the diseased population increases the false positive results. The introduction of a systematic error in the direction of the healthy population would increase the false negative results. Random error The introduction of random analytical error, generally, deteriorates test accuracy. Sensitivity & specificity – Standard error Same as in binomial samples. Sensitivity: SE = SQRT[Sens • (1 – Sens)/ndiseased)] Specificity: SE = SQRT[Spec • (1 – Spec)/nnon-diseased)] Assumption: n • Sens • (1 – Sens) >5 Otherwise, a more complicated formula should be used. Confidence intervals: e.g., Sens ± 1.96 SE Statistics & graphics for the laboratory

ROC – Receiver Operating Curve
ROC analysis ROC was developed during World War II for the analysis of radar images. Radar operators had to decide whether a blip on the screen represented an enemy target, a friendly ship, or just noise. Their ability to do so was called the Receiver Operating Characteristics. It was not until the 1970's that ROC was recognized as useful for interpreting medical test results. A ROC plot is a plot of sensitivity (TP) versus 1- specificity (FP) as the underlying values used for the cutoff (decision threshold) traverses the entire range of results. ROC depends on distance of distributions ROC does NOT depend on analytical bias ROC DETERIORATES with increase of analytical imprecision Smaller distance Bigger distance Statistics & graphics for the laboratory

ROC ROC-analysis Perfect and worthless test Tests compared by ROC Test A is superior to Test B -Test A, at all cutoffs, is closer to the upper left corner of the plot. -The area under the curve is greater for Test A than Test B. Statistics & graphics for the laboratory

Predictive values Bayesian statistics The Bayes' theorem of conditional probability in general terms: "Post-test" = "Pre-test" x Likelihood Bayes' theorem comes in two equivalent forms: One uses the probability of disease Another uses the odds of disease This leads us to: Predictive values Post-test probabilities Odds & Likelihood ratios Predictive values & 2 x 2 table Positive predictive value (PPV) = TP/(TP + FP) Negative predictive value (NPV) = TN/(TN + FN) A positive predictive value of 80% means that 80% of persons with Test+ have the disease. Depends on prevalence! Statistics & graphics for the laboratory

Predictive values Predictive values Predictive values & Prevalence Example: Urinary tract infection; WBC ≥ ++ Under the given SENS & SPEC, the PPV increases with the prevalence! Predictive values & Post-test Probabilities The post-test probability of disease present (D+) when the test is positive (T+) = PPV. The post-test probability of D-/T- = NPV The post-test probability of D+/T- = 1 - NPV The post-test probability of D-/T+ = 1 – PPV Discriminatory power of a test for disease (D+) Compare PPV with 1 – NPV of a test for D+ Diagnostic Measures- calculator Statistics & graphics for the laboratory

Post-test probabilities
An EXCEL file shows the connection between post-test probability D+/T+ (= PPV) and the post-test probability of D+/T- (= 1 – NPV) with varying distances of healthy and diseased. PPV 1-NPV Statistics & graphics for the laboratory

Influence of bias Under the given circumstances, bias (here in the direction of the diseased) decreases the post-test probability of D+/T+ and D+/T-. The net effect is that the discriminatory power decreases. Influence of imprecision Under the given circumstances, imprecision decreases the post-test probability of D+/T+ and and increases that of D+/T-. The net effect is that the discriminatory power of the test is deteriorated. Statistics & graphics for the laboratory

To test or not to test? To test or not to test…? Case study: Urinary tract infection A woman of 32 years has the last few days experienced a little increased urgency and some pain when she goes to the toilet. What is the probability that she has a urinary tract infection. With a probability above 75% you will treat and not test. With a probability of less than 15% you will not treat nor test. WBC ≥ +2: sens = 0.82 and spec. = 0.88 Nitritis pos: sens = 0.5 and spec. = 0.90 In this case you estimate the pre-test probability to 20% and you test. Statistics & graphics for the laboratory

Case study: Urinary tract infection
Post-test probabilities Case study: Urinary tract infection Two independent tests WBC and Nitritis In this case, we use the 2 tests consecutivley. We take the post-test prabability of WBC (63%) as pre-test probability (= prevalence) for the nitritis test. In that way, we arrive at a total post-test probability of 89%. (D+/T-) Statistics & graphics for the laboratory

”Double Bayes” A 30 year old woman has pain in her stomach and you wonder if this can be due to an ulcus duodeni. 95% of ulci is caused by Helicobacter pylori. However 15% of the population (of this age) carries Helicobacter pylori without having any symptoms. You have a rapid test with a sensitivity of 85% and specificity of 80% to detect Helicobacter pylori. What is the probability that she has an ulcus if she has a positive rapid test? What is the probability that the woman has ulcus if the test is negative? Probability: combination ulcus/bacteria With the epidemiologic information about ulci and Helicobacter Pylori, we are able to set up a 2x2 table before doing the test. However, again, we introduce a subjective statement of the doctor about the pre-test probability: chosen at 30% according to the person and symptoms. Calculations with a total population of 1000 Pre-test probability of ulcus to be 30%: 0.3*1000 = 300 Sens=95%: 0.95*300 = 285 Spec=85%: 0.85*700 = 595 Then, we split the table in two 2x2 tables, one for bacteria+ and one for bacteria-. Those will be used as the new totals of the tables (bottom). Now, we make the test, and calculate the respective fields with the sensitivity and specificity data of the test. With the symptoms given by the patient, the doctor estimates the pre-test probability of ulcus to be 30%. 95% of patients with ulcus have bacteria: sens=95% 15% of healthy have bacteria: spec = 85% Statistics & graphics for the laboratory

”Double Bayes” Post-test probabilities of ulcus Rapid test - sensitivity 85%, specificity 80% to detect Helicobacter pylori bacteria. Bacteria +:calculate with sensitivity Calculate "New" TP = 285 * Sens = 242$ Calculate "New" FP = 105 * Sens = 89$ Calculate "New" FN = 285 – 242 = 43# (similar TN) Bacteria -: calculate with specificity Calculate "New" FN = 15 * Spec = 12$ Calculate "New" TN = 595 * Spec = 476$ Calculate "New" TP = 15 – 12 = 3# (similar FP) Pos. pred value for ulcus = (242+3)/( )=0.54 Neg. pred value for ulcus = (16+476)/( )=0.9 Statistics & graphics for the laboratory

Odds Odds Pre-test Odds = Diseased/Non-diseased = Prevalence/(1-Prevalence) = (TP + FN)/(FP +TN) Post-test Odds = Diseased with T+/Non-diseased with T+ = TP/FP Odds & Probability If you have 10 people, 7 are healthy and 3 have the disease. Odds for disease = 3/7 Probability for disease = 3/10 Probability Total number of possibilities are always in the denominator Odds Total number of possibilities are the sum of denominator and nominator. Statistics & graphics for the laboratory

Likelihood ratio Likelihood ratio Likelihood (probability) for a pos. test in the diseased population divided by the likelihood for a pos. test in the non diseased population (LR+) LR+: The ratio of the true postive rate to the false positive rate . = Sensitivity/(1 – Specificity) = [TP/(FN + TP)]/[FP/(TN + FP)] LR–: Likelihood ratio for a negative test (LR-): (1–sensitivity)/specificity or [FN/(TP+FN)]/[TN/(FP+TN)] or The ratio of the false negative to the true negative rate. It can be shown that The Likelihood ratio (LR) can be expressed as: = Post-test Odds/Pre-test Odds and therefore: Post-test Odds = LR x Pre-test Odds Likelihood ratios for intervals of test results (Goldstein and Mushlin. J Gen Intern Med 1987;2:20-24. Statistics & graphics for the laboratory

Likelihood ratio Likelihood ratio The best test to use for ruling in a disease is the one with the largest likelihood ratio of a positive test. The better test to use to rule out disease is the one with the smaller likelihood ratio of a negative test. The Positive [Negative] Likelihood ratio measures the diagnostic power of a test to change the pre-test into the post-test probability of a disease being present [absent]. The Table below shows how much LRs change disease likelihood. Likelihood ratios – Advantages over Sensitivity/Specificity 1. They give direct information about the power of a test to discriminate between sick/healthy. 2. They allow the direct calculation of Post-test probabilities from Pre-test Probabilities with the Bayes Theorem. For this purpose, however, Pre- and Post test Probabilites have to be transformed into "Odds". 3. LRs can be used to directly calculate the discriminatory power of test cascades. 4. For continuous data, LRs can be calculated at different cut-off values and thus allow a more precise estimation of the discriminatory power of a specific test result. For completeness: Diagnostic Odds ratio = LR+/LR- = (TP/FP)/(FN/TN) Importance of prevalence Odds and probabilities for a disease are PREVALENCE dependent. Likelihood ratios are NOT prevalence dependent Note: LR>1 [<1] include [exclude] condition. Statistics & graphics for the laboratory

All diagnostic measures
Statistics & graphics for the laboratory

Fagan Nomogram Fagan Nomogram Statistics & graphics for the laboratory

Optimal study design The STARD initiative The STARD Initiative – Towards Complete and Accurate Reporting of Studies on Diagnostic Accuracy ( See also More EBM/Test utility - Prosp Hierarchy of major study designs Review of Randomised control clinical trial (RCT) RCT (interventional) Cohort (observational) Case control Best design = prospective, blind comparison of the test and reference standard in a consecutive (or randomly selected) series of patients from a relevant clinical population. Internal validity Selection bias - for example, we select sicker patients to receive active treatment and fitter patients to receive inactive treatment. Observer bias - for example, we know that a patient had active treatment so we subconsciously encourage her to rate her quality of life as higher than it really is. Participant bias - for example, in a study of aspirin versus no treatment, people allocated to no treatment take aspirin anyway. Withdrawal bias or drop out bias - when we lose people to follow up, those that remain for analysis at the end of the study may not be representative of the group originally included at the start of the study. Recall bias - for example, mothers of children with leukemia may remember living near high voltage power cables because they fear a link between power lines and cancer, while mothers of children without leukemia are likely to forget whether they lived near a power line, because they regard it as a trivial fact. Instrument or measurement bias Publication bias - results from researchers and journals being biased towards publishing only positive results. Validity > Statistics & graphics for the laboratory

External validity ("Bazian")
Optimal study design External validity ("Bazian") Was the question relevant to me? Schematic representation of a randomized controlled trial. Assessment of study quality Critical appraisal checklist Study design Internal validity External validity What are the results? - sensitivity, specificity, LR, ROC, CI, prevalence, thresholds, etc. Best design = prospective, blind comparison of the test and reference standard in a consecutive (or randomly selected) series of patients from a relevant clinical population. Statistics & graphics for the laboratory

Critical appraisal checklist
Optimal study design Critical appraisal checklist Internal validity – spectrum of diseases Normal persons compared to persons with the disease. > Overestimation of TP and TN Verification bias Did the result of the test being evaluated influence the decision to perform the reference standard? Use of different reference standards in test positive and test negative cases leads often to misclassification of FN as TN, and overestimates both sensitivity and specificity. For example: It is difficult to estimate the value of CRP in diagnosing appendicitis if only patients with elevated CRP are operated on and the histological examination of appendix is used as the reference standard these and follow up as reference standard for the others. Review bias If interpretation of results of the reference test and the experimental test are not blinded, this may lead to overestimation of both sensitivity and specificity External validity Can I use the results in my practice? Specificity falls - more disease which are similar (FP rate increases) and sensitivity increases - disease in a more advanced stage (FN rate decreases) What are the results? The results must be clearly stated with e.g. sensitivity, specificity, LR, ROC, CI, prevalence, thresholds, etc. See also Critical appraisal worksheets Statistics & graphics for the laboratory

The 2 X 2 table, including some measures for test accuracy
Glossary The 2 X 2 table, including some measures for test accuracy True Positive (TP) = Postive with Test & Positive with Gold Standard False Positive (FP) = Postive with Test & Negative with Gold Standard False Negative (FN) = Negative with Test & Positive with Gold Standard True Negative (TN) = Negative with Test & Negative with Gold Standard Statistics & graphics for the laboratory

Glossary Glossary Specific, unconditional measures (independent of prevalence) Sensitivity & Specificity (see also Figures below) Sensitivity: TP/(TP+FN); true positive rate = The proportion of people with the target disorder who have a positive test (used to assist in assessing and selecting a diagnostic test/sign/symptom). Strongly depends on a cutoff-point; meaningless when healthy and diseased populations are the same! For a test to be useful in ruling out a disease, it must have a high sensitivity (>SnNOut = Sensitivity, negative [=test result], out). Specificity: TN/(FP+TN); true negative rate = Proportion of people without the target disorder who have a negative test (used to assist in assessing and selecting a diagnostic test/sign/symptom). For a test to be useful at confirming a disease (ruling in), it must have a high specificity (>SpPIn = Specificity, positive [=test result], in). -Sensitivity & Specificity are interrelated (when Sn, Sp & vice versa) and should be interpreted together. This means, for example, it is not possible to produce SnNOuts or SpPIns by simply adjusting the threshold (cut-off). -In theory, Sensitivity & Specificity are independent of prevalence. In practice however, the 2 populations (healthy, sick) may contain different grades of disease or health in different situations. In a low prevalence situation, for example, the diseased population may be shifted to the left because it contains more patients with less severe disease than in a high prevalence situation ("error of spectrum"). Statistics & graphics for the laboratory

Glossary Likelihood ratios Likelihood ratio (LR) = The likelihood that a given test result would be expected in a patient with the target disorder compared with the likelihood that this same result would be expected in a patient without the target disorder. Likelihood ratio for a positive test (LR+): sensitivity/(1–specificity) or [TP/(TP+FN)]/[FP/(FP+TN)] = The ratio of the true postive rate to the false positive rate (calculation: substitute in 1 –specificity the "1" by (FP+TN)/(FP+TN). The best test to use for ruling in a disease is the one with the largest likelihood ratio of a positive test. Likelihood ratio for a negative test (LR-): (1–sensitivity)/specificity or [FN/(TP+FN)]/[TN/(FP+TN)] = The ratio of the false negative to the true negative rate. The better test to use to rule out disease is the one with the smaller likelihood ratio of a negative test. The Positive [Negative] Likelihood ratio measures the diagnostic power of a test to change the pre-test into the post-test probability of a disease being present [absent]. The Table below shows how much LRs change disease likelihood. Likelihood ratios – Advantages over Sensitivity/Specificity 1. They give direct information about the power of a test to discriminate between sick/healthy. 2. They allow the direct calculation of Post-test probabilities from Pre-test Probabilities with the Bayes Theorem (see below). For this purpose, however, Pre- and Post test Probabilites have to be transformed into "Odds" (see below). 3. LRs can be used to directly calculate the discriminatory power of test cascades. 4. For continuous data, LRs can be calculated at different cut-off values and thus allow a more precise estimation of the discriminatory power of a specific test result. Note: LR>1 [<1] include [exclude] condition. Statistics & graphics for the laboratory

Glossary Glossary Global, unconditional measures (independent of prevalence) Diagnostic odds ratio (DOR): LR+/LR- (Odds: see below: Bayes' Theorem) Area under the Receiver Operating Characteristic (ROC) curve (see also Figure below) ROC shows the relationship between specificity (or better 1-specificity) and sensitivity when the cut-off value is moved over the whole range of values (from sick to healthy). Statistics & graphics for the laboratory

Glossary Glossary Specific, conditional measures (dependent on prevalence) Prevalence or Pre-Test Probability: (TP+FN)/(TP+FP+FN+TN) = The proportion of people with the target disorder in the population at risk at a specific time (point prevalence) or time interval (period prevalence). Predictive Values Positive [Test] Predictive Value (PPV) [for Disease, D+]: TP/(TP+FP) = Proportion of people with a positive test who have the target disorder. Negative [Test] Predictive Value (NPV) [for Health, D-]: TN/(FN+TN) = Proportion of people with a negative test result who are free of the target disorder. Post-Test Probabilities Post-Test Probability [for D+] Positive Test = PPV (see also below: Bayes' Theorem; can also be calculated with LR+) Post-Test Probability [for D+] Negative Test = 1–NPV (also calculated with LR-) Post-Test Probability [for D-] Negative Test = NPV (also calculated with [1/LR-]) Post-Test Probability [for D-] Positive Test = 1–PPV (also calculated with [1/LR+]) Global, conditional measure (dependent on prevalence) Accuracy: (TP+TN)/(TP+FP+FN+TN) = The proportion of patients for whom a correct diagnosis has been made. Statistics & graphics for the laboratory

The Bayes' theorem, generally: "Post-test" = "Pre-test" x LR
Glossary The Bayes' theorem, generally: "Post-test" = "Pre-test" x LR Bayes' theorem comes in two equivalent forms: One uses the probability of disease Another uses the odds of disease Odds = A ratio of the number of people incurring an event (e.g., disease) to the number of people who have non-events (e.g., no disease). Pre-test Odds for disease = (TP+FN)/(FP+TN) Bayes' theorem, generally: "Post-test" = "Pre-test" x LR with Probability Post-test Probability = [Pre-test Probability/(1-Pre-test Probability)] * LR/{[Pre-test Probability/(1-Pre-test Probability)] * LR + 1} Note: Pre-test Probability/(1-Pre-test Probability) = Prevalence/(1-Prevalence) = Pre-test Odds with Odds Post-test Odds (T+ or T–) = Pre-test Odds x Likelihood ratio (LR+ or LR–) The likelihood ratio, which combines information from sensitivity and specificity, gives an indication of how much the odds of disease change based on a positive or a negative result. You need to know the pre-test odds, which incorporates information about prevlance of the disease, characteristics of your patient pool, and specific information about this patient. You then multiply the pre-test odds by the likelihood ratio to get the post-test odds. Pre-test Odds: Prevalence/(1–Prevalence) = The odds that the patient has the target disorder before the test is carried out. Post-test odds: Pre-test odds x Likelihood ratio = The odds that the patient has the target disorder after the test is carried out. Statistics & graphics for the laboratory

Glossary Glossary Calculation example Sensitivity: 0.9; Specificity: 0.83; Prevalence for disease (D+): 0.1 > Prevalence for D-: 0.9; Pre-test Odds for D+: 0.111; Pre-test Odds for D-: 9 Measures of diagnostic test accuracy – Use and relationship The test Sensitivity, Specificity, Likelihood ratio, and ROC characterize a test and are independent of the prevalence of a disease. However, except ROC, they are dependent on the chosen cut-off. ROC, in fact, shows the relationship between sensitivity and specificity when the cut-off value is moved over the whole range of values (from sick to healthy). The patient (tested/not tested) Predictive Values, Pre- and Post-test Probabilities, and Pre- and Post-test Odds are used to decide whether a test should be done for a particular patient and if a test is done, they give information about the probability of the presence/absence of a disease. They are dependent on the prevalence of a disease. Post-test Probabilities and Predictive Values are identical (the Post-test Probability of a positive test = Positive Predictive Value) or closely related (the Post-test Probability of a negative test = 1–Negative Predictive Value). The Post-test Odds give similar information as the two before, however, they carry it in different numbers. Odds are preferred by many because Post-test Odds can easily be calculated from Pre-test Odds and the Likelihood ratio: Post-test Odds = Pre-test Odds x Likelihood ratio (Bayes' Theorem). Usually, Post-test Probabilites and Post-test Odds are calculated for Disease (D+), however, they also can be calculated for Disease absent (D-) (see above). While a nomogram is available for obtaining Post-test Probabilities from Pre-test Probabilities and the Likelood ratio ("Fagans Nomogram"), it is more accurate to calculate them with so-called "Bayesian Calculators" that are available for free on the net. References 1. The Bayes Library of Diagnostic Studies and Reviews. 2nd edition 2002. 2. Henderson AR. Assessing test accuracy and its clinical consequences: a primer for receiver operating characteristic curve analysis [Review]. Ann Clin Biochem 1993;30: Statistics & graphics for the laboratory

Diagnostic measures and their main use
Glossary Diagnostic measures and their main use Diagnostic Test -Sensitivity, Specificity, PPV, NPV, LR+, and LR- Prospective Study - Relative Risk (RR), Absolute Relative Risk (ARR), and Number Needed to Treat (NNT) Case-control Study - Odds Ratio (OR) Randomized Control Trial (RCT) - Relative Risk Reduction (RRR), ARR, and NNT Glossary of terms Case-control study A study which involves identifying patients who have the outcome of interest (cases) and patients without the same outcome (controls), and looking back to see if they had the exposure of interest. Retrospective Cohort Study Involves identification of 2 groups (cohorts) of patients, one which received the exposure of interest, and one which did not, and following these cohorts forward for the outcome of interest. Prospective: Present > Future; "Past assembled" > Present Control Event Rate (CER) The frequency with which the outcome of interest occurs in the study group not receiving the experimental therapy. Event rate The proportion of patients in a group in whom the event is observed. Thus if out of 100 patients, the event is observed in 27, the event rate is Control event rate (CER) refers to the proportion of patients in the control group who experience the event and the experimental event rate (EER) is the proportion of patients in the experimental group who experience the event of interest. The patient expected event rate (PEER) refers to the rate of events we'd expect in a patient who received conventional therapy or no treatment. Experimental event rate (EER) The proportion of patients in the experimental treatment group who are observed to experience the outcome of interest. Likelihood ratio The likelihood that a given test result would be expected in a patient with the target disorder compared with the likelihood that this same result would be expected in a patient without the target disorder. Negative predictive value Proportion of people with a negative test result who are free of the target disorder. Statistics & graphics for the laboratory

Glossary of terms (ctd.)
Number needed to treat (NNT) The number of patients that we need to treat with a specified therapy in order to prevent one additional bad outcome. Calculated as the inverse of the absolute risk reduction (1/ARR). Odds A ratio of the number of people incurring an event to the number of people who have non-events. Odds ratio (OR) The ratio of the odds of having the target disorder in the experimental group relative to the odds in favour of having the target disorder in the control group (in cohort studies or systematic reviews) or the odds in favour of being exposed in subjects with the target disorder divided by the odds in favour of being exposed in control subjects (without the target disorder). Positive predictive value Proportion of people with a positive test who have the target disorder. Post-test odds The odds that the patient has the target disorder after the test is carried out (calculated as the pre-test odds x likelihood ratio). Pre-test probability (prevalence) The proportion of people with the target disorder in the population at risk at a specific time (point prevalence) or time interval (period prevalence). Randomised control clinical trial (RCT) A group of patients is randomised into an experimental group and a control group. These groups are followed up for the variables/outcomes of interest. Relative risk reduction (RRR) This is a measure of treatment effect and is calculated as (CER-EER)/CER. Risk Ratio The ratio of risk in the treated group (EER) to the risk in the control group (CER). This is used in randomised trials and cohort studies and is calculated as EER/CER. Sensitivity The proportion of people with the target disorder who have a positive test. It is used to assist in assessing and selecting a diagnostic test/sign/symptom. Specificity Proportion of people without the target disorder who have a negative test. It is used to assist in assessing and selecting a diagnostic test/sign/symptom. Statistics & graphics for the laboratory

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