Introduction This topic covers a variety of statistical principles used in research and study design Measure of Central Tendency Mode defined as the value that occurs most often best for data which is allocated into distinct categories (nominal data) Median defined as the value that occurs at the middle of all values of the variable (half are greater, half are less) not affected by extreme values good for all levels of measurement except nominal data especially good for skewed distributions Mean defined as arithmetic average the most frequently used measure of central tendency uses all values of data highly sensitive to extreme values (especially skewed distributions) Sensitivity Definition probability that test results will be positive in patients with disease Equation sensitivity = a / (a + c) or sensitivity = TP / (TP + FN) Relevance sensitive tests are useful for screening since they are unlikely to miss a patient with disease Example a new test is developed to quickly diagnose HIV. There are 10 patients in the study group with the disease. Upon testing of all 10 patients, only 6 results return positive. What is the sensitivity of the new test? solution sensitivity = a / (a + c) sensitivity = 6 / 10 sensitivity = 60% Disease Positive Disease Negative Test Positive (a) true positive = 6 (b) false positive Test Negative (c) false negative = 4 (d) True negative TOTAL a + c = 10 b + d Specificity Definition probability test result will be negative in patients without disease Equation specificity= d / (b + d) or specificity = TN / (FP + TN) Relevance specific tests are useful for confirmation as they don't result in treatment of an unaffected individual Example in a population of 90 patients who are disease free, a test incorrectly diagnoses 5 patients with disease. What is the specificity of this test? solution specificity = d / (b + d) specificity = 85 / 90 specificity = 94.4% Disease Positive Disease Negative Test Positive (a) true positive (b) false positive = 5 Test Negative (c) false negative (d) true negative = 85 TOTAL a + c b + d (90) False Positive Rate Definition patients without the disease who have a positive test result Equation false positive rate = b / (b + d) Disease Positive Disease Negative Test Positive (a) true positive (b) false positive Test Negative (c) false negative (d) true negative False Negative Rate Definition patients with disease who have a negative test result Equation false negative rate = c / (a + c) Disease Positive Disease Negative Test Positive (a) true positive (b) false positive Test Negative (c) false negative (d) true negative Positive Predictive Value Definition probability patient with a positive test actually has the disease dependent on prevalence of disease Equation PPV = a / (a + b) or PPV = TP / (TP + FP) Example you are evaluating a new serum diagnostic test for Lyme disease that claims sensitivity 90% and specificity 0f 95%. The prevalence of Lyme disease is known to be 10% in late spring in the study of patients who present with fever, arthralgias, and rash. solution PPV = a / (a + b) PPV = 9 / (9 + 4.5) PPV = 67% use sensitivity, specificity, and prevalence to calculate the quadrants Disease Positive Disease Negative Test Positive (a) true positive = 9 (b) false positive = 4.5 Test Negative (b) false negative = 1 (d) true negative = 85.5 TOTAL a+c = 10 b+d = 90 Negative Predictive Value Definition probability patient with a negative test actually has no disease dependent on prevalence of disease Equation NPV = d / (c + d) or NPV = TN / (FN + TN) Example 200 patients are enrolled in a study to evaluate the accuracy of a ELISA-based test for the diagnosis of influenza. 100 patients were diagnosed by the gold-standard method. 80 of the patients with influenza had a positive ELISA-based test as did 5 of the patients without influenza. What is the negative predictive value of this test? solutionNPV = TN / (FN + TN) NPV = 95 / (20 + 95) NPV = 83%Disease PositiveDisease NegativeTest Positive(a) true positive = 80(b) false positive = 5Test Negative(c) false negative = 20(d) true negative = 95 Likelihood Ratio Definition likelihood that a given test result would be expected in a patient with the target disorder compared to the likelihood that that same result would be expected in a patient without the target disorder Classification positive likelihood ratio definition describe how the likelihood of a disease is changed by a positive test result equation positive likelihood ratio = sensitivity / (1 - specificity) negative likelihood ratio definition describe how the likelihood of a disease is changed by a negative test result equation negative likelihood ratio = (1 - sensitivity) / specificity Incidence Definition number of newly reported cases of a disease in specific time period per unit measurement of population Prevalence Definition the total number of cases of a disease present in a location at any time point Determined by performing cross-sectional studies Relative Risk Definition risk of developing disease for people with known exposure compared to risk of developing disease without exposure obtained from cohort studies when RR > 1, the incidence of the outcome is greater in the exposed/treated group Equation incidence risk of YES = a / (a + b) incidence risk of NO =c / (c + d) relative risk = [(a / a + b)] / [(c / c + d)] Disease Status Risk Present Absent Yes a b No c d Example a study is performed concerning the relationship between blood transfusions and the risk of developing hepatitis C. A group of patients is studied for three years. Disease Status Transfused Hepatitis C Healthy Yes 75 595 No 16 712 Odds Ratio Definition represents the odds that an outcome will occur given a particular exposure, compared to the odds that the outcome will occur without the exposure obtained from case-control studies (retrospective) also obtained from the output of logistic regression models odds ratio's approximate RR when the outcome is rare (usually defined as <10%) Equation OR = (a x d) / (b x c) Disease Status Risk Present Absent Yes a b No c d Example a study is performed concerning the relationship between blood transfusions and the risk of developing hepatitis C. A group of patients is studied for three years. Disease StatusTransfusedHepatitis CHealthyYes75595No16712 Number Needed to Treat Definition number of patients that must be treated in order to achieve one additional favorable outcome Equation number needed to treat = (1 / absolute risk reduction) Example you learn the number-needed-to-screen with FOBT is nearly 1000 to prevent colon cancer. What is the absolute risk reduction associated with FOBT? solution absolute risk reduction (ARR) = 1 / number needed to treat ARR = 1 / 1000 ARR = .1% Post-test Odds of Disease Equations post-test probability = (pretest probability) X (likelihood ratio) likelihood ratio = sensitivity / (1 - specificity) pre-test odds = pre-test probability / (1 - pre-test probability) post-test probability = post-test odds / (post-test odds + 1) Power Definition an estimate of the probability a study will be able to detect a true effect of the intervention a power analysis to determine sample size should be performed prior to initiation of the study Equation power = 1 - (probability of a type-II, or beta error) Effect size Definition magnitude of the difference in the means of the control and experimental groups in a study with respect to the pooled standard deviation Variance Definition an estimate of the variability of each individual data point from the mean Type II Error (beta) Definition a false negative difference that can occur by detecting no difference when there is a difference or accepting a null hypothesis when it is false and should be rejected Equation power = 1 - (type-II error) Clinical significance a study that fails to find a difference may be because there actually is no difference or the study is not adequately powered Type I Error (alpha) Definition rejecting a null hypothesis even though it is true Clinical significance by definition, alpha-error rate is set to .05, meaning there is a 1/20 chance a type-I error has occurred Related principle Bonferroni correction post-hoc statistical correction made to P values when several dependent or independent statistical tests are being performed simultaneously on a single data set Confidence Interval Definition the interval that will include a specific parameter of interest, if the experiment is repeated 95% and 99% most commonly used 95% calculated based on mean +/- 1.96 standard deviations most commonly used by convention 99% calculated based on mean +/- 2.58 standard deviations Clinical significance Infers statistical significance, precision of findings, and clinical difference Statistical Inference Definition used to test specific hypotheses about associations or differences among groups of subjects/sample data Classification parametric inferential statistics continuous data that is normally distributed nonparametric inferential statistics continuous data that is not normally distributed (skewed) categorical data Study types when comparing two means Student's t-test used for parametric data Mann-Whitney or Wilcoxon rank sum test used for non-parametric data when comparing proportions chi-square test used for two or more groups of categorical data Fisher exact test used when sample sizes are small or number of occurrences in a group is low when comparing three or more groups Analysis of variance (ANOVA) Choosing the Right Test Comparison Parametric Nonparametric Continuous Data Two groups Paired Dependent (paired) t-test Wilcoxon Signed-Rank Test Unpaired Independent t-test Mann-Whitney U test Three or more groups Analysis of variance (ANOVA) Kruskal-Wallis test Categorical data Two or more variables Chi-square Chi-square Two or more variables (when the sample size is small) Fisher exact test Fisher exact test Funnel Plot Definition is a simple scatter plot of the intervention effect estimates from individual studies against some measure of each study’s size or precision and is used to detect publication bias in meta-analyses Clinical Significance this method is based on the fact that larger studies have smaller variability, whereas small studies, which are more numerous, have larger variability. Thus the plot of a sample of studies without publication bias will produce a symmetrical, inverted-funnel-shaped scatter, whereas a biased sample will result in a skewed plot. Receiver Operating Characteristic (ROC) Curve Definition a graphical representation of the diagnostic ability of different tests used to determine responsiveness Variables False positive rate (1 - specificity) is plotted on the x-axis True positive rate (sensitivity) is plotted on the y-axis Interpretation Area under the ROC curve (C-statistic) used to compare different tests, higher C-statistics mean better diagnostic ability of test an area under the ROC curve of 0.5 is a useless test Survivorship Analysis Overview often used to measure success of joint replacements analyzes data from patients with different lengths of follow-up for analysis, it is assumed that all patients had their operation simultaneously chance of implant surviving for a particular length of time is calculated as the survival rate calculation method is either life table or product limit method May be analyzed with the Kaplan-Meier method Life table method annual success rate, determined from the failure rate, is cumulated to give a survival rate for each successive year, this can change only once per year Product limit method same as life table method, but the survival rate is recalculated each time a failure occurs Minimal Clinically Important Difference (MCID) The difference in outcome measures that will have clinical relevance Difficult to study and measure, very few outcome tools have established and universally accepted MCID Helps to reconcile the statistical significance and clinical relevance of study results that use outcome tools Repeated Measurement Reliability Interrater/interobserver Reliability A measurement of the degree of agreement between two or more assessors Measured with Cohen's kappa Intrarater/intraobserver Reliability A measurement of the reliability of a single assessor making multiple measurements/observations of a single subject Measured with Intraclass correlation coefficient (ICC)