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Epidemiology / Statistics

Sensitivity(ability of a test to detect true positives = true postitives / (true positive + false negatives)
Specificity (ability of a test to detect true negatives = true negatives / (true negatives + false postives)
Accuracy = (true positives + true negatives) / (false positives + false negatives)
Positive Predictive value(probability that an individual actually has the condition if the test is positive) = True positives / (true positives + false positives)
Negative Predictive value(probability that an individual does not have the condition if the test is negative) = true negatives / (true negatives + false negatives)

Prevalence = number of cases in a population at a given time.

Incidence = Number of newly diagnosed cases over a specific time period.

Alpha (Type I) error

  • error in hypothesis testing where a statistically significant association is found when none exists (false positive).
  • rejecting a true null hypothesis
  • controlled by increasing the significance level.
  • Statistical significance provides the probability of committing a Type I error and is demonstrated by the P value.
  • P<0.05 = 5% probability of committing a Type 1 error

Beta (Type II) error

  • error in hyposthesis testing in where no statistically significant association is found when there is a true association (false negative).
  • may occur if study lacks power, ie you need more data to prevent Type II errors.
  • accepting a false null hypothesis
  • Power analysis is used to determine if the sample size is large enough to demonstate statistical significance.
  • In general the power of a study shoud be at least 0.8 (80%)

Discrete Data

  • Discrete data falls into specific categories such as gender or the presence or absence of a risk factor such as smoking.
  • Chi-square test
  • Yates correction for continuity
  • Fishers exact test

Continuous Data

  • Continuous data can be displayed on a curve such as height, weight, or 40-yard dash time.
  • Student's t-test (one sample{normal distribution}, independent two-sample{normal distribution} and paired{not-independent})
  • ANOVA

ANOVA

  • test of choice for multiple groups of continuous data.
  • used to compare means of three or more groups.
  • useful only for normally distributed, independent data.
  • One-way ANOVA: used to test differences bewtween 3 or more independent groups.
  • One-way ANOVA for repeated measures: used when the subjects are dependent groups (same subjects used for each treatment).
  • 2by2 ANOVA: used to evaluate effects of two or more treatment variables.
  • Posterior comparisions = Bonferroni method, student-Newman-Kauls procedure, Tukey method, Scheffe method.

T-Test

  • used for comparison of two groups of continuous data.
  • Paired t-test = dependent = used for two groups of paired (same individual) and normally distributed continous data.
  • Student t-test = independent = used for two independenet groups of normally distributed data.

Chi-Square Test

  • used for measuring binary or ordinal data.
  • compares discrete (categorical) variables as opposed to continuous variables.

Fischers Exact Test

  • used for measuring binary or ordinal data

Kruskal Wallis Test

  • used for nonparametric testing with more then two groups.
  • used to compare medians of three or more independent groups where the data is not normally distributed.

Mann-Whitney Test

  • used to compare two groups of nonparametric data.
  • nonparametric statistical significance test for assessing whether the difference in medians between 2 observed distributions is statistically significant. Requires two independent samples.

Wilcoxon Test

  • used to compare two groups of nonparametric data.

Simple Regression

  • used to determine if these is a relationship between a dependent variable and an independent variable.

Logistic Regression

  • assesses the effect of one or more variables on one dichotomous variable. Dichotomous variables have on two variables (male/female).

Bonferroni Correction

  • performed to adjust for the number of comparisons and decrease the risk of committing a type I error. Performed by dividing the p value by the number of comparisions.

Relative Risk

  • Magnitude of association between exposure to a risk factor and an injury.
  • Determined by dividing the incidence of those exposed most to an injury by the incidence of the control group.

Absolute Risk

  • the arithmetic difference in the rate of adverse outcomes between control and experimental subjects.

Incidence

  • the proportion of new cases within a specific time interval

Odds Ratio

  • compares a study group with a control group with the probability of exposure with a specific outcome compared to the probability of an exposure without the same outcome.

Prevalence

  • the proportion of individuals with a disease or condition at a single point in time.

Confidence Interval

  • range between two estimated values.
  • 95% confidence interval = +/- 1.96 * (SEM). SEM=standard error of the mean=standard deviation/square root of n.

Scheffe comparision

  • post hoc test that assess group differences following ANOVA

Newman-Keuls

  • post hoc test that assess group differences following ANOVA

Correlation Analysis (r value)

  • provides unitless number that summarizes strength of association between 2 variables.
  • The closer the value is to 1 or -1 the stronger the association.
  • Positive number means as the values change in the same direction.
  • Negative number means the values are inversely related.

R2

  • the coeffecient of determination
  • represents the percentage of the independent variable that explains the variance in the study

Variance

  • =standard deviation squared

Poisson Regression

  • analysis in which the dependent varialbe in an experiment or observational study is a count the follows the Poisson destribution.

Analysis of Covariance

  • tests for equality among group means, when the value of the dependent variable is affected by additional information related to the independent variable.

Validity

  • degree to which the measuremen represents a true value

Reliability

  • ability of researchers to reproduce or repeat the same measurements.

Tests for Interobserver reliability

  • kappa coefficient, weight kappa, Cronback's alpha
  • Person product-moment correlation for continuous variables

Descriptive Study

  • demonstrate associations between disease and variables, but do no demonstrate cause-effect relationships.
  • Case report / case series
  • Correlational Study: large sample study identifying associations between disease and variables.
  • Cross sectional study: takes a snapshot of a population and derives assocations with disease. Does not determine case and effect.

Analytical Study

  • allow for hypothesis testing and statical analysis
  • Cohort study: condition is not manipulated but observed and recorded. Can be retrospective or prospective
  • Case-Control study: cohort study with participants selected based on disease. Beneficial for rare diseases. Can not be used for rare exposures, cannot directly measure incidence, subject to selection and recall bias.
  • Prospective Cohort study: minimizes potential bias and inscreased strength of conclusions.

Intervention Study

  • clinical trials
  • prospective, randomized, single vs double blinded
  • Reduces bias and confounding

Selection Bias: study error resulting when comparisions are made between groups that differ in important ways other than the factor under consideration

Measurement Bias: study error resulting when quantitative or qualitative data collected from the treatment groups differ. Generally found in retrospective studies.

Sampling Bias: study error which occurs when patients in the study differ systematically from the population in which the results are generalized.

Publication Bias: research error which occurs when published studies differ systematically from unpublished studies which may be of higher quality, but not show as great a statistical significance.

 

 

 

References:

  • Wojtys EM, AJSM 1996;24:564
  • Kuhn JE, AJSM 1996;24:702
  • Greenfield ML, Wojtys EM, Kuhn JE. A statistics primer. Tests for continuous data. Am J Sports Med. 1997 Nov-Dec;25(6):882-4.
  • Kuhn JE, Greenfield ML, Wojtys EM. A statistics primer. Statistical tests for discrete data. Am J Sports Med. 1997 Jul-Aug;25(4):585-6.
  • Kocher MS, JBJS 2004;86A:607

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