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Biostatistics: A Review Tony Gerlach, Pharm.D, BCPS Statistics • Methods for collecting , classifying, summarizing & analyzing data • Descriptive – Frequency, Histogram, Measure central Tendency, Measure of spread, Scatter plot • Inferential – Conclusion or generalization made about a population from study using a sample population Variables • Discrete (Nonparametric) – Nominal: classified into groups with no particular order or severity (Yes/NO) • E.g., Sex, mortality, Disease State – Ordinal: Ranked in specific order but no consistent level of magnitude between groups • E.g., NYHA class, Trauma scores, Likert scales 1 Variables • Continuous (Parametric) – Interval: Data are ranked in specific order with constant change in magnitude with zero point arbitrary • E.g., Fahrenheit Temperature – Ratio: Like interval but with an absolute zero • E.g., Heart Rate, Age, Blood pressure Normal (Gaussian) Distribution • Bell Shape • Mu: Mean • Theta: Standard Deviation (SD) – 68% of population are within +/- 1 SD – 95% of population are within +/- 2 SD Descriptive Statistics • Mean: Average – Only for Continuous data – Sensitive to outliers • Median: Point where half of observations fall below and above – Used with ordinal & continuous data – Insensitive to outliers • Mode: Most common value – For all data types • Mode=Median=Mean for Normal Distribution 2 Standard Deviation • Calculated to reflect range of samples • Appropriate for normal or nearly normal data • Therefore can only use continuous data Standard Error of the Mean (SEM) • SEM is estimated from Standard deviation • SEM = SD/ √ n • Like any normal distribution 95% of sample means lie with in +/- 2 SEM of mean • Use to calculate Confidence intervals Range SD SEM Interval/Ratio data Yes Yes Yes Ordinal data Yes No No Descriptive of sample variability Yes Yes No Assists in Statistical Inference No Yes Yes Used to calculate Confidence Intervals No No Yes 3 Hypothesis Testing • Null hypothesis (H0): No difference between group (X=Y) • Is used to determine if any observed difference between groups is due to chance alone • If H0 is rejected = statistical difference between groups • If H0 is accepted = no statistical difference (any difference due to chance) Hypothesis Testing • Choose correct statistical test based on: – Type of data (nominal, ordinal, continuous) – Study design (parallel, crossover) – Presence of confounding variables • Depending on statistics value H0 is accepted or rejected Decision Errors H0 True H0 False Accept H0 No Error (A) True Positive (TP) Type II Error (B) False negative (FN) Reject H0 Type 1 Error (C) False Positive (FP) No Error (D) True Negative (TN) • Type I Error: Concluding H0 is false when really true (Wrongly concluding statistical difference between groups) • Type II Error: Concluding H0 is true when it is really false (Wrongly concluding group equal) 4 Decision Errors • P-value: is calculated chance Type I error has occurred • Probability of making Type I error is α • When α level is set a priori, H0 when p< α • Probability of Type II error is β • Holding other variables constant α and β are inversely related Sensitivity & Specificity • Sensitivity: positivity of test or is test sensitive to detect disease presence = 100 X A/(A+B) or 100 X TP / (TP+FN) • Specificity: negativity of test or is test specific enough to test absence of disease = 100 X B/(B+D) or 100 x FN/(FN=TN) Power • Is the probability of making correct decision and ability to detect difference= 1 - β • Analogous to β • β = 1/α i.e. if α=0.05, β=20% & Power = 80% • As Increase α Decrease β • Increased by – Increasing α – Increasing n – Magnitude of difference being studied (Δ) – One tail versus two tail • Decreased by – Poor study design – Incorrect statistical test 5 Statistical Significance • Size of p-value not related to importance of results – Smaller p-values mean less likely chance explains difference • Statistically significance does not mean clinically significance • Lack of statistical difference does not mean results are not important – Lancet 2000;356:2139-43 Dopamine in ARF Statistical Test Type of variable Statistical test Nominal Chi squared Fishers Exact Test Wilcoxan Rank Sum Mann Whitney U Student’s t-test Ordinal Continuous Confidence Intervals (CI) • P-value tells if difference between groups, but not magnitude • CI give idea of magnitude of difference with point estimate • All values in CI are statistically possible • CI that include zero interpreted as p>0.05 • What is difference between 90% and 95% CI • Changes in MAP for a drug is 95% CI –12 mmHg, (-22 to –10) Means with 95% confidence drug a reduces MAP between 22 and 10 mmHg with a best point estimate of 12 mmHg 6 Correlation • Used to estimate strength of relationship between 2 variables • R is correlation coefficient range -1 to +1 • -1 is perfect negative correlation or indirect relationship • +1 is perfect positive correlation or direct relationship • Correlation is quantitative way to measure strength of relationship OR • Simply recognizes relation but does not imply causation (chicken or egg) Regression • Regression PREDICTIVE, correlation is not! • Math method to describe relationship with goal to develop equation for prediction of one variable from one or more variables • Often use line regression where • Y = MX + B X is independent variable Y is dependent variable R2 is used for regression • Intensive Care Med 2004;30:1537-43 • BIS XP and RASS R2 0.36 , p=0.011 • Means 36% of time BIS predicted RASS score Types of Studies • Case Reports • Case Studies • Case – Control Studies • Cohort – Retrospective – Prospective • Randomized Clinical Trials 7 Case Control Studies • Advantages – Causal influence on relatively uncommon conditions – Allows for smaller n than cohort – Allows investigation of many causes – Can be done inexpensively and fast • Disadvantages – Selection of control can be difficult – Confounding and bias are concerns Cohort Studies • Can be prospective or retrospective • Advantages – Allows study of more than one disease and /or exposures – Less bias than case control • Disadvantages – Cost more – Long time to conduct – Larger n – Bias can be introduced via outcome information Randomized Controlled Trials • Advantages – Best design to determine causality – Minimizes bias via randomization – May be parallel or crossover design • Disadvantages – Cost – Time 8 Relative Risks (RR) and Odds Ratios (OR) • Estimate the magnitude of exposure between exposure and disease • Interpreted based on their difference from unity (1.0) • Like Confidence Intervals given as range and point Disease Exposure Yes No Yes A B No C D • RR can not be directly calculated for most case control studies • Use RR for Cohort Studies RR = (A/A+B)/(C/C+D) • Use OR for Case-Control Studies OR = (A/C)/(B/D) N Engl J Med 2004;351:1089-96. ABX Use Person-Years Deaths RR (95% CI) Current Use Erythromycin 5305 10 2.01 (1.08-3.75) Current Use amoxicillin 6846 8 1.18 (0.59-2.36) Former use of erythromycin 111779 100 0.89 (0.72-1.09) None 1126013 1358 1.0 194 3 5.35 (1.72-16.64) Current use of erythromycin and CYP3A inhibitor 9 Which is the Best Agent? • All drug have been shown to decrease incidence of DVT in ICU patients • Drug A has an absolute reduction of 6.1% • Drug B has a relative risk reduction of 20% • Drug C reduced DVT from 30.8% (placebo) to 24.7% • Drug D shows you need to treat 16 patients to prevent one DVT Application • Absolute Reduction = % placebo - % study drug e.g. 30.8%-24.7% • Relative Reduction = (placebo – study)/Placebo e.g., (30.8%-24.7%)/30.8% • Number Needed to Treat (NNT) = 1/(placebo-study) e.g., 1/(30.8-24.7) Survival Analysis • Studies entry into study and death – Kaplan-Meier Curve – Cox Regression Model AKA – Proportional hazards regression analysis • Hazard Ratio (HR) – Use log rank formula to calculate slopes of curves – Interpreted similar to OR or RR – From Clin Infec Dis 2004;39:797-802 HR , 0.27; 95% CI , 0.09-0.78; p=0.011 10 Meta Analysis • Sum greater that parts • Advantages – Combines results of many studies – Greater statistical power • Disadvantages – Studies may not have same inclusion, hypothesis, outcomes – Publication bias • May not fine studies that have not been published “Likeness to truth is not the same thing as truth” Socrates Resources • • • • • • • • Ann Emerg Med 1990;86-9. Ann Emerg Med 1990;309-15. Ann Emerg Med 1990;591-7 Ann Emerg Med 1990;820-5 Ann Emerg Med 1990;1054-9 Ann Emerg Med 1990;1462-8. Graphpad.com Bmj.com/collections/statbk.index.shtml 11