Transcript Slide 1
Randomized Clinical Trials (RCT) Randomized Clinical Trials (RCT) Designed to compare two or more treatment groups for a statistically significant difference between them – i.e., beyond random chance – often measured via a “p-value” (e.g., p < .05). Examples: Drug vs. Placebo, Drugs vs. Surgery, New Tx vs. Standard Tx Let X = decrease (–) in cholesterol level (mg/dL); possible expected distributions: Experiment Treatment population Control population significant? 1 2 H0 : 1 2 X 0 Patients satisfying inclusion criteria R A N D O M I Z E Treatment Arm End of Study RANDOM SAMPLES Control Arm T-test F-test (ANOVA) Randomized Clinical Trials (RCT) Designed to compare two or more treatment groups for a statistically significant difference between them – i.e., beyond random chance – often measured via a “p-value” (e.g., p < .05). Examples: Drug vs. Placebo, Drugs vs. Surgery, New Tx vs. Standard Tx Let T = Survival time (months); population survival curves: S(t) = P(T > t) 1 survival probability Kaplan-Meier estimates AUC difference significant? S2(t) Control S1(t) Treatment 0 H0 : S1 (t ) S2 (t ) T End of Study Log-Rank Test, Cox Proportional Hazards Model Case-Control studies Cohort studies Observational study designs that test for a statistically significant association between a disease D and exposure E to a potential risk (or protective) factor, measured via “odds ratio,” “relative risk,” etc. Lung cancer / Smoking Case-Control studies Cohort studies PRESENT PAST FUTURE cases E+ vs. E– ? controls reference group D+ vs. D– E+ vs. E– relatively easy and inexpensive subject to faulty records, “recall bias” D+ vs. D– ? measures direct effect of E on D expensive, extremely lengthy… Example: Framingham, MA study Both types of study yield a 22 “contingency table” of data: D+ D– E+ a b a+b E– c d c+d a+c b+d n where a, b, c, d are the numbers of individuals in each cell. H0: No association between D and E. End of Study Chi-squared Test McNemar Test Surveys, prevalence studies, etc. Surveys, prevalence studies, etc. The analytical techniques that apply to longitudinal studies (i.e., observations over time) are also appropriate for these cross-sectional studies (i.e., observations at a fixed time). PRESENT PAST FUTURE Many publicly available datasets from large federal studies on disease prevalence / incidence rates, birth / mortality rates, population trends, etc., are archived at the National Center for Health Statistics . As seen, testing for association between categorical variables – such as disease D and exposure E – can generally be done via a Chi-squared Test. But what if the two variables – say, X and Y – are numerical measurements? Furthermore, if sample data does suggest that one exists, what is the nature of that association, and how can it be quantified, or modeled via Y = f (X)? JAMA. 2003;290:1486-1493 correlation coefficient regression methods Other statistical issues along the way… • BIAS - Sources? What can we do about it? • How do we check if standard assumptions are valid, and what do we do if they are violated, or we can’t tell? • Do these techniques generalize, and if so, how? What are some other applications?