Introduction to Experimental and Observational Study Design KNNL – Chapter 16

Experimental and Observational Studies Experimental Studies – Units (aka Subjects in human studies) assigned at random to treatments/conditions – Experimental Factors – Conditions with 2 or more levels, which are assigned to units. If there is more than one factor, treatments are combinations of factor levels assigned to units. Observational Studies – Units are sampled from two or more populations/subpopulations – Observational Factors – Set of levels of Populations/subpopulations used in the study Causation is directly obtained in Experimental Studies, not in Observational Studies Mixed Designs  Experimental & Observational Factors

Basics of Experimental Studies Explanatory Factors – Conditions (with 2 or more levels) that are assigned to units. – Crossed Factors – Factors with levels that are the same within levels of the other factor(s) – Nested Factors – Factors with levels that are different within levels of the other factor(s) Treatments – Combinations of factor levels given to units Experimental Units – Units used in the study, which are subject to randomization to treatments. Randomization Process - Use of random number generator to assign units to treatments Outcome measurement(s) obtained from treated units

Completely Randomized and Blocked Designs Experiment with One 2 Levels (Treatments) Completely Randomized Design – Take all subjects, and randomize so that half receive Trt A, and other half receive Trt B Y i =     X i1 +  i X i1 = 1 if subject i received A, 0 if B Randomized Block Design – Generate blocks of subjects that are similar wrt external criteria (gender, age,…) and randomize treatments to subjects within blocks. Helps make treatment groups more similar. Y = Overall Mean + Trt Effect + Block Effect + Error

Standard Experimental Designs - I Completely Randomized Design (CRD) – Units randomized to treatments with no restrictions on randomization process Factorial Experiments – CRD with two or more crossed factors. Treatment effects are made up of main factor effects and interaction effects Randomized Complete Block Design (RCBD) – Units are grouped into blocks. Treatments randomly assigned to units within blocks

Standard Experimental Designs - II Nested Designs – Levels of Factor B differ across levels of Factor A Crossed/Nested Designs – Designs with both crossed and nested factors Repeated Measures Designs – Each unit is measured multiple times – Each subject receives each treatment once – Each subject receives only one treatment, but is measured at multiple time points Split-Plot Designs – Two (or more) sizes of experimental units due to randomization restrictions for factors

Standard Experimental Designs - III Incomplete Block Designs – Block Designs with block sizes smaller than the number of treatments 2-Level Factorial Experiments – Several (possibly many) factors, each at 2 levels (low/high). With k factors, there will be 2 k treatments 2-Level Fractional Factorial Designs – Experiments with only a subset of all 2 k treatments to reduce cost, but still obtain estimates of main effects and lower-order interactions Response Surface Designs – Designs used to fit polynomial regression models for numeric factors

Observational Study Designs Cross-Sectional Studies – Observations made from populations/subpopulations at a single time point or interval. Prospective Studies – Groups are formed by levels of a potential causal factor, then observed over time for some measurable outcome. Retrospective Studies – Studies where subjects are identified based on the outcome of interest, potential risk factors are identified that previously occurred Matching – Subjects from different populations are matched, based on external factors – like blocking