Introduction to Experimental and Observational Study Design Experimental

Introduction to Experimental and Observational Study Design

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 • Response measurement(s) obtained on measurement units which may differ from experimental units

Completely Randomized and Blocked Designs • Experiment with One Factor @ 2 Levels (Treatments) • Completely Randomized Design – Take all units, and randomize so that half receive Trt A, and other half receive Trt B Yi = b 0+b 1 Xi 1+ei Xi 1 = 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. Blocks may be units that receive each treatment 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 unit receives each treatment once – Each unit 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 a subset of all 2 k treatments to reduce cost, to obtain estimates of main effects and lower-order interactions • Response Surface Designs – Designs used to fit optimize responses along levels of numeric factors • Mixture Designs – Optimize responses at mixtures of input factors (typically chemical inputs)

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 • Longitudinal Studies – Observations made over multiple time points on same subjects.