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EMR 6550: Experimental and QuasiExperimental Designs Dr. Chris L. S. Coryn Kristin A. Hobson Fall 2013 Agenda • Quasi-experimental designs that use both control groups and pretests • Interrupted time-series designs • Design and power problems Designs that Use Both Control Groups and Pretests Untreated Control Group Design with Dependent Pretest and Posttest Samples NR O1 NR O1 X O2 O2 • A selection bias is always present, but the pretest observation allows for determining the magnitude and direction of bias Outcome Pattern 1 Treatment Control • Both groups grow apart at different average rates in the same direction • This pattern is consistent with treatment effects and can sometimes be causally interpreted, but it is subject to numerous threats, especially selection-maturation Outcome Pattern 2 Treatment • Spontaneous growth only occurs in the treatment group Control • Not a lot of reliance can be placed on this pattern as the reasons why spontaneous growth only occurred in the treatment group must be explained (e.g., selection-maturation) Outcome Pattern 3 Treatment Control • Initial pretest differences favoring the treatment group diminish over time • Same internal validity threats as outcome patterns #1 and #2 except that selectionmaturation threats are less plausible Outcome Pattern 4 Control Treatment • Initial pretest differences favoring the control group diminish over time • Subject to numerous validity threats (e.g., selection-instrumentation, selection-history), but generally can be causally interpreted Outcome Pattern 5 Treatment Control • Outcomes that crossover in the direction of relationships • Most amenable to causal interpretation and most threats cannot plausibly explain this pattern Modeling Selection Bias • Simple matching and stratifying – Overt biases with respect to measured variables/characteristics • Instrumental variable analysis – Statistical modeling of covariates believed to explain selection biases • Hidden bias analysis – Difference with respect to unmeasured variables/characteristics – Sensitivity analysis (how much hidden bias would need to be present to explain observed differences) • Propensity score analysis – Predicted probabilities of group membership – Propensities then used for matching or as covariate Effect-Decay Functions Delayed Effect Immediate Effect, No Decay Large Response Small Program Onset Program Termination Response Small Program Onset Program Termination Response Small Time Early Effect, Slow Decay Immediate Effect, Rapid Decay Large Large Time Program Onset Program Termination Time Program Onset Program Termination Time Large Response Small Untreated Control Group Design with Dependent Pretest and Posttest Samples Using a Double Pretest NR O1 O2 NR O1 O2 X O3 O3 • Permits assessment of selection-maturation on the assumption that the rates between O1 and O2 will continue between O2 and O3 • Testable only on the control group Untreated Control Group Design with Dependent Pretest and Posttest Samples Using Switching Replications NR O1 NR O1 X O2 O2 O3 X O3 • A strong design and only a pattern of historical changes that mimics the time sequence of the treatment introductions can serve as an alternate explanation • The addition of treatment removal (X) can strengthen cause-effect claims Untreated Control Group Design with Dependent Pretest and Posttest Samples Using Reversed Treatment Control Group NR O1 X+ O2 NR O1 X- O2 • Interpretation of this design depends on producing two effects with opposite signs • Adding a control is useful • Ethically, often difficult to use a reversed treatment Interrupted Time-Series Designs Interuppted Time-Series • A large series of observations made on the same variable consecutively over time – Observations can be made on the same units (e.g., people) or on constantly changing units (e.g., populations) • Must know the exact point at which a treatment or intervention occurred (i.e., the interruption) • Interrupted time-series designs are powerful cause-probing designs when experimental designs cannot be used and when a time series is feasible Types of Effects • Form of the effect (slope or intercept) • Permanence of the effect (continuous or discontinuous) • Immediacy of the effect (immediate or delayed) Analytic Considerations • Independence of observations – (Most) statistical analyses assume observations are independent (one observation is independent of another) – In interrupted time-series, observations are autocorrelated (related to prior observations or lags) – Requires a large number of observations to estimate autocorrelation • Seasonality – Observations that coincide with seasonal patterns – Seasonality effects must be modeled and removed from a time-series before assessing treatment impact Simple Interrupted TimeSeries Design O1 O2 O3 O4 O5 X O6 O7 O8 O9 O10 • The basic interrupted time-series design requires one treatment group with many observations before and after a treatment Change in Intercept 20 18 Intervention 16 14 12 10 8 6 Change in intercept 4 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Change in Slope 35 Intervention 30 25 20 15 10 Change in slope 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Weak and Delayed Effects 35 Intervention 30 25 20 15 10 5 Impact begins 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 Validity Threats • With most interrupted time-series designs, the major validity threat is history – Events that occur at the same time as the treatment was introduced • Instrumentation is also often a threat – Over long time periods, methods of data collection may change, how variables are defined and/or measured may change • Selection is sometimes a threat – If group membership changes abruptly Additional Designs O1 O1 O2 O2 O3 O3 O5 O5 X O6 O6 OA1 OA2 OA3 OA4 OA5 OB1 OB2 OB3 OB4 OB5 X X OA6 OA7 OA8 OA9 OA10 OB6 OB7 OB8 OB9 OB10 O1 O2 O3 O4 O4 O4 X O7 O7 O8 O8 O9 O10 O9 O10 O5 O6 O7 O8 X O9 O10 O11 O12 • (1) nonequivalent control group, (2) nonequivalent dependent variable, and (3) removed treatment Nonequivalent Control Group 80 Intervention 70 Treatment group 60 50 40 Control group 30 20 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Nonequivalent Dependent Variable Intervention 35 30 25 Nonequivalent dependent variable 20 Dependent variable 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Removed Treatment Introduction 30 Removal 25 Treatment period 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Design and Power Problems Problem #1 • A school administrator wants to know whether students in his district are scoring better or worse than the national norm of 500 on the SAT • He decides that a difference of 20-25 points or more from this normative value would be important to detect • He anticipates that the standard deviation of scores in his district is about 80 points – Determine the number of students necessary for power at 95% to detect a difference of 20 and 25 points – Graph both – Diagram the design of the study Problem #2 • Patients suffering from allergies are nonrandomly assigned to a treatment and placebo condition and asked to rate their comfort level on a scale of 0 to 100 • The expected standard deviation is 20 and a difference of 10-20 is expected (treatment = 50-60 and placebo = 40) – Determine the number of patients necessary for power at 95% to detect a difference of 10 and 20 points – Graph both – Diagram the design of the study Problem #3 • The cure rate for two current treatments are 10% and 60%, respectively • The alternative treatments are expected to increase the cure rate by 10% – Determine the number of patients necessary for power at 95% to detect a difference of 10% for both scenarios – Graph both – Diagram the design of the studies