STAT 509 - Lesson 9: Sample Size and Power - Part II

Comprehensive vocabulary flashcards covering the concepts, trial designs, statistical hypotheses, and SAS procedures for superiority, equivalence, and non-inferiority trials from STAT 509 Lesson 9.

Superiority trial objective

Establish that the experimental therapy is better than, or statistically different from, its control.

Equivalence trial objective

Demonstrate that the experimental therapy is neither clinically inferior nor clinically superior to the active control within a prespecified equivalence margin.

Non-inferiority trial objective

Demonstrate that the experimental therapy is not unacceptably worse than the active control.

Placebo-controlled trial

A trial comparing experimental therapy with placebo; it usually gives an unambiguous research hypothesis.

Confirmatory trial

A term often used for a placebo-controlled trial.

Active control

An established effective therapy used as the comparison group instead of placebo, typically used when placebo would be unethical.

Standard-of-care

The accepted best available treatment for a disease/condition; it may include drugs, devices, surgery, diet, exercise, or combinations.

Combination superiority design

A design that compares standard-of-care + experimental therapy versus standard-of-care + placebo therapy to show the combination is superior to standard-of-care alone.

Zone of clinical equivalence

A prespecified interval of treatment differences considered clinically equivalent; it must be chosen before the trial begins.

Equivalence margin ($\Psi$)

The maximum clinically acceptable magnitude of difference from the active control on either side.

General equivalence zone formula

For difference $D = \mu_E - \mu_C$, clinical equivalence requires $-\Psi < D < \Psi$.

Assay-sensitivity assumption

The active control should be a therapy previously proven superior to placebo and should be expected to retain that effect in the current trial.

External validity check

Comparing current active-control performance with prior active-control-versus-placebo trials by examining response levels, compliance, and withdrawal rates.

Intention-to-treat (ITT) analysis

Includes data on all randomized patients according to randomized assignment, regardless of protocol violations, adherence, withdrawal, or taking the other treatment.

Protocol analysis (Per-protocol)

Analyzes subjects according to treatment received and excludes subjects with eligibility violations, noncompliance, or other protocol deviations.

Non-inferiority zone (larger is better)

For $D = \mu_E - \mu_C$, non-inferiority requires $D > -\Psi$.

Equivalence null hypothesis ($H_0$)

$H_0: D \le -\Psi$ OR $D \ge \Psi$; the treatments are non-equivalent.

Equivalence alternative hypothesis ($H_A$)

$H_A: -\Psi < D < \Psi$; the treatments are equivalent within the prespecified margin.

Non-inferiority null hypothesis ($H_0$)

$H_0: D \le -\Psi$, assuming larger outcomes are better.

Non-inferiority alternative hypothesis ($H_A$)

$H_A: D > -\Psi$.

TOST

Two One-Sided Tests; the standard logic for equivalence testing where both non-inferiority and non-superiority nulls must be rejected.

Pooled variance ($s_p^2$)

$s_p^2 = \frac{(n_E-1)s_E^2 + (n_C-1)s_C^2}{n_E+n_C-2}$.

Non-inferiority t statistic ($t_{NI}$)

$$t_{NI} = \frac{(\bar{x}_E-\bar{x}_C)+\Psi}{s_p \times \sqrt{1/n_E + 1/n_C}}$$

Berger-Hsu equivalence confidence set

A confidence set where the lower endpoint is $\min(0, \hat{D} - t_{1-\alpha} \times SE)$ and the upper endpoint is $\max(0, \hat{D} + t_{1-\alpha} \times SE)$.

Equivalence CI decision rule

Conclude equivalence at significance level $\alpha$ only if the entire corresponding confidence interval lies within $(-\Psi, \Psi)$.

NI lower confidence limit ($L$)

$L = \hat{D} - t_{1-\alpha} \times SE(\hat{D})$, when larger responses are better.

NI decision rule

Conclude non-inferiority if the lower confidence limit is greater than $-\Psi$.

VALIANT trial

A real non-inferiority example comparing valsartan, captopril, or valsartan+captopril in post-MI heart-failure patients.

Continuous equivalence approximate sample size formula

$n_C \approx (1+1/AR) \times \sigma^2 \times \frac{(z_{1-\alpha} + z_{1-\beta/2})^2}{(\Psi - |D_0|)^2}$, where $n_E = AR \times n_C$.

Event-driven equivalence planning

Expressing power for time-to-event equivalence in terms of the required number of observed events.

Constant hazard equation

$S(t) = e^{-\lambda \times t}$, so $\lambda = -\frac{\ln(S(t))}{t}$.

Withdrawal adjustment formula

$N_{adjusted} = \frac{N}{1-W}$, where $W$ is the anticipated withdrawal proportion.

SAS procedure for continuous equivalence (Example 9.3)

Uses PROC POWER with the TWOSAMPLEMEANS statement and TEST=EQUIV_DIFF.

SAS procedure for binary non-inferiority (Example 9.4)

Uses PROC POWER with TWOSAMPLEFREQ, TEST=PCHI, and SIDES=1 as an adaptation.

SAS procedure for time-to-event non-inferiority (Example 9.5)

Uses PROC POWER with TWOSAMPLESURVIVAL, TEST=LOGRANK, and SIDES=1 as an adaptation.