Parallel Random Designs

Derived from this video S4b Sample size and power for cluster randomised trial

Notes

4.b Parallel arm cluster randomization (no repeated measure) 4.c Loongitudinal cluster randomization (repeated measure)

1.0 Parallel arm cluster randomization (no repeated measures)

  1. Target difference or "effect size"

  2. Measure of variation:

    • Standard deviation if continuous outcome ()
    • Control arm proportion if dichotomous outcome (proportion: )

  3. Desired statistical power (1- )

    • or 1 - probabiility of a type-II error.
    • Type II error = failing to delcare a significant difference when it does exist.
    • Generally try to achieve power of +80%.

  4. Desired level of significance ()

    • Probability of Type-I error
    • Type-1 Error: Declaring significant difference when one doesn't exist.
    • Generally try to keep error rate < 5%.

1.1 Mean Testing: Null Hypothesis: H0:

  • 2 treatment conditions: intervention & control
  • Superior design (is the intervention superior than control?)
  • Equal allocation (1:1 randomization t:c)
  • Consider continuous & dichotomous

Note, that these are for an individually not cluster randomized designs.

Calculated Size:

Observations needed per arm .

1.2 Proportion testing: Null Hypothesis: H0:

  • 2 treatment conditions: intervention & control
  • Superior design (is the intervention superior than control?)
  • Equal allocation (1:1 randomization t:c)
  • Consider continuous & dichotomous

Note, that these are for an individually not cluster randomized designs.

Observations needed per arm .

2.0 Examples

Let's assume that we want to incrementally increase our enrollment rate, .

is currently set to be:

Let's say we have a magic wand that incrementally increases the relative enrollment rate by 30%, i.e., .

Question: How many people would we need to observe this relative increase in enrollment rate with a given statistical certainty?

Answer:

Let's use this equation to calculate:

You would need: participants in each arm to observe a relative shift of % in enrollment rate (i.e., a p1 of and a p2 of ). Note that the relative increase is a common framing, but one that is somewhat mathematically confusing.