Package {ssPilot}

Main trial sample size using the non-central t-distribution

Description

Calculates the required main-trial sample size per treatment arm using the non-central t-distribution (NCT) approach described by Julious and Owen.

Usage

nct_sample_size(
  pilot_n,
  sd,
  effect,
  power = 0.9,
  alpha = 0.05,
  allocation = 1,
  max_n = 10000
)

Arguments

Details

See also ssPilot::optimized_nct_sample_size.

Value

A list containing the pilot-trial sample size per arm, pilot-trial degrees of freedom, required main-trial sample size per arm, main-trial degrees of freedom, central t critical value, non-central t quantile, and the right-hand side of Equation (4).

References

Julious SA and Owen RJ. Sample size calculations for clinical studies allowing for uncertainty about the variance. Pharmaceut Stat 2006; 5: 29–37.

Examples

nct_sample_size(
  pilot_n = 12,
  sd = 1,
  effect = 0.50,
  power = 0.90,
  alpha = 0.05
)

Optimize pilot sample size using the non-central t-distribution

Description

Determines the pilot-trial sample size per treatment arm that minimizes the total sample size required for the pilot and main trials using the non-central t-distribution (NCT) approach.

Usage

optimized_nct_sample_size(
  sd,
  effect,
  power = 0.9,
  alpha = 0.05,
  allocation = 1,
  min_pilot_n = 10,
  max_pilot_n = 100,
  max_main_n = 10000
)

Arguments

Details

The function evaluates a range of possible pilot sample sizes and calls [nct_sample_size()] for each candidate pilot size. The optimal pilot sample size is the one that minimizes the combined pilot and main-trial sample size per arm.

Value

A list containing:

optimal_pilot_n_per_arm

Optimal pilot sample size per arm.

main_n_per_arm

Required main-trial sample size per arm corresponding to the optimal pilot size.

total_n_per_arm

Combined pilot and main-trial sample size per arm.

pilot_degrees_of_freedom

Degrees of freedom from the pilot trial.

main_degrees_of_freedom

Degrees of freedom from the main trial.

critical_value

Critical value from the corresponding main-trial calculation.

nct_quantile

Non-central t quantile from the corresponding calculation.

equation_value

Sample-size equation value from the corresponding calculation.

optimization_results

Data frame containing the results for all candidate pilot sample sizes.

References

Whitehead, A. L., Julious, S. A., Cooper, C. L., & Campbell, M. J. (2016). Estimating the sample size for a pilot randomised trial to minimise the overall trial sample size for the external pilot and main trial for a continuous outcome variable. Statistical Methods in Medical Research, 25(3), 1057–1073.

Examples

results <- optimized_nct_sample_size(
  sd = 1,
  effect = 0.50,
  power = 0.90,
  alpha = 0.05
)
plot(results)

Optimized pilot sample size using the UCL method

Description

Finds the pilot-trial sample size per treatment arm that minimizes the combined pilot and main-trial sample size using the upper confidence limit approach.

Usage

optimized_ucl_sample_size(
  sd,
  effect,
  power = 0.9,
  alpha = 0.05,
  allocation = 1,
  conf_level = 0.8,
  min_pilot = 10,
  max_pilot = 100
)

Arguments

Value

A list containing the optimal pilot sample size per arm, the corresponding main-trial sample size per arm, the total sample size per arm, the confidence level used, and a data frame containing the optimization results for all candidate pilot sample sizes.

References

Whitehead, A. L., Julious, S. A., Cooper, C. L., & Campbell, M. J. (2016). Estimating the sample size for a pilot randomised trial to minimise the overall trial sample size for the external pilot and main trial for a continuous outcome variable. Statistical Methods in Medical Research, 25(3), 1057–1073.

Examples

results <- optimized_ucl_sample_size(
  sd = 1,
  effect = 0.50,
  power = 0.90,
  alpha = 0.05,
  conf_level = 0.80
)
plot(results)

Plot pilot and main-trial sample size relationship

Description

Creates a plot showing the relationship between pilot-trial sample size and the corresponding main-trial sample size from an optimized sample size calculation. The combination that minimizes the total sample size is highlighted.

Usage

## S3 method for class 'sspilot'
plot(x, ...)

Arguments

Value

A ggplot object showing pilot-trial sample size against main-trial sample size, with the optimal combination highlighted.

Examples

ucl_results <- optimized_ucl_sample_size(
  sd = 1,
  effect = 0.50,
  power = 0.90,
  alpha = 0.05
)

plot(ucl_results)

Standard sample size for a two-arm continuous outcome trial

Description

Calculates the required main-trial sample size per treatment arm assuming the population standard deviation is known.

Usage

standard_sample_size(sd, effect, power = 0.9, alpha = 0.05, allocation = 1)

Arguments

Value

Required sample size per treatment arm.

Examples

standard_sample_size(
  sd = 1,
  effect = 0.5,
  power = 0.90,
  alpha = 0.05
)

Main trial sample size using the upper confidence limit method

Description

Calculates the required main-trial sample size per treatment arm using the upper confidence limit (UCL) approach described by Browne.

Usage

ucl_sample_size(
  pilot_n,
  sd,
  effect,
  power = 0.9,
  alpha = 0.05,
  allocation = 1,
  conf_level = 0.8
)

Arguments

Details

Browne recommends an 80 level. However, Sim and Lewis, set X at 0.95 or the 95

Value

A list containing the degrees of freedom, upper confidence limit for the variance, upper confidence limit for the standard deviation, and main-trial sample size per treatment arm.

References

Browne RH. On the use of a pilot sample for sample size determination. Stat Med 1995; 14: 1933–1940.

Sim J and Lewis M. The size of a pilot study for a clinical should be calculated in relation to considerations of precision and efficiency. J Clin Epidemiol 2012; 65: 301–308.

Examples

ucl_sample_size(
  pilot_n = 16,
  sd = 1,
  effect = 0.50,
  power = 0.90,
  alpha = 0.05,
  conf_level = 0.80
)