SSR_WMW: Sample size reassessment rule for rank based randomization...
In floatofmath/adaperm: Permutation tests for adaptive designs

Description Usage Arguments Details Value Functions Author(s) References See Also

Re-computes the sample size based on first stage observations and assuming that a WMW test is performed at the end of the trial. It estimates the overall (across all stages) number of control-group observations required to achieve the target power. The returned value may be smaller than the preplanned sample size, even the first stage sample size - so any minimum sample size restrictions need to be enforced outside of the function. The maximum (overall control-group) sample size however is enforced internally.

cond_power_rule_w_ts(x1, y1, z2, pp, target = 0.9, alpha = 0.025,
  maxN = length(x1) * 6, propn = 1/2)

predictive_power_rule_w_ts(x1, y1, m = 2 * length(x1), target = 0.9,
  alpha = 0.025, maxN = length(x1) * 6, propn = 1/2)

approximate_power_rule_w_ts(x1, y1, m = 2 * length(x1), pp, lambda = 1e-04,
  alpha = 0.025, maxN = length(x1) * 6, propn = 1/2)

combination_power_rule_w_ts(x1, y1, m = 2 * length(x1), pp, lambda = 1e-04,
  alpha = 0.025, maxN = length(x1) * 6, propn = 1/2)

optimal_power_rule_w_ts(x1, y1, z2, pp, lambda = 1e-04, alpha = 0.025,
  maxN = length(x1) * 6, propn = 1/2)

`x1`	first stage (control-group) sample
`y1`	first stage (control-group) sample
`z2`	second stage blinded combined sample
`pp`	list with prespecified order probabilities p1, p2, p3 (see `order_probabilities` and `delta2res` for details)
`target`	desired target power
`alpha`	significance level of the preplanned test
`maxN`	maximum overall (control-group) sample size
`propn`	proportion of the total number of observations in the control group
`m`	preplanned overall (control-goup) sample size
`lambda`	penalty factor for additional sample in the combined objective

The function cond_power_rule_w_ts recomputes the sample size using the sample size formula of power.w.test to achieve the target power target assuming the order probabilities pp with a second stage WMW test at the level of the conditional error rate of the preplanned test.

The function predictive_power_rule_w_ts recomputes the order probabilities based on the first stage observations and reestimates the sample size required to achieve the target power using the sample size formula of power.w.test.

The functions approximate_power_rule_w_ts, combination_power_rule_w_ts and optimal_power_rule_w_ts compute the sample size that maximizes the combined objective CP(x1,y1) - lambda*nA defined in [Jennison and Turnbull (2015)]. approximate_power_rule_w estimates the conditional power using the power formula of power.w.test with weighted averages of the prespecified order proabibilities pp and the order probabilities estimated from the first stage obseravtions. comb_power_rule_w_ts estimates the conditional power using the power formula of power.w.test of a second stage WMW with the prespecified order probabilities at the level of the conditional error of the inverse normal combination WMW test, finally optimal_power_rule_w_ts estimates the conditional power in the same way however using the conditional error rate of the preplanned randomization test - which requires knowledge of the blinded second stage observations.

reassessed overall sample size

cond_power_rule_w_ts: Conditional power rule for the WMW test
predictive_power_rule_w_ts: Predicitive power rule for the WMW test
approximate_power_rule_w_ts: Efficient power rule for the WMW test using approximate conditional order probabilities
combination_power_rule_w_ts: Efficient power rule for the WMW test using the combination test conditional power
optimal_power_rule_w_ts: Efficient power rule for the WMW test using the conditional power of a second stage WMW test

float

Lehmann, Erich Leo, and H. J. D'abrera. Nonparametrics: statistical methods based on ranks. Springer, 2006.

Jennison, Christopher, and Bruce W. Turnbull. "Adaptive sample size modification in clinical trials: start small then ask for more?." Statistics in medicine 34.29 (2015): 3793-3810.

Bauer, Peter, and Franz Koenig. "The reassessment of trial perspectives from interim data—a critical view." Statistics in medicine 25.1 (2006): 23-36.

order_probabilities that estimates order probabilities from observations, delta2res that computes order probabilisities for normally distributed observations

floatofmath/adaperm documentation built on May 16, 2019, 1:18 p.m.