nvDT {DunnettTests} R Documentation

## To calculate the least sample size required to achieve a certain power

### Description

For the problem of comparing means of k treatment groups to the mean of one control group, the implementation of the function needs the following three assumptions: 1. The k treatment groups have identical treatment effect size. 2. The sample allocation ratio is pre-specified, and meanwhile the samples to be assigned to each of the k treatment groups are expected to be equal at size n. 3. The alternative hypotheses are one-sided. With the violations assumption 2, the sample size could not be evaluated numerically, and with the violation of assumption 1 and 3, the evaluation of sample size needs great computational effort and thus not implemented. In the situation, simulation-based evaluation is suggested.

### Usage

```nvDT(ratio,power,r,k,mu,mu0,contrast,sigma=NA,dist,alpha=0.05,mcs=1e+05,testcall)
```

### Arguments

 `ratio` The pre-specified ratio of sample size in each of the treatment groups to the sample size in the control group `power` The power required to be achieved. `r` The least number of null hypotheses to be rejected, e.g.,when r=1, the sample size is evaluated on disjunctive power and when r=k, the sample size is evaluated on conjunctive power. `k` Number of hypotheses to be tested, k≥ 2 and k≤ 16. `mu` Assumed population mean in each of the k treatment groups. `mu0` Assumed population mean in the control group. `contrast` If mu and mu0 are concerned of means of continous outcome, specify contrast="means"; if mu and mu0 are concerned of proportions of binary outcome, specify contrast="props". `sigma` The population error variance, which should be specified when contrast="means"; if contrast="props", set sigma=NA as default and it will be calculated based on mu and mu0 specified within the function. `dist` Whether the sample size is calculated for t-distributed test statistics (dist="tdist") or standard normally distributed test statistics (dist="zdist"). `alpha` The pre-specified overall significance level, default=0.05. `mcs` The number of monte-carlo sample points to numerically approximate the power for a given sample size, refer to Equation (4.3) and Equation (4.5) in Dunnett and Tamhane (1992). `testcall` The applied Dunnett test procedure: "SD"=step-down Dunnett test; "SU"=step-up Dunnett test.

### Value

Return a LIST containing:

 `"least sample size required in each treatment groups"` value of n `"least sample size required in the control group"` value of n0

### Author(s)

FAN XIA <phoebexia@yahoo.com>

### References

Charles W. Dunnett and Ajit C. Tamhane. A step-up multiple test procedure. Journal of the American Statistical Association, 87(417):162-170, 1992.

`powDT`
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