## Adjusting for ex­pect­ed drop­out-rate [Power / Sample Size]

Dear all,

regularly I come across interesting methods for adjusting the sample size. Strange enough many people apply this formula:
$$n_{\textrm{adj}}=100\times n_{\textrm{des}}\times (1+dor) \tag{1}$$
where nadj is the adjusted sample size (dosed subjects), ndes the desired sample size (as estimated for the desired power), and dor the expected dropout-rate in percent. nadj is rounded up to give balanced sequences (crossover) or equal group sizes (parallel). This formula is flawed – especially for high sample sizes and/or high dropout-rates.
Example: 2×2 crossover and expected dropout-rate 15%

 ndes  nadj   n   12    14   12   24    28   24   30    36   31   36    42   36   48    56   48   64    74   63   72    84   71   96   112   95  120   138  117  144   166  141

If one applies this formula, the number of eligible subjects n might be lower than desired – resulting in a potential drop in power. Don’t shoot yourself in the foot. Use this one instead:
$$n_{\textrm{adj}}=100\times n_{\textrm{des}}/ (100-dor) \tag{2}$$
which gives:

 ndes  nadj   n   12    16   14   24    30   26   30    36   31   36    44   37   48    58   49   64    76   65   72    86   73   96   114   97  120   142  121  144   170  145

If the dropout-rate is ≈ as expected, the desired power will always be preserved (since n ≥ ndes).
(1) is flawed because the actual dropout-rate is based on the dosed subjects (i.e., calculated down­wards from nadj – not upwards from ndes).
On the other hand for low sample sizes and/or dropout-rates (2) might be overly con­ser­vative. Of course you could “pick out the best” from both (i.e., the nadj which will lead to the lowest nndes).

A nice statement* [about an anticipated dropout rate of 15%]:

Note a very common mistake when calculating the total sample size is to multiply the evaluable sample size by 1.15 and not divide by 0.85.

An all to common error though in daily life many people fail to calculate the net value from the total amount and VAT as well. If the total is 110.– and the VAT is 10%, the net value is 100.– (i.e., 110/1.10) and not 99.– (110×0.90)…

• Julious SA. Sample Sizes for Clinical Trials. Boca Raton: CRC Press; 2010. p.53.

Dif-tor heh smusma 🖖
Helmut Schütz

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