First, the corrected chi-square involves 2n+2 estimations of the logistic regression coefficients, n being the number of bootstraps. In comparison, only two models must be parameterized in the logistic regression. As a consequence, the logistic regression approach is much faster to run (less than a second versus 2.5 minutes for the corrected chi-square for a model with 6 factors in full interaction and 300 individuals, for 1000 bootstraps, using a desktop computer with an Intel(R) core(TM)2 Quad CPU Q6600 processor). Second, the corrected chi-square is more robust than the logistic regression, especially for small sample size. A first solution would be to use the corrected chi-square as soon as simulation times are acceptable. For a 5% rejection threshold, a more straightforward alternative is to use the corrected chi-square by default as soon as the ratio between the sample size and the number of parameters is below 10 and the logistic regression in the opposite case. However, we did not test all potential situations and further analyses are needed to determine the limit of robustness of the logistic regression approach (in particular in situations where the probability of infection is not 50% and can be affected by risk factors).