Title:

The place of crossover designs in infertility trials

Many people regard infertility as an unsuitable condition in which to run crossover designs. Because if treatments are successful, then some women will become pregnant in the first period of treatment and if they become pregnant in the first period they are very unlikely to be treated in the second period. If data from only one period are available, then it will not be possible to perform the withinpatient comparison. Hence, it could be argued, such designs are inherently unsuitable since they have a builtin tendency to produce missing data. To sum up this point of view, crossover designs in infertility are likely to produce fewer data than one would wish and should be avoided. We see things differently, however. Suppose a parallel design is employed. If a couple is entered onto a parallel group design in infertility, they will have been allocated to one or the other treatment only. If the woman fails to achieve pregnancy, having been given that treatment, what could then be more natural than to offer the couple the chance of trying another? If another treatment is tried, then will it not be appropriate to record the outcome? Hence, in the worst case one will have all the data one would have from a parallel group trial but in practice one is likely to have more. How can more data be worse than less?Thus, to sum up our point of view, a crossover trial is likely to produce more data than one would otherwise have had and should be encouraged. A debate along these lines has been running for some years now, with some promoting and occasionally running crossover trials and others criticising them for doing so. In this thesis we use the logistic random effects model to illustrate that the message that the crossover design should be avoided is not the correct one. Rather, when using the crossover design one should be sure to analyze it correctly. The study has found that treatment estimates obtained by allowing women to get pregnant twice has lower standard errors than treatment estimates obtained by conducting the realistic infertility trials. In the scenario involving no period effects the two treatment estimates are not biased. In the scenario involving period effect, the standard errors of the treatment estimate obtained in the realistic data increases rapidly, while the standard errors of treatment estimate obtained by allowing women to get pregnant twice are not dissimilar from the standard errors obtained in the scenario involving no period effect. There is nothing wrong in conducting crossover designs in infertility provided appropriate statistical methods are employed. With the infertility crossover data set we can obtain not only conditional treatment estimates but also marginal estimates. Whereas in the parallel design we can only obtain marginal estimates. The study has found that if the treatment estimate say theta, can be obtained using parallel design data set, then surely, theta can be obtained using the crossover design data set, but not vice versa. Moreover the treatment estimate theta obtained using the crossover data set will be more consistent than the treatment estimate obtained using the parallel design. We recommend that crossover designs be used in infertility trials because it will surely benefit couples as couples will be have the opportunity to try both treatments.
