Data
In this study, we used data from patients who were diagnosed with testicular germ cell tumors and referred to the CECOS national network of sperm banks for sperm cryopreservation. Information was obtained from the national network of sperm banks (in Alsace, Aquitaine, Auvergne, Basse-Normandie, Bretagne, Centre, Champagne-Ardenne, Franche-Comté, Haute-Normandie, Ile de France, Languedoc-Roussillon, Lorraine, Midi-Pyrénées, Nord-Pas de Calais, Pays de la Loire, Picardie, Provence-Alpes-Côte d’Azur, and Rhône-Alpes) for the period 1990 to 2013.
Incidence was calculated from the number of sperm cryopreservations divided by the total French male population (men aged 18–49 years, with a mean annual number of 17,823,090 person-years, provided by the National Institute of Statistics (INSEE)). Incidence was expressed per 100,000 person-years. The National Cancer Agency (Institut National du Cancer, INCa) provided the estimated incidence of men presenting with testicular cancer between 1990 and 2012 [14].
Statistical analysis
In order to estimate trends in the incidence of sperm cryopreservation, we used two statistical models.
Firstly, the Poisson regression model, which is commonly used in this type of estimation [15, 16]. The mathematical equation for the Poisson regression model is (Y| t) = elog(exposure) + β ’ t. Exposure represents the person-years and was calculated on the total French male population. β’ is the estimated coefficient which gives the average annual percent change of incidence of sperm cryopreservation.
Secondly, we used the Verhulst (or growth logistic) model [17, 18] defined through the following mathematical eq. \( \mathrm{Y}\left(\mathrm{t}\right)=\frac{Y(0)K}{Y(0)+\left(K-Y(0)\right){e}^{- rt}} \) where Y(0) is the sperm cryopreservation incidence in 1990, and K and r the estimated coefficients. The coefficient r is called the proportionality coefficient or Malthusian parameter (rate of maximum population growth). The second parameter K is called the carrying capacity and gives the maximum sperm cryopreservation incidence or the sperm cryopreservation plateau (level-off). In order to estimate r and K, the mean square error method (MSE) was used. A range of r and K values were first defined and the MSE was then calculated for each r and K value. We selected the couple (r, K) which had the smallest MSE.
Finally, the predictions of trends in sperm cryopreservation incidence given by the two models (the Poisson regression model and the Verhulst model) were compared with the true sperm cryopreservation incidence rate observed in the CECOS network of French regional sperm banks.
The statistical analyses were performed using R software (CRAN) with a significance level of .05.
The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.