In order to assess the time at which the distant @entity3 were initiated, a model has been developed to simulate the natural history of @entity1 @entity0 . The @entity3 appearance curves were fitted to those observed for @entity5 of various sizes among the 2648 @entity1 treated at the Institut Gustave Roussy from 1954 to 1972. The model assumes that @entity3 are initiated when the @entity5 reaches a threshold volume (distribution of this volume was estimated in a previous article). Two patterns of growth were considered: exponential and Gompertzian. Distributions of @entity5 and @entity3 doubling times are fixed according to the literature. A relationship between @entity5 and @entity3 doubling time is estimated. Simulations were used to optimize @entity3 growth duration as a function of the @entity3 doubling time. The ages of the @entity3 at @entity5 diagnosis are calculated. With exponential growth, it was necessary to introduce correlations to obtain a satisfactory fit of the @entity3 appearance curves: between the @entity5 volume at diagnosis and the doubling time (R1 = -0.3), and between the @entity5 volume at @entity3 initiation and the doubling time (R2 = 0.3). The growth duration of the @entity3 before their detection was found to equal about 18 @entity3 doubling times at detection and the mean ratio between the doubling time of a @entity5 and its @entity3 equal to 2.2. With Gompertzian growth, it was impossible to adjust satisfactorily the proportions of @entity3 at diagnosis as a function of the primary @entity5 volume. However, when we ignore this, the best fit was obtained when the duration of @entity3 growth before detection was about the same as for exponential growth. With either growth pattern, the model predicts that the proportion of @entity1 with @entity3 would be reduced by approximately 30% if the primary @entity5 were treated 12 months earlier. This prediction is consistent with the results of the screening programs for @entity0 .

A simulation model of the natural history of @entity1 XXXX .

@entity1 :: ('9606', 'Species') :: ['human', 'patients'] @entity5 :: ('MESH:D009369', 'Disease') :: ['tumours', 'tumour'] @entity0 :: ('MESH:D001943', 'Disease') :: ['breast cancer'] @entity3 :: ('MESH:D009362', 'Disease') :: ['metastasis', 'metastases']
@entity0 :: (MESH:D001943,Disease) :: ['breast cancer']
