Published data on time trends in the incidence of childhood leukaemia show inconsistent patterns, with some studies showing increases and others showing relatively stable incidence rates. Data on time trends in childhood cancer incidence from the Childhood Cancer Registry of Piedmont, Italy were analysed using two different approaches: standard Poisson regression and a Bayesian regression approach including an autoregressive component. Our focus was on acute lymphoblastic leukaemia (ALL), since this is hypothesised to have an infectious aetiology, but for purposes of comparison we also conducted similar analyses for selected other childhood cancer sites (acute non-lymphoblastic leukaemia (AnLL), central nervous system (CNS) tumours and neuroblastoma (NB)). The two models fitted the data equally well, but led to different interpretations of the time trends. The first produced ever-increasing rates, while the latter produced non-monotonic patterns, particularly for ALL, which showed evidence of a cyclical pattern. The Bayesian analysis produced findings that are consistent with the hypothesis of an infectious aetiology for ALL, but not for AnLL or for solid tumours (CNS and NB). Although sudden changes in time trends should be interpreted with caution, the results of the Bayesian approach are consistent with current knowledge of the natural history of childhood ALL, including a short latency time and the postulated infectious aetiology of the disease.