Priors Sample Clauses

Priors. I use prior settings introduced in chapter 3 for the number of stage s and constant θ in the Armitage-Doll model. In addition, I use a Gaussian autoregressive prior model in the forward direction to smooth effects on period and cohort. Non-informative priors will be defined for the first two parameters for period and cohort. Suppose the projection is need for N future periods, so for the P + N period effects: x x0 ∼ N (0, 1000000 τ ), 1 β β2|β1 ∼ N (0, 1000000 τ ), 1 β βp|β1,...,p—1 ∼ N (2βp—1 − βp—2, τ ) 3 ≤ p ≤ P + N, τβ ∼ gamma(0.0001, 0.0001). For C + N cohort effects: γ γ1 ∼ N (0, 1000000 τ ), 1 γ γ2|γ1 ∼ N (0, 1000000 τ ), 1 γ γc|γ1,...,c—1 ∼ N (2γc—1 − γc—2, τ ) 3 ≤ c ≤ C + N, τγ ∼ gamma(0.0001, 0.0001).

Priors. In cancer development, the mutation rate µ is considered much smaller than the cell division rate α and the cell death rate β [Xxxxxxxxxx and Xxxx, 2009]. Therefore, p + q ≈ −(α − β). The quantity α−β represents the net proliferation rate of intermediate cells [Moolgavkar and Luebeck, 1992]. For colon cancer, Xxxxxxxxxx and Luebeck [1992] estimated the quantity of α−β as approximately 0.107 per cell per year which indicates on the average level a stem cell experiences an effective clonal expansion approximately once every 10 years. In addition, Xxxxxxxxxx and Luebeck [1992] also estimated the quantity of β/α as close to 1 through fitting the two and three-stage clonal expansion carcinogenesis models. The parameter q is much smaller than p and can be estimated as q ' µ/(1 − β/α). Based on Moolgavkar and Luebeck’s calculation [1992], the estimated mutation rates and initiation rates are on the magnitude of 10—6 to 10—8 . Therefore, I summarize the prelim- inary information and make our noninformative priors as follows: r ∼ Uniform(0, 10—5), p ∼ Uniform(−0.2, 0), q ∼ Uniform(0, 10—5).