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Then, the logarithm of the marginal full likelihood for Cox cure regression is where, S i (t) = exp[-exp(β T Z i )Λ0 t)] and θ = (α T, β T T The estimate of (θ, Λ0) is obtained by maximizing l f over (θ, Λ0).
For an observation i, the full likelihood for vQTL with genotype uncertainty is L i = ∑ j = 1 3 p i j N (μ + x i T β + r j α, σ 2 exp (z i T γ + r j θ ) ) = ∑ j = 1 3 p i j f i j with variables other than f ij defined as for Equation 3. Let l i = log(L i), g ij = log(f ij), and ψ be the parameter vector, and assume observations are independent given the parameters such that L = ∑ i n L i.
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We performed full likelihood analysis for several lethalities around N 5) = 5 − 6 and N 8) = 7 − 9 and found that indeed the impact is rather marginal unless the deviation leads to a substantially smaller likelihood value.
For the fragment loss model, ρ F tends to be underestimated for the full likelihood but not for the start likelihood.
Moreover, the Cox partial likelihood instead of the full likelihood is usually considered for these models.
The estimates based on the start likelihood and on the full likelihood are very similar for the independent loss models.
The usual tools for computing optimal designs with full likelihood are no longer valid for partial information.
With S species, there are 4S+9 parameters needed for the full likelihood Θ in growth and abundance models, and 4S+8 (without ε) for mortality.
A partial information matrix is built in this case and optimal designs are computed and compared with the optimal designs for the full likelihood information.
The model fitting for the full likelihood model was achieved with the BUGS code in the Appendix.
For this reason, a marginal type of full likelihood considered by Boag [ 15] is available for Cox cure regression.
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Justyna Jupowicz-Kozak
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