Correction: Parameter estimation for multistage clonal expansion models from cancer incidence data: A practical identifiability analysis.

[This corrects the article DOI: 10.1371/journal.pcbi.1005431.].

Table 1 and Figs 4, 5, 7, 8 and 10 are incorrect. There is an error in the value of the threshold used to calculate the confidence intervals. The authors have provided the corrected versions here.

Table 1

Best-fit parameters and likelihood-based 95% confidence intervals.

Best-fit parameters and likelihood-based 95% confidence intervals for the fits of the two-, three-, and four-stage clonal expansion models (with parameterizations using only practically identifiable parameter combinations and given in Eqs. (2), (9), and (11) respectively) to age-specific incidence of pancreatic cancer.

Model	Parameter combination	Value	Likelihood-based 95% CI
Two-stage
	p_2=12(−(α−β−μ_1)−(α−β−μ_1)^2−4αμ_1)	-1.29E-1	(-1.32E-1, -1.26E-1)
	q_2=12(−(α−β−μ_1)+(α−β−μ_1)^2−4αμ_1)	6.21E-6	(5.58E-6,6.88E-6)
	r2 = vX/α	1.50E-2	(1.38E-2,1.65E-2)
Three-stage
	p_3=12(−(α−β−μ_2)−(α−β−μ_2)^2−4αμ_2)	-1.38E-1	(-1.42E-1,-1.34E-1)
	q_3=12(−(α−β−μ_2)+(α−β−μ_2)^2−4αμ_2)	1.57E-5	(1.38E-5,1.76E-5)
	r_3=νXμ_1/α	2.35E-2	(2.23E-2,2.49E-2)
Four-stage
	p_4=12(−(α−β−μ_3)−(α−β−μ_3)^2−4αμ_3)	-1.50E-1	(-1.57E-1,-1.43E-1)
	q_4=12(−(α−β−μ_3)+(α−β−μ_3)^2−4αμ_3)	4.59E-5	(3.90E-5,5.32E-5)
	r3 = (vXμ1μ2/α)1/3	2.66E-2	(2.54E-2,2.80E-2)

Fig 4

Two-stage model profile likelihoods.

Profiles of the relative negative log-likelihood (NLL) of the two-stage clonal expansion model as each of the parameter combinations p2, q2, and νX/α are varied while the remaining parameters are fit. The gray dotted line gives the α = 0.05 threshold for simultaneous confidence intervals based on the relative negative log-likelihood. All three parameters are identifiable.

Fig 5

Three-stage model profile likelihoods.

Profiles of the relative negative log-likelihood (NLL) of the three-stage clonal expansion model as each of parameter combinations p3, q3, νX, and μ1/α are varied while the remaining parameters are fit. The gray dotted line gives the α = 0.05 threshold for simultaneous confidence intervals based on the relative negative log-likelihood. Parameter combinations p3 and p4 are identifiable, while νX and μ1/α are practically unidentifiable.

Fig 7

Profile likelihood for the reparameterized combination of the three-stage model.

Profile of the relative negative log-likelihood (NLL) as the parameter varied while the remaining parameters are fit in the three-stage clonal expansion model. The gray dotted line gives the α = 0.05 threshold for simultaneous confidence intervals based on the relative negative log-likelihood. Parameter combination r3 is identifiable.

Fig 8

Four-stage model profile likelihoods.

Profiles of the relative negative log-likelihood (NLL) of the four-stage clonal expansion model as each of parameter combinations p4, q4, νX, μ1, and μ2/α are varied while the remaining parameters are fit. The gray dotted line gives the α = 0.05 threshold for simultaneous confidence intervals based on the relative negative log-likelihood. Parameter combinations p4 and q4 are identifiable, while νX, μ1, and μ2/α are practically unidentifiable.

Fig 10

Profile likelihood for the reparameterized combination of the four-stage model.

Profile of the relative negative log-likelihood (NLL) as the parameter r4 = (νXμ1μ2/α)1/3 is varied while the remaining parameters are fit in the four stage clonal expansion model. The gray dotted line gives the α = 0.05 threshold for simultaneous confidence intervals based on the relative negative log-likelihood. Parameter combination r4 is identifiable.