. 2018 Dec 13;13(12):e0208876. doi: 10.1371/journal.pone.0208876

Table 2. Parameters used to simulate datasets.

Simulation Parameters
Mean Model
Intercept (β₀) = 14.00 units
Intervention effect (∂) = 2 OR -2 units
Linear time trend (τ) = 0.25 units per month
Intervention additional time trend (ψ) = 0.15 OR 0.25 OR -0.50 units per month
Non-linear calendar time trend $2 s i n (\frac{(t - 1) π}{12})$ {for scenarios D5, D6, D25-D30}
such that κ₁ ∈ (0, 0.52, 1.00, 1.41, 1.73, 1.98, 2.00, 1.93, 1.73, 1.41, 1.00, 0.52, 0)
Non-linear calendar time trend $2 s i n (\frac{(t - 1) π}{6})$ {for scenarios D7, D8, D31-D36}
such that κ₂ ∈ (0, 1.00, 1.73, 2.00, 1.73, 1.00, 0, -1.00, -1.73, -2.00, -1.73, -1.00, 0)
where t ∈ (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
Non-linear exposure time trend $s i n (\frac{(d - 1) π}{12})$ {for scenarios D25-D30}
such that ξ₁ ∈ (0, 0, 0.26, 0.50, 0.71, 0.87, 0.97, 1.00, 0.97, 0.87, 0.71, 0.50, 0.26)
Non-linear exposure time trend $s i n (\frac{(d - 1) π}{6})$ {for scenarios D31-D36}
such that ξ₂ ∈ (0, 0, 0.50, 0.87, 1.00, 0.87, 0.50, 0, -0.50, -0.87, -1.00, -0.87, -0.50)
where d ∈ (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
Fixed Effects Parameterisations for each Scenario
D1, D2: y_itk = 14	D19, D20: y_ik(t) = 14 + 0.25t + 0.25d_tk
D3, D4: y_ik(t) = 14 + 0.25t	D21, D22: y_ik(t) = 14 − 2x_tk + 0.25t − 0.50d_k
D5, D6: y_itk = 14 + κ_1t	D23, D24: y_ik(t) = 14 + 0.25t − 0.50d_tk
D7, D8: y_itk = 14 + κ_2t	D25, D26: y_itk = 14 + 2x_tk + κ_1t
D9, D10: y_itk = 14 + 2x_tk	D27, D28: y_itk = 14 + 2x_tk + κ_1t + ξ_1d
D11, D12: y_ik(t) = 14 + 2x_tk + 0.25t	D29, D30: y_itk = 14 + κ_1t + ξ_1d
D13, D14: y_ik(t) = 14 + 2x_tk + 0.25t + 0.15d_tk	D31, D32: y_itk = 14 + 2x_tk + κ_2t
D15, D16: y_ik(t) = 14 + 0.25t + 0.15d_tk	D33, D34: y_itk = 14 + 2x_tk + κ_2t + ξ_2d
D17, D18: y_ik(t) = 14 + 2x_tk + 0.25t + 0.25d_tk	D35, D36: y_itk = 14 + κ_2t + ξ_2d

y_itk is the HoNOS score for participant i at time step t in cluster k, x_tk is an indicator variable for whether at time step t cluster k was under the control or intervention condition, t is the calendar time, d_tk is the exposure time to the intervention in cluster k at calendar time t, κ₁ and κ₂ are sets of parameters corresponding to the non-linear calendar time coefficients, ξ₁ and ξ₂ are sets of model parameters for the effects of different non-linear exposure times d to the intervention.