Number of patients in cohort, control arm and intervention arm | N, Ncon, Nint |
Number of clusters in trial | K |
Size of each cluster | J = 620 |
Treatment allocated to kth cluster | Zk = 0/1 for control/intervention |
Treatment received by ith individual from kth cluster | Xik = 0/1 for control/intervention |
Time until CVD event for ith individual from the kth cluster | \( {\mathrm{T}}_{\mathrm{ik}}^{\mathrm{c}}\sim \mathrm{Weibull}\left({\upgamma}_{\mathrm{c}},{\uplambda}_{\mathrm{c}}{\mathrm{e}}^{-\left(\upbeta {\mathrm{X}}_{\mathrm{ik}}+{\upvarepsilon}_{\mathrm{ik}}+{\mathrm{U}}_{\mathrm{k}}\right)/{\upgamma}_{\mathrm{c}}}\right) \) |
Time until mortality (censoring distribution) for the ith individual from the kth cluster | \( {\mathrm{T}}_{\mathrm{ik}}^{\mathrm{m}}\sim \mathrm{Weibull}\left({\upgamma}_{\mathrm{m}},{\uplambda}_{\mathrm{m}}{\mathrm{e}}^{-\left({\upvarepsilon}_{\mathrm{ik}}+{\mathrm{U}}_{\mathrm{k}}\right)\kern0.1em /\kern0.1em {\upgamma}_{\mathrm{m}}}\right) \) |
Common baseline hazard function for time until CVD event | \( {\mathrm{h}}^{\mathrm{c}}\left(\mathrm{t}\right)={\upgamma}_{\mathrm{c}}{\mathrm{t}}^{\upgamma_{\mathrm{c}}-1}/\kern0.1em {\uplambda_{\mathrm{c}}}^{\upgamma_{\mathrm{c}}},\kern1em {\upgamma}_{\mathrm{c}}=1.2,{\uplambda}_{\mathrm{c}}=36 \) |
Common baseline hazard function for time until mortality | \( {\mathrm{h}}^{\mathrm{m}}\left(\mathrm{t}\right)={\upgamma}_{\mathrm{m}}{\mathrm{t}}^{\upgamma_{\mathrm{m}}-1}/{\uplambda_{\mathrm{m}}}^{\upgamma_{\mathrm{m}}},\kern0.5em {\upgamma}_{\mathrm{m}}=1.2,{\uplambda}_{\mathrm{m}}=55 \) |
Individual hazard function for time until CVD event | \( {\mathrm{h}}_{\mathrm{ik}}^{\mathrm{c}}\left(\mathrm{t}\right)={\mathrm{h}}^{\mathrm{c}}\left(\mathrm{t}\right){\mathrm{e}}^{\left({\upvarepsilon}_{\mathrm{ik}}+{\mathrm{U}}_{\mathrm{k}}+\upbeta {\mathrm{X}}_{\mathrm{ik}}\right)} \) |
Individual hazard function for time until mortality | \( {\mathrm{h}}_{\mathrm{ik}}^{\mathrm{m}}\left(\mathrm{t}\right)={\mathrm{h}}^{\mathrm{m}}\left(\mathrm{t}\right){\mathrm{e}}^{\left({\upvarepsilon}_{\mathrm{ik}}+{\mathrm{U}}_{\mathrm{k}}\right)} \) |
Individual level random effects | ɛ ik ∼ N(0, σ ɛ 2) |
Cluster level random effects | U k ∼ N(0, σ u 2) |
Intervention effect | β = − 0.32 |
Ten year risk of a CVD event | rik = P(T cik < 10| Xik = 0, εik, Uk) |
Individual and average probability of patient refusing treatment | \( {p}_{ik},\;p={\displaystyle {\sum}_{i,k}\frac{p_{ik}}{N}} \) |
Individual and average probability of clinician refusing to offer treatment | \( {q}_{ik},\kern0.5em q={\displaystyle {\sum}_{i,k}\frac{q_{ik}}{N}} \) |
Correlation between patient refusal probability and patient risk | ρ p |
Correlation between clinician refusal probability and patient risk | ρ q |
Censoring indicator | C ik = I(T ik c ≥ min(T ik m, T max )) |
Trial follow up time | T max = 3 |
Random variable observed for each patient | Y ik = min(T ik c, T ik m, T max ) |