ABSTRACT
FIGURE 7.6: Observed longitudinal trajectory for Patient 51 from the PBC dataset.
our illustration we will use Patient 51 from the PBC study whose longitudinal trajectory of log serum bilirubin measurements is depicted in Figure 7.6. We can observe that this patient had stable bilirubin levels for the rst three visits, but afterward she showed a steep increase in her longitudinal prole indicating a worsening of her condition. In our sensitivity analysis we will compare six joint models with dierent specications for the relative risk submodel for the composite event (death or transplantation), namely:
(I) hi(t) = h0(t) expf 1D-pnci + 2ProtTimei + 1mi(t)g; (II) hi(t) = h0(t) expf 1D-pnci + 2ProtTimei + 2m0i(t)g; (III) hi(t) = h0(t) expf 1D-pnci + 2ProtTimei + 1mi(t) + 2m0i(t)g;
(IV) hi(t) = h0(t) exp 1D-pnci + 2ProtTimei + 1mi(t)
+ int1 fProtTimei mi(t)g ;
(V) hi(t) = h0(t) exp 1D-pnci + 2ProtTimei + 2m
+ int2 fProtTimei m0i(t)g ;
(VI) hi(t) = h0(t) exp 1D-pnci + 2ProtTimei + 1mi(t) + 2m
and the same longitudinal submodel, as presented in Section 7.1.3, which uses
yi(t) = mi(t) + "i(t)
= (0 + bi0) + (k + bik) >B(t; 4; 4) + "i(t):
Relative risks models (I){(III) assume that the risk for the composite event at time t depends on the true level of log serum bilirubin at the same time point, the slope of the true trajectory at t, or on both the true level and the slope at t, respectively. Similarly, models (IV){(VI) assume the same type of relationships, but also include the interaction terms between the true level of the marker and/or the slope of the trajectory with the dummy variable of abnormal prothrombin time at baseline.
