**A comparison of sequential and joint fitting of pain intensity and dropout hazard in acute pain studies**

Paul Matthias Diderichsen (1), Sandeep Dutta (2)

(1) Abbott Laboratories A/S, Emdrupvej 28C, DK-2100 København Ø, Denmark, (2) Abbott Laboratories, Abbott Park, Illinois, USA

**Objectives**: Subjects in acute pain studies not receiving adequate pain relief have a high risk of dropping out of the study. The non-random dropout necessitates the construction of appropriate dropout models in order to reproduce the observed data in simulation. For simplicity, such dropout models may be developed in a sequential manner, where a pain intensity (PI) model is developed and used to explain the observed dropout from an acute pain Phase 2 study (N=91). However, when dropout depends on unobserved data (between observations of PI), the dropout and PI should be modeled simultaneously. The objective of this work was to compare the estimates obtained from fitting PI and dropout data sequentially vs. simultaneously.

**Methods**: The PK and PI following administration of study drug were modeled as described in [1]. The risk of dropping out was modeled using an informed dropout model (ID [2]), where the hazard was defined as the product of a baseline hazard and an exponential function of the model-predicted PI, modified by a pain memory factor as described in [1]. Parameter values for the three models were estimated in NONMEM, initially using a sequential approach. The joint likelihood for observing the PI data (Y_{O}) and dropout data (T) is given by [2]:

*P*(*Y _{0},T*)=

*∫P*(

*T*|

*Y*,

_{0}*η*)

*P*(

*Y*,

_{0}*η*)

*P*(

*η*)d

*η*

The conditional likelihood for the dropout data depends on the random effect, η, and should therefore be fit simultaneously with the PI data. In order to investigate the error made by fitting the ID model sequentially, the PI and dropout model parameters were fit simultaneously and compared to the results from the sequential analysis.

**Results**: Dropout model parameter estimates changed up to 14% when PI and dropout model parameters were fit simultaneously instead of sequentially, however no PI model parameter changed more than 4%.

**Conclusions**: In acute pain studies where dropout can be assumed to truly depend on PI, dropout data is expected to contain information about the underlying PI. Hence simultaneous fitting of PI & dropout data is expected to improve the fit of the PI and the PI dependent hazard. In the present analysis, jointly fitting the dropout and PI data using the ID model did not provide a visibly better fit compared to the sequential fit. This was possibly due to the intensive PKPD sampling which reduced the amount of additional pain intensity information contained in the underlying model as compared to observed data.

**References**:

[1] Diderichsen et al.: Modeling “Pain Memory” is Central to Characterizing the Hazard of Dropping Out in Acute Pain Studies, ACOP 2009 (poster)

[2] Hu and Sale: A Joint Model for Nonlinear Longitudinal Data with Informative Dropout, J Pharmacokinetics and Pharmacodynamics, 30, 2003