In Chapter 2, the initial analyses showed that adherence to both drugs has a sig- nificant effect on the treatment end-point (SVR), with higher adherence significantly increasing the chance of achieving SVR. This confirms the fact that adherence is cru- cial for effectiveness of the medication regimen for treating chronic hepatitis C. We also found other significant factors that affect SVR. It was seen that women have higher probability of attaining SVR than men. We also saw that race plays an important role in determining chances for a positive drug response and that Caucasians have signifi- cantly higher chances of attaining SVR than others. We further saw that the severity of infections (fibrosis score) does affect SVR and patients with higher baseline infection scores have less chances of a full recovery (this reaffirms results found in Conjeevaram et al. (2006)). The combined analysis showed some interesting results as well. The individual effects of the drugs were found significant by the IDS test while the joint effect was found significant by both the IDS and SDS tests. This shows that adherence
to the combined regimen is important to improve chances of achieving SVR, confirming results obtained from the Phase-II drug trials.
Figure 2.8 showed that the effect of interaction between adherence to the drugs can also have a serious impact on SVR. Our results showed that adherence on week 3 has tremendous bearing on the final outcome, which supports the conclusion that adherence in the first few weeks of the regimen is extremely important. This certainly is a new discovery with regards to existing knowledge about adherence in treatment for chronic hepatitis C, and gives a better perception of the temporal relationship of early adherence with the medical end-point SVR. It would thus be interesting to see whether a similar trend is noticed in the proposed triple therapy which is the current point of focus in the medical community for treatment of chronic hepatitis C, and care should be taken to remedy factors that influence early adherence.
Overall, these analyses show a much clearer picture of the relationship between adherence to the drug regimen in the context of achieving a positive end-point after hepatitis C treatment. It reveals trends of this relationship and shows the importance of early adherence in such a context. In addition, it shows that methods used here can be used as a generalize framework for similar analyses in other medical trials and drug regimens. It also illustrates that simply knowing whether adherence is important may not be good enough, and it may be equally important to quantitatively characterize this relationship over the length of the study.
The method we used here does not assume a Markovian structure, and the param- eters are interpreted conditionally on covariates at t, and not all s < t. Hence the formulation for the conditional mean model will still hold true in absence of a Markov structure, that is, in situations where the responseY(t) depends on covariates at times
s < t. This might often be true in analyses where adherence is modeled in a temporal framework, conditional on the factor contributing to it. Some of these factors might
have a delayed effect on adherence but that would not hamper the foundation of the functional generalized linear model proposed here. Temporal Process Regression can also be used to magnify these temporal relationships over any subintervals of the actual length of the study and conduct analyses within them. This allows for better under- standing of these patterns with respect to different stages of the treatment regime, and allows us to correct for factors that might only affect the response within those intervals in concern. Also as we saw in this analysis, temporal process regression does allow us to model the temporal nature of interactions between factors, like, in our case, interactions between adherence to different drugs in a multi-drug therapy.
However, there are still concerns with regards to usage of these methods in spe- cific situations, and certain necessary assumptions that we inherently make in such a framework. One basic necessity is full availability of data at most of the times of mea- surements, and higher percentages of missing data may raise a few issues that need to addressed. In certain cases, imputations or other Bayesian or frequentist methods may work well, and in some other cases, like ours, where the response was in fact a measure- ment done post treatment, assumption of it being constant across the study duration might be a good solution. The hypothesis tests used here (SDS and IDS) work in most situations, but however not any one of them dominates the other in terms of power. SDS might be too conservative in some situations, but it can potentially be more pow- erful than IDS in others. Hence it is better to use both tests in any given analysis, and to use one of them to re-evaluate results obtained from the other. Also since temporal process regression is a functional version of the generalized linear model, it does suffer from a few parametric assumptions, especially on the link, and the variance function. But as is the case in generalized linear models, misspecifications of these assumptions can be easily remedied by known techniques.