Abstract
BackgroundIn clinical trials and survival analysis, participants may be excluded from the study due to withdrawal, which is often referred to as lost-to-follow-up (LTF). It is natural to argue that a disease would be censored due to death; however, when an LTF is present it is not guaranteed that the disease has been censored. This makes it important to consider both cases; the disease is censored or not censored. We also note that the illness process can be censored by LTF. We will consider a multi-state model in which LTF is not regarded as censoring but as a non-fatal event.MethodsWe propose a multi-state model for analyzing semi-competing risks data with interval-censored or missing intermediate events. More precisely, we employ the additive and multiplicative hazards model with log-normal frailty and construct the conditional likelihood to estimate the transition intensities among states in the multi-state model. Marginalization of the full likelihood is accomplished using adaptive importance sampling, and the optimal solution of the regression parameters is achieved through the iterative quasi-Newton algorithm.ResultsSimulation is performed to investigate the finite-sample performance of the proposed estimation method in terms of the relative bias and coverage probability of the regression parameters. The proposed estimators turned out to be robust to misspecifications of the frailty distribution. PAQUID data have been analyzed and yielded somewhat prominent results.ConclusionsWe propose a multi-state model for semi-competing risks data for which there exists information on fatal events, but information on non-fatal events may not be available due to lost to follow-up. Simulation results show that the coverage probabilities of the regression parameters are close to a nominal level of 0.95 in most cases. Regarding the analysis of real data, the risk of transition from a healthy state to dementia is higher for women; however, the risk of death after being diagnosed with dementia is higher for men.
Highlights
In clinical trials and survival analysis, participants may be excluded from the study due to withdrawal, which is often referred to as lost-to-follow-up (LTF)
We considered a multi-state model for semi-competing risks data, for which there exists information on fatal events, but information on non-fatal events may not be available due to lost to follow-up
It was quite difficult to handle nonparametric estimation procedures for the baseline transition intensity associated with the nuisance parameter because the total number of parameters is proportional to the number of subjects
Summary
In clinical trials and survival analysis, participants may be excluded from the study due to withdrawal, which is often referred to as lost-to-follow-up (LTF). We will consider a multi-state model in which LTF is not regarded as censoring but as a non-fatal event. In classical time-to-event or survival analysis, subjects are under risk for one fatal event. For illustration purposes of our methodologies, a dataset named PAQUID (Personnes Agées Quid) is analyzed to investigate the meaningful prognostic factors associated with dementia. These data were initially analyzed by [7] using the conventional Cox model [8, 9]. We employ a semi-competing risks model where death may occur after dementia has occurred (i.e., been diagnosed), but death censors the disease. Many studies have been conducted under semi-competing risks frameworks [4, 5, 11]
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