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BackgroundAnalyzing time-to-onset of adverse drug reactions from treatment exposure contributes to meeting pharmacovigilance objectives, i.e. identification and prevention. Post-marketing data are available from reporting systems. Times-to-onset from such databases are right-truncated because some patients who were exposed to the drug and who will eventually develop the adverse drug reaction may do it after the time of analysis and thus are not included in the data. Acknowledgment of the developments adapted to right-truncated data is not widespread and these methods have never been used in pharmacovigilance. We assess the use of appropriate methods as well as the consequences of not taking right truncation into account (naive approach) on parametric maximum likelihood estimation of time-to-onset distribution.MethodsBoth approaches, naive or taking right truncation into account, were compared with a simulation study. We used twelve scenarios for the exponential distribution and twenty-four for the Weibull and log-logistic distributions. These scenarios are defined by a set of parameters: the parameters of the time-to-onset distribution, the probability of this distribution falling within an observable values interval and the sample size. An application to reported lymphoma after anti TNF- α treatment from the French pharmacovigilance is presented.ResultsThe simulation study shows that the bias and the mean squared error might in some instances be unacceptably large when right truncation is not considered while the truncation-based estimator shows always better and often satisfactory performances and the gap may be large. For the real dataset, the estimated expected time-to-onset leads to a minimum difference of 58 weeks between both approaches, which is not negligible. This difference is obtained for the Weibull model, under which the estimated probability of this distribution falling within an observable values interval is not far from 1.ConclusionsIt is necessary to take right truncation into account for estimating time-to-onset of adverse drug reactions from spontaneous reporting databases.

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We investigate the parametric maximum likelihood estimator for truncated data when the truncation value is different according to the observed individual or item. We extend Lehmann's proof (1983) of the asymptotic properties of the parametric maximum likelihood estimator in the case of independent nonidentically distributed observations. Two cases are considered: either the number of distinct probability distribution functions that can be observed in the population from which the sample comes from is finite or this number is infinite. Sufficient conditions for consistency and asymptotic normality are provided for both cases.

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