خطاهای اندازه گیری جهت سن شروع در مطالعات هم‌گروهی (کوهورت) رایج

ABSTRACT Measurement Error for Age of Onset in Prevalent Cohort Studies

Prevalent cohort studies of chronic diseases involving screening populations and sampling individuals with the condition of interest for prospective follow-up [1] . Examples of such studies include cancer screening trials [2] , studies of HIV prevalence [3] and studies of dementia [4] [5] . The prevalent cohort design is both more efficient and more practical than the incident cohort design [6] in which a cohort of disease-free individuals are followed for disease onset, and only the subset of individuals developing the disease yields information on the time from disease onset to death. The prevalent cohort design features a form of response-dependent sampling, however, in the sense that diseased individuals with long survival times are preferentially selected for inclusion into the cohort [1] [2] [7] ; some authors refer to the resulting data as “length-biased”. Valid statistical inference depends critically on adequately addressing the sampling scheme in the likelihood construction, and there are two broad frameworks for analysis, both of which make use of the retrospectively reported time of disease onset recorded at the time of sampling.Analysis in the conditional framework is based on the fact that individuals who died before the time of screening cannot be sampled, and so the survival times among sampled individuals are left-truncated by the time from disease onset to enrollment. The unconditional framework is based on the density of the survival times derived under the prevalent cohort sampling scheme. That is, if the disease incidence is stationary, the onset times follow a time homogeneous Poisson process, and the resulting left truncation times have a constant density. If the probability that an individual is sampled is proportional to their survival time, the density of times subject to this sampling scheme can be derived and used for likelihood construction.For the conditional approach, parametric, nonparametric and semiparametric methods are relatively straightforward and have seen considerable application [3] [8] [11] . Wang [10] proposed a product-limit estimator for left-truncated survival times which maximizes the conditional likelihood and loses no information when the distribution of the truncation time variable is unspecified. For semiparametric Cox models, the partial likelihood approach can be adopted for left-truncated data but with an adjusted risk set [8] [11] [12] . Wang et al. [12] argued that the nonparametric and semiparametric estimators are efficient when the distribution of the truncation time is unspecified but can be inefficient when the distribution of truncation time is parameterized.Unconditional analyses [5] [13] -[16] are based on the joint distribution of the backward recurrence time (time from disease onset to sampling) and the forward recurrence time (time from sampling to death). Vardi [13] [14] and Asghrian et al. [5] developed the nonparametric maximum likelihood estimator (NPMLE) for right-censored length-biased survival times, but this NPMLE does not have closed form and its limiting distribution is intractable [15] [16] . Huang and Qin [17] derived a new closed-form nonparametric estimator that incorporates the information about the length-biased sampling. Wang [18] proposed pseudo-likelihood for length-biased failure times under the Cox proportional hazards model, but this method cannot be applied to right-censored failure times. Luo and Tsai [19] and Tsai [20] derived pseudo-partial-likelihood estimators for right-censored lengthbiased data which have closed-form and retain high efficiency. Shen et al. [21] considered modeling covariate effects for length-biased data under time transform and accelerated failure time models. Qin and Shen [22] recently proposed two estimating equations for fitting the Cox proportional hazards model that are formulated based on different weighted risk sets.Both conditional and unconditional analyses make use of the retrospectively reported times of disease onset, with the latter further based on the assumption of a stationary (Poisson) incidence process. However, there is often considerable error and uncertainty in the retrospectively reported onset times. This is particularly true for onset times related to disease featuring cognitive impairment or mental health disorders. In some settings the reported times may better represent times of symptom onset, rather than the actual start of the disease process which may lead to underestimation of disease duration. In other settings the errors may lead to earlier or later reported onset times.The purpose of this article is to examine the impact of measurement error in the retrospectively reported onset time for both the conditional and unconditional frameworks. The remainder of the paper is organized as follows. In Section 2, we introduce notation and likelihood construction for prevalent cohort data. The impact of misspecification of the disease onset time is explored in Section 3 by simulation for the unconditional and conditional approaches, and methods for correcting for this measurement error are described in Section 4. General remarks and topics for further research are given in Section 5.