The extensive application of prospective prevalent cohort studies on disease duration demands for an appropriate methodology which takes the biases arising from left truncation into account. In such studies, right censored lifetime data are commonly analysed by conditioning on observed truncation times, where truncation distributions are ignored. However, it is often reasonable to assume a uniform distribution for truncation times. The observed survival times are thus length-biased. This property could be used to develop a more informative strategy known as the unconditional approach. The cumulative hazard rate function is one of the key quantities that is used in survival analysis. We propose the unconditional nonparametric maximum likelihood estimator (NPMLE) of the unbiased cumulative hazard function to study the distribution of lifetime data in the presence of length-bias and informative censoring. The uniform strong consistency and asymptotic normality of the NPMLE are discussed and used to obtain confidence intervals. The finite-sample properties of the NPMLE are inspected through a simulation study. The procedures are applied to a set of real data on patients with dementia.

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