In studying natural history of a disease, incident studies provide the best quality estimates; in contrast, prevalent studies introduce a sampling bias, which, if the onset time of the disease follows a stationary Poisson process, is called length bias. When both types of data are available, combining the samples under the assumption that failure times in incident and prevalent cohorts come from the same distribution function, could improve the estimation process from a revalent sample. We verify this assumption using a Smirnov type of test and construct a likelihood function from a combined sample to parametrically estimate the survival through maximum likelihood approach. Finally, we use Accelerated Failure Time models to compare the effect of covariates on survival in incident, prevalent, and combined populations. Properties of the proposed test and the combined estimator are assessed using simulations, and illustrated with data from the Canadian Study of Health and Aging.

In studying natural history of a disease, incident studies provide the best quality estimates; in contrast, prevalent studies introduce a sampling bias, which, if the onset time of the disease follows a stationary Poisson process, is called length bias. When both types of data are available, combining the samples under the assumption that failure times in incident and prevalent cohorts come from the same distribution function, could improve the estimation process from a revalent sample. We verify this assumption using a Smirnov type of test and construct a likelihood function from a combined sample to parametrically estimate the survival through maximum likelihood approach. Finally, we use Accelerated Failure Time models to compare the effect of covariates on survival in incident, prevalent, and combined populations. Properties of the proposed test and the combined estimator are assessed using simulations, and illustrated with data from the Canadian Study of Health and Aging.

In studying natural history of a disease, incident studies provide the best quality estimates; in contrast, prevalent studies introduce a sampling bias, which, if the onset time of the disease follows a stationary Poisson process, is called length bias. When both types of data are available, combining the samples under the assumption that failure times in incident and prevalent cohorts come from the same distribution function, could improve the estimation process from a revalent sample. We verify this assumption using a Smirnov type of test and construct a likelihood function from a combined sample to parametrically estimate the survival through maximum likelihood approach. Finally, we use Accelerated Failure Time models to compare the effect of covariates on survival in incident, prevalent, and combined populations. Properties of the proposed test and the combined estimator are assessed using simulations, and illustrated with data from the Canadian Study of Health and Aging.

Cross-sectional surveys are often used in epidemiological studies to identify subjects with a disease. When estimating the survival function from onset of disease, this sampling mechanism introduces bias, which must be accounted for. If the onset times of the disease are assumed to be coming from a stationary Poisson process, this bias, which is caused by the sampling of prevalent rather than incident cases, is termed length-bias. A one-sample Kolomogorov-Smirnov type of goodness-of-fit test for right-censored length-biased data is proposed and investigated with Weibull, log-normal and log-logistic models. Algorithms detailing how to efficiently generate right-censored length-biased survival data of these parametric forms are given. Simulation is employed to assess the effects of sample size and censoring on the power of the test. Finally, the test is used to evaluate the goodness-of-fit using length-biased survival data of patients with dementia from the Canadian Study of Health and Aging.

Cross-sectional surveys are often used in epidemiological studies to identify subjects with a disease. When estimating the survival function from onset of disease, this sampling mechanism introduces bias, which must be accounted for. If the onset times of the disease are assumed to be coming from a stationary Poisson process, this bias, which is caused by the sampling of prevalent rather than incident cases, is termed length-bias. A one-sample Kolomogorov-Smirnov type of goodness-of-fit test for right-censored length-biased data is proposed and investigated with Weibull, log-normal and log-logistic models. Algorithms detailing how to efficiently generate right-censored length-biased survival data of these parametric forms are given. Simulation is employed to assess the effects of sample size and censoring on the power of the test. Finally, the test is used to evaluate the goodness-of-fit using length-biased survival data of patients with dementia from the Canadian Study of Health and Aging.

Cross-sectional surveys are often used in epidemiological studies to identify subjects with a disease. When estimating the survival function from onset of disease, this sampling mechanism introduces bias, which must be accounted for. If the onset times of the disease are assumed to be coming from a stationary Poisson process, this bias, which is caused by the sampling of prevalent rather than incident cases, is termed length-bias. A one-sample Kolomogorov-Smirnov type of goodness-of-fit test for right-censored length-biased data is proposed and investigated with Weibull, log-normal and log-logistic models. Algorithms detailing how to efficiently generate right-censored length-biased survival data of these parametric forms are given. Simulation is employed to assess the effects of sample size and censoring on the power of the test. Finally, the test is used to evaluate the goodness-of-fit using length-biased survival data of patients with dementia from the Canadian Study of Health and Aging.

Cross-sectional surveys are often used in epidemiological studies to identify subjects with a disease. When estimating the survival function from onset of disease, this sampling mechanism introduces bias, which must be accounted for. If the onset times of the disease are assumed to be coming from a stationary Poisson process, this bias, which is caused by the sampling of prevalent rather than incident cases, is termed length-bias. A one-sample Kolomogorov-Smirnov type of goodness-of-fit test for right-censored length-biased data is proposed and investigated with Weibull, log-normal and log-logistic models. Algorithms detailing how to efficiently generate right-censored length-biased survival data of these parametric forms are given. Simulation is employed to assess the effects of sample size and censoring on the power of the test. Finally, the test is used to evaluate the goodness-of-fit using length-biased survival data of patients with dementia from the Canadian Study of Health and Aging.

<p>The motivating forestry background for this thesis is the need for fast, non-destructive, and cost-efficient methods to estimate fibre length distributions in standing trees in order to evaluate the effect of silvicultural methods and breeding programs on fibre length. The usage of increment cores is a commonly used non-destructive sampling method in forestry. An increment core is a cylindrical wood sample taken with a special borer, and the methods proposed in this thesis are especially developed for data from increment cores. Nevertheless the methods can be used for data from other sampling frames as well, for example for sticks with the shape of an elongated rectangular box.</p><p>This thesis proposes methods to estimate fibre length distributions based on censored mixture data from wood samples. Due to sampling procedures, wood samples contain cut (censored) and uncut observations. Moreover the samples consist not only of the fibres of interest but of other cells (fines) as well. When the cell lengths are determined by an automatic optical fibre-analyser, there is no practical possibility to distinguish between cut and uncut cells or between fines and fibres. Thus the resulting data come from a censored version of a mixture of the fine and fibre length distributions in the tree. The methods proposed in this thesis can handle this lack of information.</p><p>Two parametric methods are proposed to estimate the fine and fibre length distributions in a tree. The first method is based on grouped data. The probabilities that the length of a cell from the sample falls into different length classes are derived, the censoring caused by the sampling frame taken into account. These probabilities are functions of the unknown parameters, and ML estimates are found from the corresponding multinomial model.</p><p>The second method is a stochastic version of the EM algorithm based on the individual length measurements. The method is developed for the case where the distributions of the true lengths of the cells at least partially appearing in the sample belong to exponential families. The cell length distribution in the sample and the conditional distribution of the true length of a cell at least partially appearing in the sample given the length in the sample are derived. Both these distributions are necessary in order to use the stochastic EM algorithm. Consistency and asymptotic normality of the stochastic EM estimates is proved.</p><p>The methods are applied to real data from increment cores taken from Scots pine trees (Pinus sylvestris L.) in Northern Sweden and further evaluated through simulation studies. Both methods work well for sample sizes commonly obtained in practice.</p>

The motivating forestry background for this thesis is the need for fast, non-destructive, and cost-efficient methods to estimate fibre length distributions in standing trees in order to evaluate the effect of silvicultural methods and breeding programs on fibre length. The usage of increment cores is a commonly used non-destructive sampling method in forestry. An increment core is a cylindrical wood sample taken with a special borer, and the methods proposed in this thesis are especially developed for data from increment cores. Nevertheless the methods can be used for data from other sampling frames as well, for example for sticks with the shape of an elongated rectangular box. This thesis proposes methods to estimate fibre length distributions based on censored mixture data from wood samples. Due to sampling procedures, wood samples contain cut (censored) and uncut observations. Moreover the samples consist not only of the fibres of interest but of other cells (fines) as well. When the cell lengths are determined by an automatic optical fibre-analyser, there is no practical possibility to distinguish between cut and uncut cells or between fines and fibres. Thus the resulting data come from a censored version of a mixture of the fine and fibre length distributions in the tree. The methods proposed in this thesis can handle this lack of information. Two parametric methods are proposed to estimate the fine and fibre length distributions in a tree. The first method is based on grouped data. The probabilities that the length of a cell from the sample falls into different length classes are derived, the censoring caused by the sampling frame taken into account. These probabilities are functions of the unknown parameters, and ML estimates are found from the corresponding multinomial model. The second method is a stochastic version of the EM algorithm based on the individual length measurements. The method is developed for the case where the distributions of the true lengths of the cells at least partially appearing in the sample belong to exponential families. The cell length distribution in the sample and the conditional distribution of the true length of a cell at least partially appearing in the sample given the length in the sample are derived. Both these distributions are necessary in order to use the stochastic EM algorithm. Consistency and asymptotic normality of the stochastic EM estimates is proved. The methods are applied to real data from increment cores taken from Scots pine trees (Pinus sylvestris L.) in Northern Sweden and further evaluated through simulation studies. Both methods work well for sample sizes commonly obtained in practice.

The thesis investigates the impact of age-biased sampling on the accuracy of lifetime prediction models for traffic signs. The bias in question originates from age-biased sampling as a result of the inspection paradox. This phenomenon occurs because longer intervals have a higher probability of being observed compared to shorter intervals, leading to a skewed representation in the data. The research employs a dual approach: firstly, conducting an extensive analysis of real data on traffic sign longevity using a Weibull Survival Model. This analysis is based on the data set compiled by Saleh et al., (2023). Secondly, the study sets up a Monte Carlo simulation to systematically explore the effects of varying degrees and patterns of age bias on the sample. The simulation parameters are derived from the original Weibull Model parameters, obtained from the real dataset. This approach ensures that the simulations closely replicate the actual parameters and estimates. The comparison of the true shape, scale, intercept, and the coefficients associated with the covariates against the simulated estimates indicates a significant bias in the dataset. The study also examines the impact of this bias on the predictive capabilities of various models: Weibull Modeling, Cox Proportional Hazards, Kaplan Meier, and Random Survival Forest. This is done by comparing the true means and medians of the simulated data with the estimates from each model. The findings show that all models exhibit large deviations from the actual means and medians at varying bias levels in the simulated data. The accuracy of the predictions is measured using the Brier Score. This score also shows significant deviations from the prediction accuracy of the original Weibull Model applied to the real dataset, especially when the bias levels vary across simulated datasets. Given these findings, the study advises against using the aforementioned methods for lifetime modeling of traffic signs when there is age bias due to the inspection paradox.