Background: Survival analysis is sometimes called time-to-event analysis. The Cox model is used widely in survival analysis, where the covariates act multiplicatively on unknown baseline hazards. However, the Cox model requires the proportionality assumption, which limits its applications. The additive hazards model has been used as an alternative to the Cox model, where the covariates act additively on unknown baseline hazards. Objectives and methods: In this thesis, performance of the Cox multiplicative hazards model and the additive hazards model have been demonstrated and applied to the transfer, lifting and repositioning (TLR) injury prevention study. The TLR injury prevention study was a retrospective, pre-post intervention study that utilized a non-randomized control group. There were 1,467 healthcare workers from six hospitals in Saskatchewan, Canada who were injured from January 1, 1999 to December 1, 2006. De-identified data sets were received from the Saskatoon Health Region and Regina Quappelle Health Region. Time to repeated TLR injury was considered as the outcome variable. The models goodness of fit was also assessed. Results: Of a total of 1,467 individuals, 149 (56.7%) in the control group and 114 (43.3%) in the intervention group had repeated injuries during the study period. Nurses and nursing aides had the highest repeated TLR injuries (84.8%) among occupations. Back, neck and shoulders were the most common body parts injured (74.9%). These covariates were significant in both Cox multiplicative and additive hazards models. The intervention group had 27% fewer repeated injuries than the control group in the multiplicative hazards model (HR= 0.63; 95% CI=0.48-0.82; p-value=0.0002). In the additive model, the hazard difference between the intervention and the control groups was 0.002. Conclusion: Both multiplicative and additive hazards models showed similar results, indicating that the TLR injury prevention intervention was effective in reducing repeated injuries. The additive hazards model is not widely used, but the coefficient of the covariates is easy to interpret in an additive manner. The additive hazards model should be considered when the proportionality assumption of the Cox model is doubtful.

Background: Survival analysis is sometimes called time-to-event analysis. The Cox model is used widely in survival analysis, where the covariates act multiplicatively on unknown baseline hazards. However, the Cox model requires the proportionality assumption, which limits its applications. The additive hazards model has been used as an alternative to the Cox model, where the covariates act additively on unknown baseline hazards. Objectives and methods: In this thesis, performance of the Cox multiplicative hazards model and the additive hazards model have been demonstrated and applied to the transfer, lifting and repositioning (TLR) injury prevention study. The TLR injury prevention study was a retrospective, pre-post intervention study that utilized a non-randomized control group. There were 1,467 healthcare workers from six hospitals in Saskatchewan, Canada who were injured from January 1, 1999 to December 1, 2006. De-identified data sets were received from the Saskatoon Health Region and Regina Quappelle Health Region. Time to repeated TLR injury was considered as the outcome variable. The models goodness of fit was also assessed. Results: Of a total of 1,467 individuals, 149 (56.7%) in the control group and 114 (43.3%) in the intervention group had repeated injuries during the study period. Nurses and nursing aides had the highest repeated TLR injuries (84.8%) among occupations. Back, neck and shoulders were the most common body parts injured (74.9%). These covariates were significant in both Cox multiplicative and additive hazards models. The intervention group had 27% fewer repeated injuries than the control group in the multiplicative hazards model (HR= 0.63; 95% CI=0.48-0.82; p-value=0.0002). In the additive model, the hazard difference between the intervention and the control groups was 0.002. Conclusion: Both multiplicative and additive hazards models showed similar results, indicating that the TLR injury prevention intervention was effective in reducing repeated injuries. The additive hazards model is not widely used, but the coefficient of the covariates is easy to interpret in an additive manner. The additive hazards model should be considered when the proportionality assumption of the Cox model is doubtful.

Aalen’s additive hazards model has gained increasing attention in recently years because it model all covariate effects as time-varying. In this thesis, our goal is to explore the application of Aalen’s model in assessing treatment effect at a given time point with varying covariate effects. First, based on Aalen’s model, we utilize the direct adjustment method to obtain the adjusted survival of a treatment and comparing two direct adjusted survivals, with univariate survival data. Second, we focus on application of Aalen’s model in the setting of competing risks data, to assess treatment effect on a particular type of failure. The direct adjusted cumulative incidence curve is introduced. We further construct the confidence interval of the difference between two direct adjusted cumulative incidences, to compare two treatments on one risk.

In survival analysis interest often lies in the relationship between the survival function and a certain number of covariates. It usually happens that for some individuals we cannot observe the event of interest, due to the presence of right censoring and/or left truncation. A typical example is given by a retrospective medical study, in which one is interested in the time interval between birth and death due to a certain disease. Patients who die of the disease at early age will rarely have entered the study before death and are therefore left truncated. On the other hand, for patients who are alive at the end of the study, only a lower bound of the true survival time is known and these patients are hence right censored. In the case of censored and/or truncated responses, lots of models exist in the literature that describe the relationship between the survival function and the covariates (proportional hazards model or Cox model, log-logistic model, accelerated failure time model, additive risks model, etc.). In these models, the regression coefficients are usually supposed to be constant over time. In practice, the structure of the data might however be more complex, and it might therefore be better to consider coefficients that can vary over time. In the previous examples, certain covariates (e.g. age at diagnosis, type of surgery, extension of tumor, etc.) can have a relatively high impact on early age survival, but a lower influence at higher age. This motivated a number of authors to extend the Cox model to allow for time-dependent coefficients or consider other type of time-dependent coefficients models like the additive hazards model. In practice it is of great use to have at hand a method to check the validity of the above mentioned models. First we consider a very general model, which includes as special cases the above mentioned models (Cox model, additive model, log-logistic model, linear transformation models, etc.) with time-dependent coefficients and study the parameter estimation by means of a least squares approach. The response is allowed to be subject to right censoring and/or left truncation. Secondly we propose an omnibus goodness-of-fit test that will test if the general time-dependent model considered above fits the data. A bootstrap version, to approximate the critical values of the test is also proposed. In this dissertation, for each proposed method, the finite sample performance is evaluated in a simulation study and then applied to a real data set.

Survival analysis often includes dealing with data that are censored. This thesis focuses on censoring in the form of current status data. We discuss seve- ral methods of regression analysis of current status data and focus mainly on a method that assumes that the time to event follows the additive hazards mo- del. Under the assumption of proportional hazards for the monitoring time, this method does not require knowing the baseline hazard function and allows us to use the theory and software which were developed for Cox model. We also pre- sent a modification of this method, a two-step estimator, and show that it is asymptotically normal and has the advantage of lower asymptotic variance.