Study population
The study consists of young adult survivors of colorectal cancer and matched cancer-free controls in Ontario, Canada. This cohort was recently studied by Forbes et al. [1] to compare long-term survival of young adult survivors and controls. Young adults have been defined by the Canadian Cancer Society of Canada as persons aged 20 to 44 years [17]. All individuals diagnosed with CRC in Ontario between January 1, 1992 and December 31, 1999, and aged 20 to 44 years at the time of diagnosis of CRC were eligible for inclusion. Diagnosis date and type of cancer diagnosis are retrieved from the Ontario Cancer Registry (OCR), a comprehensive population-based cancer registry created to capture all incident cases of cancer in the province. Patients were considered survivors if they were alive 5 years after diagnosis. Individuals were excluded if they died within 5 years of diagnosis, or if they had a diagnosis of any other cancer before their diagnosis of CRC.
Controls were identified using Ontario’s Registered Persons Database (RPDB). Five controls were randomly matched to each young adult survivor on calendar year of birth, sex, and geographic location. The referent date for a control was defined as the date of diagnosis for their corresponding matched young adult CRC survivor. Controls were only eligible for inclusion if they had no prior diagnosis of cancer before their referent date and survived a minimum of 5 years after the referent date. After the 5-year mark, survivors and controls were followed until their date of death, date of OHIP (Ontario Health Insurance Plan) eligibility loss, or until date of study end (December 31st, 2007).
Admissions to a hospital for acute illness are identified using the Canadian Institute for Health Information Discharge Abstract Database (CIHI-DAD). Over each individual’s follow-up period, the number of admissions and the date of each admission are recorded. Permission for data access was obtained from the Institute of Clinical Evaluative Sciences (ICES), Toronto, Ontario.
Multistate models
Multistate models use distinct states to describe changes in a patient’s condition over time. Events correspond to transitions from one state to another, and the event times correspond to the transition times [14]. The multistate model treats death as an absorbing event, as no further admissions can occur after this point [16, 18]. Note that the common survival model can be viewed as a 2-state model, where the first state represents an “alive” state and the second represents the “dead” state. Survival analysis aims to characterize the distribution of the transition time to the dead state, whereas a multistate analysis aims to describe the distribution of several transitions (not only to the dead state).
The multistate model assumes the baseline rate function is dependent on the number of prior events. A patient cannot be at risk for their kth admission without experiencing admission k-1. Time t is measured as time in years starting from 5 years after the diagnosis date (for survivors) or from 5 years after the referent date (for controls). At any given time t, the multistate model allows the patients who are at risk for their 10th admission, for example, to have a different baseline rate function than patients who are at risk for their 1st admission. Similarly, the model assumes the baseline rate function for death varies depending on the number of admissions experienced. The model also allows for separate regression parameters to be estimated for each transition. The instantaneous transition rate [14, 15, 19] can be expressed as a proportional rate regression model
(1)
Function λi,js(t) represents the instantaneous rate for a transition from state j to state s at time t for the ith patient. The baseline instantaneous transition rate function λ0, js(t) and parameter vector β
js is specific to each j→s transition. The random effect νi accounts for the heterogeneity in the j→s transitions rates between patients [20]. Note that if we are interested in the estimate of a common regression parameter, then parameter vector β
js in the model can simply be replaced by β. Figure 1 provides a multistate diagram for characterizing the occurrence of hospital admissions and death. Patients in state 2, for example, are alive and have experienced two admissions; patients are in state D if they have died. From each non-absorbing state, patients can either make a forward transition to the next non-absorbing state or can make a transition to death. All models/graphs were run and created using the statistical package R [21].
The multistate methodology is custom made for prospective cohort data and it is important to be aware of methods for handling matching under such models. Cluster-specific random effects [19] can be incorporated into the multi-state model to handle correlation that may arise from matching (that is, each matched group can be considered a cluster). Our model includes patient-specific random effects, as it is important to account for variation in the transition rates between patients. In theory, one can incorporate both patient-specific and cluster-specific random effects.