Introduction
Multi-state models are used in a variety of epidemiological settings, enabling the study of individuals transitioning through different states across time, portraying with sufficient complexity the real-world issue under study and providing useful and meaningful predictions [
1‐
11]. Measures that can be estimated via the use of multi-state models include, but are not limited to, the probability of being in a state (or a cluster of states) across time, the probability of transitioning from one state to another, the mean length of stay in a state, and the probability of ever visiting a state, as well as the hazard rates/ratios for each transition. Typical examples of multi-state models applications are studying acute [
10] or chronic disease progression [
4,
7], recurrent events such as repeated hospitalizations [
6] and cost-effectiveness in health economic settings [
11]. In each setting, the multi-state structure used depends on the research question of interest and the information available in the research data. If a simple measure such as the probability of an event is of interest, then a single event, simple survival analysis may suffice. The information available in the data also drives which kind of research questions can be explored. When the data include information about a state of interest repeatedly over time, more complicated multi-state structures can be implemented, making use of the full richness of the data, to answer composite, realistic research questions. Accompanying the application of more complex multi-state structures, a series of choices with regard to modelling the transition rates, such as choice of timescale and sharing information across transitions, are also available.
Following a diagnosis of breast cancer (BC), many women experience psychological distress including feelings of sadness, fear, anxiety, and depression. The association between BC diagnosis and the development of depression has been previously studied, either using logistic regression [
12] or survival analysis for time to first depression diagnosis [
13], with an increased risk of depression for individuals diagnosed with BC or cancer in general, compared to a matched population comparison group. As routine primary care information on a diagnosis of depression is often unavailable, many researchers turn to administrative drug prescription databases in order to study proxy measures of mental health on a population level [
14‐
16]. Prescription data offers a readily available, affordable, quantifiable, population-wide measure of antidepressant drug use which can be useful as a proxy of quality of life, including psychological status over time [
17].
Breast Cancer Data Base Sweden 2.0 (BCBaSe 2.0) is a linked research database that includes data on dispensed drug prescription from the Swedish Prescribed Drug Registry both before and after a diagnosis of BC, repeatedly over time, from 2006 to 2013, with this information also being available for an age-matched population comparison group of BC free women [
18]. The aim of the study is to explore different and novel research questions using the registry-based repeated prescriptions of antidepressants, building from simple ones to more complex, realistic ones by using multi-state structures ranging from single-event survival analysis up to developing bidirectional and recurrent multi-state structures that account for the recurring start and stop of medication.
Based on the longitudinal nature of the prescribed antidepressants data and under certain assumptions, we can classify each woman as being on a medication cycle or a discontinuation period, a status that can change multiple times during follow-up. We start from simpler and commonly used structures such as a single-event survival model (two-state structure) studying the risk for antidepressant medication initiation (first medication cycle), move to a competing risk setting with antidepressants initiation and death as competing events and then a three-state illness-death model, allowing an individual to transition from medication initiation to the death state. We then add a medication discontinuation period state, allowing the study of being in the first antidepressant medication cycle. A backwards transition from a medication discontinuation period state back to a new medication cycle is added (bidirectional structure), allowing an individual to be able to transition multiple times between a period of medication use and a discontinuation period. Then a multi-state structure with recurrent couples of medication cycles and discontinuation periods is proposed, allowing for a more flexible modelling of the medication use patterns, with or without sharing information across transitions.
The bidirectional structure along with the recurrent multi-state structure enabled us to study, among others, the total probability of being and total length of stay in a medication cycle on a population level or conditional on entering a medication cycle, making use of the full richness of information found in the prescribed drug register. The simpler structures do not make full use of the richness of the data, answering simpler, yet still important research questions. We also advocate sensitivity analyses to investigate how probability estimates derived from the more complex structures, are influenced by different medication cycle definitions or different timescale approaches when modelling the transition intensity rates.
Discussion
We addressed a variety of research questions when dealing with registry-based repeated prescriptions of antidepressants for women with BC diagnosis and BC- free population comparators, using multi-state models, building up from simple towards complex structures, motivating each step of the process. Each step from one multi-state structure to the next one allowed the use of more information available in the prescription data, thus addressing more complex research questions, or added more flexibility in the structure or was motivated in order to address issues/limitations of the preceding structure. While each multi-state structure, no matter how simple, has its own utility and answers specific research questions, we aimed in utilizing the full richness of our data with the more complex structures while also considering different modelling choices.
If, for example, the research question of interest was limited to “What is the probability of ever being prescribed a medication and still be alive up to time t after the start of the follow-up”, then, a three-state illness-death model structure would suffice. However, since we wanted to utilize all the information available in the prescribed drug register regarding antidepressants, more complex research questions such as the probability of being in a medication cycle, including the recurring cycles or studying the susceptibility for antidepressant medication use given past medication cycles can be addressed. Synthetic example datasets with the multi-state data structures used in this study are provided in the Supplementary material. The robustness of the estimated probabilities derived from the different multi-state structures for different definitions of being in an antidepressant medication cycle was assessed via a sensitivity analysis, showing that the complex multi-state structures (Recurrent multi-state, Bidirectional, “Emulated bidirectional”) are relatively insensitive to alternative medication cycle definitions.
As mentioned in the description of the multi-state structures used in this study (Sect. 2), even the more complex models present limitations. The bidirectional model cannot take into account information from past medication cycles to estimate probabilities of being or length of stay in a new medication cycle. Even though we bypass this limitation by applying a recurrent multi-state structure, there is still the issue of the rise in the complexity of the structure, leading to an increased number of states that progressively become sparsely populated, which can cause precision and model convergence issues. In addition, there is the limitation of pooling individuals in a final, recurrence state (6th medication cycle), from which they can only proceed towards the death state, assuming they become, chronic antidepressant users for the rest of their follow-up. Even though the restricted recurrent multi-state model aims to tackle the precision and convergence issues, it still suffers from the chronic antidepressant users assumption as well as the assumptions made regarding the relations between the transition rates which may not necessarily be realistic.
Even though the use of different multi-state structures have been used before on data for demonstrating purposes such as in [
2,
9], to our knowledge, this is the first work that addresses probability-related research questions regarding medication use via a series of multi-state models of increasing complexity while also considering multiple modelling choices. Lauseker et al. [
7] and Le-Rademacher [
28] discuss about different multi-state structures on clinical data about Chronic Myeloid Leukemia (CML) and Acute Myeloid Leukemia (AML) respectively, but they apply a single multi-state structure comparing modelling choices. Meira-Machado et al. [
29] evaluate the Markov property of a 3-state Illness-Death model, deriving probability estimates under a semi-Markov and non-Markov assumption and comparing the structure with a single-event survival analysis with the intermediate state as a time-varying covariate, but they do not explore further multi-state structures.
Another issue to consider is choosing the timescale to be used for the transition models of the chosen multi-state structure. In the main analysis we used time since entering current state as the timescale for all transition models (“clock reset”). However, we also implemented the “clock forward” and the “clock mix” [
30] approaches as part of a sensitivity analysis in order to explore how robust are the estimations of the complex multi-state structures for different timescale choices when modelling the transition rates (Figure A4 of Additional file
1). The “clock reset” and “clock mix” approach give almost identical estimates, while the “clock forward” approach gives estimates close to the other two approaches. A limitation of this study regarding timescales is that we assumed that each transition rate is a function of either time since the start of follow-up or time since entering the current state. However, it can also be assumed that each transition rate is a function of multiple timescales simultaneously [
31]. This modelling assumption can be implemented on a multi-state model framework via the merlin package in Stata [
21] or simLexis library in Epi R package [
32] and could be compared with the modelling approaches used in the current study in future research.
Other measures derived under a MSM framework may be of primary interest such as the total length of stay in medication cycles over the follow-up time or transition rates and rate ratios for experiencing the next medication cycle among individuals with different profiles (covariate patterns). Due to space limitations, estimation results regarding these measures and their interpretation under each multi-state structure are presented in Additional file
1. A pseudo-dataset is supplied in Additional file
2 which can be used by the code in Additional files
3 and
4 to create the multi-state structures and run the multi-state models discussed in this study.
Finally, since recurrent multi-state models structures are used in this study, it is important to note that recurrent events analyses can also be approached either with recurrent multi-state models with death as an absorbing state or by the joint modelling of recurrent events and the terminal event of death [
33‐
35]. However, since the focus of this study is on exploring different research questions via multi-state models when dealing with registry- based prescription data, expanding on the use of joint frailty models is out of our scope.
Conclusions
In this study we explored how different research questions can be addressed, ranging from simple to composite ones, surpassing the single-event and competing risks settings, and defining complex bidirectional and recurrent multi-state structures, highlighting the importance of choosing a structure that properly addresses the clinical research question of interest in each case. When information on an outcome of interest that repeatedly changes over time is available, such as the medication status based on prescribed medication, in the presence of other competing events such as death, the use of novel multi-state models of adequate complexity can successfully address composite, more realistic research questions. In addition, during the application of such models, there is a number of modelling choices such as the choice of timescale for each transition and the borrowing of information across transitions that should be explored and evaluated.
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