Multistate Analysis of Life Histories with R

Life history data are generally incomplete. Usually, they do not cover for each individual in the study the entire life span or the life segment of interest. If data are collected retrospectively, observation ends at interview date, and no information is available on events and experiences after the date. Data collected prospectively are incomplete because events and other experiences are recorded during a limited period of time only. To deal with data limitations, models are introduced. The model that is considered in this chapter describes life histories. The model is based on the premise that life histories are realisations of a continuous-time Markov process. A Markov process is a stochastic process that describes a system with multiple states and transitions between the states. The time at which a transition occurs is random but the distribution of the time to transition is known. In the continuous-time Markov process, the transition time has an exponential distribution. The rate of transition out of the current state (exit rate) is the parameter of the exponential distribution. It depends on the current state only and is independent of the history of the stochastic process. In a system with multiple states, an individual who leaves the current state may enter one of several states. In competing risks models, states in the state space are viewed as competing destinations and transition rates are destination-specific. The Markov process is a first-order process: the destination state depends on the current state only and is independent of states occupied previously.

A Biograph object is a data frame of individual life history data. All information on the life history of a person is stored in a single record. That data format is known as wide format. The wide format differs from the long format, in which information on an episode or a transition is contained in a separate record. The structure of the data frame is described in Sect. 3.2 of this chapter. In a Biograph object, life history data are organised chronologically starting with the first reported state of the life course and the first transition. That data structure is consistent with the life course as a sequence of events and a sequence of states. Converting raw data from surveys, registers or follow-up studies into a Biograph object can be cumbersome. Most surveys are not organised from a life history perspective but from a life domain perspective. In Sect. 3.3, I describe how to convert the GLHS data into a Biograph object. The GLHS data structure is only one of the many possible data structures. It is not possible to develop a single conversion method for all known data structures. More on how to create a Biograph object and several examples may be found in Annex A. Data analysis may require some operations on the data before the analysis can start. In multistate modelling, that may involve the removal from the data of transitions to the same state (intrastate transitions). In the GLHS data, job changes are intrastate transitions. Other operations may change the observation window. Biograph includes functions to change the observation window. One function selects transitions between two time points (calendar time) or between two ages. Another function delineates an observation window by two events or by an event and the survey date. These operations change the structure of the data. Data restructuring is the subject of Sect. 3.4. In Sect. 3.5 of this chapter, I review formats of life history data and list functions that may be used to convert one data format into another. A description of life histories includes information on states occupied during the period of observation, on transitions between states and on the dates of transition. Different ways exist to report dates. Most people use calendar dates, but dates may also be measured as time elapsed since a reference date or a reference event. The Century Month Code (CMC), used in the GLHS, measures dates as the number of months elapsed since 1 January 1900. Other surveys may express dates differently. Section 3.5 covers different date formats and R functions, including Biograph functions, for converting one date format into another.

Data visualisation is the graphic presentation of data to reveal complex information at a glance (Steele and Iliinsky 2010). The challenge is to map data to a visual display that reveals the range of values of variables and relations between variables. Visualisation of data can be an effective introduction to formal statistical modelling. Ages at marriage may be displayed as points in a scatter plot to assess the distribution of ages and to identify outliers. The marriage duration of a person may be displayed as a line connecting age at marriage and current age or age at marriage dissolution. The end point may be marked if the marriage has been dissolved and not marked if the marriage is intact at the end of the observation period. Visualisation of life histories poses particular challenges. The first is conceptual. The life history is a multistage process of development in which stages create a basis for subsequent stages. In this book the life course is conceptualised as sequences of states and sequences of events. In each domain of life, a state and event sequence can be identified. A second challenge is embedding. The life course is embedded in a historical context, and the visualisation should reveal how developmental processes vary in time. That requires at least two time scales: age and calendar time. The Lexis diagram, named after the demographer Wilhelm Lexis (1837–1914), meets that challenge. Each line in a Lexis diagram represents the follow-up of a single individual from entry to exit on two time scales: age and calendar time. The Lexis diagram is widely used and has inspired improved visualisations of life histories. Some of that research is reviewed in the brief historical note in Sect. 5.1. A third challenge is to reveal significant information at a glance. The graph should convey essential information and highlight the unexpected.

The Comprehensive R Archive Network (CRAN) (http://cran.r-project.org/) has a number of statistical packages for multistate analysis of event histories (multistate survival analysis). These packages focus on statistical inference, i.e. the estimation of transition rates and transition probabilities from empirical data. In this Chapter, the following packages are covered: survival by Therneau and Lumley, eha by Broström, mvna and etm by Allignol et al., mstate by Putter et al. and msm by Jackson. For an up-to-date overview of packages for survival analysis, the reader is referred to the CRAN Task View on Survival Analysis, maintained by Allignol and Latouche. The Task View has a section on multistate models. For a review of methods for estimating multistate models, the reader is referred to Chap. 2 and, for a more extensive treatment, to Aalen et al. (2008), in particular Chap. 3), Beyersmann et al. (2012), and a special issue of the Journal of Statistical Software (January 2011), edited by Putter. For recent advances in demography, see Willekens and Putter (2014). In essence, the method consists of counting transitions (events) and numbers of persons at risk of a transition just before the transition occurs or in the observation interval. The chapter consists of five sections, in addition to the introduction. Section 6.1 describes the survival package, Sect. 6.2 the eha package, Sect. 6.3 the mvna and etm packages, Sect. 6.4 the mstate package and Sect. 6.5 the msm package.

The aim of this chapter is to illustrate Biograph with data from the Netherlands Family and Fertility Survey of 1998 (Onderzoek Gezinsvorming 1998 or NLOG98). Statistics Netherlands organised the survey for information on partnerships, marriage and family. In this chapter Biograph is used to study pathways to first birth. What life paths do women in the Netherlands follow between leaving parental home and motherhood? Some leave the parental home for marriage and have a child soon after marriage. Most women have a different pathway, however. The trajectory women follow determines to a large extent the age at which they become a mother. Differences in pathways can be associated with background characteristics. Three covariates are considered: religious denomination (kerk), level of education (educ) and birth cohort (cohort).

As life unfolds people move between states and enter new stages of life. The path taken depends on personal characteristics, early life experiences, context and chance. The life course can be represented as a sequence of states and modelled as a multistate process, governed by transition rates. In this book, the continuous-time Markov process is used to model life histories. Transition rates may depend on covariates.