By Jan Beyersmann
This booklet covers competing hazards and multistate types, occasionally summarized as occasion heritage research. those types generalize the research of time to a unmarried occasion (survival research) to analysing the timing of distinctive terminal occasions (competing dangers) and attainable intermediate occasions (multistate models). either R and multistate tools are promoted with a spotlight on nonparametric methods.
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Extra info for Competing Risks and Multistate Models with R
A realization of a multistate process) can be thought of as being realized as a series of nested competing risks experiments. 2 also work in the more complex multistate situation. We then discuss that such a multistate model is time-inhomogeneous Markov and introduce its transition probabilities and transition hazards. Next, the Nelson-Aalen estimator of the cumulative transition hazards is considered, and ﬁnally we show how matrixvalued product integration yields the matrix of transition probabilities as a deterministic function of the cumulative transition hazards.
Competing risks multistate model with cause-speciﬁc hazards α0j (t), j = 1, 2. every individual is in the initial state 0 at time origin. The individual stays in this state until occurrence of any ﬁrst event. Usually, there is one event of interest, modelled by transitions into state 1, and all other ﬁrst event types are subsumed into the competing event state 2. , in the case of hospital stay data, hospital mortality modelled by state 1 may be of special interest. The competing event state 2 then has the interpretation ‘discharge alive’.
2 for an in-depth treatment. 3 on competing risks generalized the standard survival set-up with one event time T and one event type to modelling diﬀerent possible event types (the competing risks) that may occur at time T . , competing risks model time until some ﬁrst event and the type of the ﬁrst event, but (by deﬁnition) potential subsequent events are not modelled. Multistate models allow for modelling both the occurrence of diﬀerent event types and the occurrence of subsequent events, the latter potentially of diﬀerent types.
Competing Risks and Multistate Models with R by Jan Beyersmann