Regression models for expected length of stay

Abstract

In multi-state models, the expected length of stay (ELOS) in a state is not a straightforward object to relate to covariates, and the traditional approach has instead been to construct regression models for the transition intensities and calculate ELOS from these. The disadvantage of this approach is that the effect of covariates on the intensities is not easily translated into the effect on ELOS, and it typically relies on the Markov assumption. We propose to use pseudo-observations to construct regression models for ELOS, thereby allowing a direct interpretation of covariate effects while at the same time avoiding the Markov assumption. For this approach, all we need is a non-parametric consistent estimator for ELOS. For every subject (and for every state of interest), a pseudo-observation is constructed, and they are then used as outcome variables in the regression model. We furthermore show how to construct longitudinal (pseudo-) data when combining the concept of pseudo-observations with landmarking. In doing so, covariates are allowed to be time-varying, and we can investigate potential time-varying effects of the covariates. The models can be fitted using generalized estimating equations, and dependence between observations on the same subject is handled by applying the sandwich estimator. The method is illustrated using data from the US Health and Retirement Study where the impact of socio-economic factors on ELOS in health and disability is explored. Finally, we investigate the performance of our approach under different degrees of left-truncation, non-Markovianity, and right-censoring by means of simulation.

Estimation of adjusted expected excess length‐of‐stay associated with ventilation‐acquired pneumonia in intensive care: A multistate approach accounting for time‐dependent mechanical ventilation

“…The coverage probability for is still very good (95.3%), whereas the coverage for is decreased (89.8%). We emphasize that these results are not surprising, because this setting forces the computation of restricted summary measures (e.g., Beyersmann & Putter, 2014;Grand & Putter, 2016) in relation (7) with = 45, whereas the true quantities are based on the support of the entire timeline (0, ∞). Note that the performance would be distinctly improved if the true values are also based on = 45 (results not shown).…”

“…and weights 1 ( ) ∶= 1 02 (0, )+ 03 (0, ) and 0 ( ) = 1 00 (0, )+ 01 (0, ) . Obviously, and are much more involved functions of the matrix of transition probabilities P compared to the more simple three-state setting established in relation (5) or the quantities used in, for example, Grand and Putter (2016). Similar to the previous subsection, we have to assume ( = ) > 0 for all ∈ {0, 1, 2, 3, 4} and times in order to ensure a proper two-group comparison.…”

Causal inference in survival analysis using pseudo‐observations

“…Because pseudo‐observations provide a general tool for analyzing mean value parameters in the presence of right‐censoring, the method lends itself to estimating an average causal effect in survival analysis. We have illustrated the use of the method for estimating the causal risk difference at a fixed point in time (possibly in the presence of competing risks) but it applies equally easily to parameters like the restricted mean life time or the number of years spent in a given state in a multi‐state model . Relying on the simple Kaplan–Meier or Aalen–Johansen estimators, a drawback is that censoring is not allowed to depend on covariates.…”

Parametric multistate survival models: Flexible modelling allowing transition‐specific distributions with application to estimating clinically useful measures of effect differences

“…Following Grand and Putter, the residual restricted expected length of stay in state b during the time period from s to τ , conditional on the patient being alive at time s and in state a (nonabsorbing), which we refer to as length of stay for simplicity, is defined as which defines the amount of time spent in state b , starting in state a at time s , up until time τ . If , and state a = b is a healthy state and all possible next states are deaths, then Equation represents life expectancy . This can be viewed as the multistate extension of restricted mean survival .…”

“…We adopt the simulation approach to calculate transition probabilities and other quantities of interest,() using a general survival simulation algorithm, which can be readily applied to any combination of transition‐specific distributions to simulate from the multistate model . Finally, we show the flexibility of the simulation approach to obtain clinically useful measures, such as total length of stay, and differences and ratios of proportions within each state for specific covariate patterns, and accompanying confidence intervals.…”