Causal inference in multi-state models-sickness absence and work for 1145 participants after work rehabilitation

Abstract

Background: Multi-state models, as an extension of traditional models in survival analysis, have proved to be a flexible framework for analysing the transitions between various states of sickness absence and work over time. In this paper we study a cohort of work rehabilitation participants and analyse their subsequent sickness absence using Norwegian registry data on sickness benefits. Our aim is to study how detailed individual covariate information from questionnaires explain differences in sickness absence and work, and to use methods from causal inference to assess the effect of interventions to reduce sickness absence. Examples of the latter are to evaluate the use of partial versus full time sick leave and to estimate the effect of a cooperation agreement on a more inclusive working life.

Methods: Covariate adjusted transition intensities are estimated using Cox proportional hazards and Aalen additive hazards models, while the effect of interventions are assessed using methods of inverse probability weighting and G-computation.

Results: Results from covariate adjusted analyses show great differences in sickness absence and work for patients with assumed high risk and low risk covariate characteristics, for example based on age, type of work, income, health score and type of diagnosis. Causal analyses show small effects of partial versus full time sick leave and a positive effect of having a cooperation agreement, with about 5 percent points higher probability of returning to work.

Conclusions: Detailed covariate information is important for explaining transitions between different states of sickness absence and work, also for patient specific cohorts. Methods for causal inference can provide the needed tools for going from covariate specific estimates to population average effects in multi-state models, and identify causal parameters with a straightforward interpretation based on interventions.

Fig. 1

Multi-state model for sickness absence and work. A model for the transitions between work (no registered benefits), sick leave benefits, partial sick leave benefits, work assessment allowance and disability pension, for patients being discharged from clinics offering comprehensive inpatient work rehabilitation

Fig. 2

Nelson-Aalen estimates of unadjusted cumulative transition intensities for the 15 transitions in the multi-state model. The five states in the model is work (Work), sick leave benefits (SickL), partial sick leave benefits (ParSL), work assessment allowance (WorkAsAl) and disability pension (Disab)

Fig. 3

Unadjusted state transition probabilities. Predictions given the patients state at baseline (time of discharge from the work rehabilitation center)

Fig. 4

State occupation probabilities. The overall probability of being in the five states over time, estimated using Eq. 3

Fig. 5

Covariate adjusted state transition probabilities with work assessment allowance as the initial state; predictions given two selected sets of covariates. Left panel: Married female aged 30 in an educational job, with a cooperation agreement on a more inclusive working life, income above NOK 300 000, higher education, working ability score 4 and mental diagnosis. Right panel: Single male aged 60 in a manual job, no cooperation agreement on a more inclusive working life, income below NOK 300 000, no higher education, work ability score 4 and musculoskeletal diagnosis

Fig. 6

The probability of being in state 1 (work) after starting in state 4 (work assessment allowance) for two covariate specific predictions. Left panel: Married female aged 30 in a educational job, with a cooperation agreement on an inclusive working life, income above NOK 300 000, higher education, working ability score 4 and mental diagnosis. Right panel: Single male aged 60 in a manual job, no agreement on a more inclusive working life, income below NOK 300 000, no higher education, work ability score 4 and musculoskeletal diagnosis

Fig. 7

Results intervening on sick leave intensities. Comparing predicted (left panel) and counterfactual (right panel) state transition probabilities for a selected set of covariates: Married male aged 45 in a service job, with no agreement on a more inclusive working life, income below NOK 300 000, no higher education, with a high to medium working ability score and musculoskeletal diagnosis. In the counterfactual scenario all transitions into sick leave have been blocked and routed into partial sick leave

Fig. 8

Inverse probability weighting results for full versus partial sick leave. State transition probabilities for the counterfactual scenarios where everyone originally on full or partial sick leave were given full sick leave (left panel) or partial sick leave (right panel). Note that time axis is restricted to the first year, to highlight the differences between these two scenarios

Fig. 9

Inverse probability weighting results for the effect of having a cooperation agreement. State transition probabilities for the counterfactual scenarios no-one has a cooperation agreement on a more inclusive working life (left panel) and the scenario where everyone has such an agreement (right panel)

Fig. 10

G-computation results for the effect having a cooperation agreement. State transition probabilities for the counterfactual scenarios no-one has a cooperation agreement on a more inclusive working life (left panels) and the scenario where everyone has such an agreement (right panels), estimated using the G-computation approach with Cox proportional hazards models (upper panels) and Aalen additive hazards models (lower panels)

Fig. 11

Effect of having a cooperation agreement. Difference in probability of returning to work for the two counterfactual scenarios where no-one has an agreement on more inclusive working life and the scenario where everyone has such an agreement, estimated using the G-computation approach. Ninety-five percent bootstrap confidence intervals are presented around the effect