Multistate Models on Pleural Effusion after Allogeneic Hematopoietic Stem Cell Transplantation

Relaxing the assumption of constant transition rates in a multi-state model in hospital epidemiology

BACKGROUND

Multi-state models are being increasingly used to capture complex disease pathways. The convenient formula of the exponential multi-state model can facilitate a quick and accessible understanding of the data. However, assuming time constant transition rates is not always plausible. On the other hand, obtaining predictions from a fitted model with time-dependent transitions can be challenging. One proposed solution is to utilise a general simulation algorithm to calculate predictions from a fitted multi-state model.

METHODS

Predictions obtained from an exponential multi-state model were compared to those obtained from two different parametric models and to non-parametric Aalen-Johansen estimates. The first comparative approach fitted a multi-state model with transition-specific distributions, chosen separately based on the Akaike Information Criterion. The second approach was a Royston-Parmar multi-state model with 4 degrees of freedom, which was chosen as a reference model flexible enough to capture complex hazard shapes. All quantities were obtained analytically for the exponential and Aalen-Johansen approaches. The transition rates for the two comparative approaches were also obtained analytically, while all other quantities were obtained from the fitted models via a general simulation algorithm. Metrics investigated were: transition probabilities, attributable mortality (AM), population attributable fraction (PAF) and expected length of stay. This work was performed on previously analysed hospital acquired infection (HAI) data. By definition, a HAI takes three days to develop and therefore selected metrics were also predicted from time 3 (delayed entry).

RESULTS

Despite clear deviations from the constant transition rates assumption, the empirical estimates of the transition probabilities were approximated reasonably well by the exponential model. However, functions of the transition probabilities, e.g. AM and PAF, were not well approximated and the comparative models offered considerable improvements for these metrics. They also provided consistent predictions with the empirical estimates in the case of delayed entry time, unlike the exponential model.

CONCLUSION

We conclude that methods and software are readily available for obtaining predictions from multi-state models that do not assume constant transition rates. The multistate package in Stata facilitates a range of predictions with confidence intervals, which can provide a more comprehensive understanding of the data. User-friendly code is provided.

Splenectomy before allogeneic hematopoietic cell transplantation for myelofibrosis: A French nationwide study

The value of pretransplant splenectomy in patients with myelofibrosis (MF) is subject to debate, since the procedure may preclude subsequent allogeneic hematopoietic cell transplantation (allo-HCT). To determine the impact of pretransplant splenectomy on the incidence of allo-HCT, we conducted a comprehensive retrospective study of all patients with MF for whom an unrelated donor search had been initiated via the French bone marrow transplantation registry (RFGM) between 1 January 2008 and 1 January 2017. Additional data were collected from the patients' medical files and a database held by the French-Language Society for Bone Marrow Transplantation and Cell Therapy (SFGM-TC). We used a multistate model with four states ("RFGM registration"; "splenectomy"; "death before allo-HCT", and "allo-HCT") to evaluate the association between splenectomy and the incidence of allo-HCT. The study included 530 patients from 57 centers. With a median follow-up time of 6 years, we observed 81 splenectomies, 99 deaths before allo-HCT (90 without splenectomy and nine after), and 333 allo-HCTs (268 without splenectomy and 65 after). In a bivariable analysis, the hazard ratio [95% confidence interval (CI)] for the association of splenectomy with allo-HCT was 7.2 [5.1-10.3] in the first 4 months and 1.18 [0.69-2.03] thereafter. The hazard ratio [95% CI] for death associated with splenectomy was 1.58 [0.79-3.14]. These reassuring results suggest that splenectomy does not preclude allo-HCT in patients with MF.

Relapse- and Immunosuppression-Free Survival after Hematopoietic Stem Cell Transplantation: How Can We Assess Treatment Success for Complex Time-to-Event Endpoints?

In most clinical oncology trials, time-to-first-event analyses are used for efficacy assessment, which often do not capture the entire disease process. Instead, the focus may be on more complex time-to-event endpoints, such as the course of disease after the first event or endpoints occurring after randomization. We propose "relapse- and immunosuppression-free survival" (RIFS) as an innovative and clinically relevant outcome measure for assessing treatment success after hematopoietic stem cell transplant (SCT). To capture the time-dynamic relationship of multiple episodes of immunosuppressive therapy during follow-up, relapse, and nonrelapse mortality, a multistate model was developed. The statistical complexity is that the probability of RIFS is nonmonotonic over time; thus, standard time-to-first-event methodology is inappropriate for formal treatment comparisons. Instead, a generalization of the Kaplan-Meier method was used for probability estimation, and simulation-based resampling was suggested as a strategy for statistical inference. We reanalyzed data from a recently published phase III trial in 201 leukemia patients after SCT. The study evaluated long-term treatment success of standard graft-versus-host disease prophylaxis plus a pretransplant antihuman T-lymphocyte immunoglobulin compared with standard prophylaxis alone. Results suggested that treatment increased the long-term probability of RIFS by approximately 30% during the entire follow-up period, which complements the original findings. This article highlights the importance of complex endpoints in oncology, which provide deeper insight into the treatment and disease process over time. Multistate models combined with resampling are highlighted as a promising tool to evaluate treatment success beyond standard endpoints. An example code is provided in the Supplementary Materials.