Assessing type I error and power of multistate Markov models for panel data-A simulation study

A semi-Markov multistate cure model for estimating intervention effects in stepped wedge design trials

Multistate models are useful for studying exposures that affect transitions among a set of health states. However, they can be challenging to apply when exposures are time-varying. We develop a multistate model and a method of likelihood construction that allows application of the model to data in which interventions or other exposures can be time-varying and an individual may to be exposed to multiple intervention conditions while progressing through states. The model includes cure proportions, reflecting the possibility that some individuals will never leave certain states. We apply the approach to analyze patient vaccination data from a stepped wedge design trial evaluating two interventions to increase uptake of human papillomavirus vaccination. The states are defined as the number of vaccine doses the patient has received. We model state transitions as a semi-Markov process and include cure proportions to account for individuals who will never leave a given state (e.g. never receive their next dose). Multistate models typically quantify intervention effects as hazard ratios contrasting the intensities of transitions between states in intervention versus control conditions. For multistate processes, another clinically meaningful outcome is the change in the percentage of the study population that has achieved a specific state (e.g. completion of all required doses) by a specific point in time due to an intervention. We present a method for quantifying intervention effects in this manner. We apply the model to both simulated and real-world data and also explore some conditions under which such models may give biased results.

Multistate Modeling of Clinical Trajectories and Outcomes in the ICU: A Proof-of-Concept Evaluation of Acute Kidney Injury Among Critically Ill Patients With COVID-19

Multistate models yield high-fidelity analyses of the dynamic state transition and temporal dimensions of a clinical condition's natural history, offering superiority over aggregate modeling techniques for addressing these types of problems.

OBJECTIVES

To demonstrate the utility of these models in critical care, we examined acute kidney injury (AKI) development, progression, and outcomes in COVID-19 critical illness through multistate analyses.

DESIGN SETTING AND PARTICIPANTS

Retrospective cohort study at an urban tertiary-care academic hospital in the United States. All patients greater than or equal to 18 years in an ICU with COVID-19 in 2020, excluding patients with preexisting end-stage renal disease.

MAIN OUTCOMES AND MEASURES

Using electronic health record data, we determined AKI presence/stage in discrete 12-hour time windows and fit multistate models to determine longitudinal transitions and outcomes.

RESULTS

Of 367 encounters, 241 (66%) experienced AKI (maximal stages: 88 stage-1, 49 stage-2, 104 stage-3 AKI [51 received renal replacement therapy (RRT), 53 did not]). Patients receiving RRT overwhelmingly received invasive mechanical ventilation (IMV) (n = 60, 95%) compared with the AKI-without-RRT (n = 98, 53%) and no-AKI groups (n = 39, 32%; p < 0.001), with similar mortality patterns (RRT: n = 36, 57%; AKI: n = 74, 40%; non-AKI: n = 23, 19%; p < 0.001). After 24 hours in the ICU, almost half the cohort had AKI (44.9%; 95% CI, 41.6-48.2%). At 7 days after stage-1 AKI, 74.0% (63.6-84.4) were AKI-free or discharged. By contrast, fewer patients experiencing stage-3 AKI were recovered (30.0% [24.1-35.8%]) or discharged (7.9% [5.2-10.7%]) after 7 days. Early AKI occurred with similar frequency in patients receiving and not receiving IMV: after 24 hours in the ICU, 20.9% of patients (18.3-23.6%) had AKI and IMV, while 23.4% (20.6-26.2%) had AKI without IMV.

CONCLUSIONS AND RELEVANCE

In a multistate analysis of critically ill patients with COVID-19, AKI occurred early and heterogeneously in the course of critical illness. Multistate methods are useful and underused in ICU care delivery science as tools for understanding trajectories, prognoses, and resource needs.

Power and sample size for multistate model analysis of longitudinal discrete outcomes in disease prevention trials

For clinical trials where participants pass through a number of discrete health states resulting in longitudinal measures over time, there are several potential primary estimands for the treatment effect. Incidence or time to a particular health state are commonly used outcomes but the choice of health state may not be obvious and these estimands do not make full use of the longitudinal assessments. Multistate models have been developed for some diseases and conditions with the purpose of understanding their natural history and have been used for secondary analysis to understand mechanisms of action of treatments. There is little published on the use of multistate models as the primary analysis method and potential implications on design features, such as assessment schedules. We illustrate methods via analysis of data from a motivating example; a Phase III clinical trial of pressure ulcer prevention strategies. We clarify some of the possible estimands that might be considered and we show, via a simulation study, that under some circumstances the sample size could be reduced by half using a multistate model based analysis, without adversely affecting the power of the trial.

Duration of Carbapenemase-Producing Enterobacteriaceae Carriage in Hospital Patients

To determine the duration of carbapenemase-producing Enterobacteriaceae (CPE) carriage, we studied 21 CPE carriers for »1 year. Mean carriage duration was 86 days; probability of decolonization in 1 year was 98.5%, suggesting that CPE-carriers' status can be reviewed yearly. Prolonged carriage was associated with use of antimicrobial drugs.

Population-based estimates of healthy working life expectancy in England at age 50 years: analysis of data from the English Longitudinal Study of Ageing

BACKGROUND

Retirement ages are rising in many countries to offset the challenges of population ageing, but people's capacity to work for more years in their later working life (>50 years) is unclear. We aimed to estimate healthy working life expectancy in England.

METHODS

This analysis included adults aged 50 years and older from six waves (2002-13) of the English Longitudinal Study of Ageing (ELSA), with linked mortality data. Healthy working life expectancy was defined as the average number of years expected to be spent healthy (no limiting long-standing illness) and in paid work (employment or self-employment) from age 50 years. Healthy working life expectancy was estimated for England overall and stratified by sex, educational attainment, deprivation level, occupation type, and region by use of interpolated Markov chain multi-state modelling.

FINDINGS

There were 15 284 respondents (7025 men and 8259 women) with survey and mortality data for the study period. Healthy working life expectancy at age 50 years was on average 9·42 years (10·94 years [95% CI 10·65-11·23] for men and 8·25 years [7·92-8·58] for women) and life expectancy was 31·76 years (30·05 years for men and 33·49 years for women). The number of years expected to be spent unhealthy and in work from age 50 years was 1·84 years (95% CI 1·74-1·94) in England overall. Population subgroups with the longest healthy working life expectancy were the self-employed (11·76 years [95% CI 10·76-12·76]) or those with non-manual occupations (10·32 years [9·95-10·69]), those with a tertiary education (11·27 years [10·74-11·80]), those living in southern England (10·73 years [10·16-11·30] in the South East and 10·51 years [9·80-11·22] in the South West), and those living in the least deprived areas (10·53 years [10·06-10·99]).

INTERPRETATION

Healthy working life expectancy at age 50 years in England is below the remaining years to State Pension age. Older workers of lower socioeconomic status and in particular regions in England might benefit from proactive approaches to improve health, workplace environments, and job opportunities to improve their healthy working life expectancy. Continued monitoring of healthy working life expectancy would provide further examination of the success of such approaches and that of policies to extend working lives.

FUNDING

Economic and Social Research Council.

Treatment effect on ordinal functional outcome using piecewise multistate Markov model with unobservable baseline: an application to the modified Rankin scale

In clinical trials, longitudinally assessed ordinal outcomes are commonly dichotomized and only the final measure is used for primary analysis, partly for ease of clinical interpretation. Dichotomization of the ordinal scale and failure to utilize the repeated measures can reduce statistical power. Additionally, in certain emergent settings, the same measure cannot be assessed at baseline prior to treatment. For such a data set, a piecewise-constant multistate Markov model that incorporates a latent model for the unobserved baseline measure is proposed. These models can be useful in analyzing disease history data and are advantageous in clinical applications where a disease process naturally moves through increasing stages of severity. Two examples are provided using acute stroke clinical trials data. Conclusions drawn in this article are consistent with those from the primary analysis for treatment effect in both of the motivating examples. Use of these models allows for a more refined examination of treatment effect and describes the movement between health states from baseline to follow-up visits which may provide more clinical insight into the treatment effect.

Comparison of multistate Markov modeling with contemporary outcomes in a reanalysis of the NINDS tissue plasminogen activator for acute ischemic stroke treatment trial

Historically, ordinal measures of functional outcome have been dichotomized for the primary analysis in acute stroke therapy trials. A number of alternative methods to analyze the ordinal scales have been proposed, with an emphasis on maintaining the ordinal structure as much as possible. In addition, despite the availability of longitudinal outcome data in many trials, the primary analysis consists of a single endpoint. Inclusion of information about the course of disease progression allows for a more complete understanding of the treatment effect. Multistate Markov modeling, which allows for the full ordinal scale to be analyzed longitudinally, is compared with previously suggested analytic techniques for the ordinal modified Rankin Scale (dichotomous-logistic regression; continuous-linear regression; ordinal- shift analysis, proportional odds model, partial proportional odds model, adjacent categories logit model; sliding dichotomy; utility weights; repeated measures). In addition, a multistate Markov model utilizing an estimate of the unobservable baseline outcome derived from principal component analysis is compared Each of the methods is used to re-analyze the National Institute of Neurological Diseases and Stroke tissue plasminogen activator study which showed a consistently significant effect of tissue plasminogen activator using a global test of four dichotomized outcomes in the analysis of the primary outcome at 90 days post-stroke in the primary analysis. All methods detected a statistically significant treatment effect except the multistate Markov model without predicted baseline (p = 0.053). This provides support for the use of the estimated baseline in the multistate Markov model since the treatment effect is able to be detected with its inclusion. Multistate Markov modeling allows for a more refined examination of treatment effect and describes the movement between modified Rankin Scale states over time which may provide more clinical insight into the treatment effect. Multistate Markov models are feasible and desirable in describing treatment effect in acute stroke therapy trials.