Armitage lecture 2010: Understanding treatment effects: the value of integrating longitudinal data and survival analysis

Modeling multiple correlated end-organ disease trajectories: A tutorial for multistate and joint models with applications in diabetes complications

State-of-the-art biostatistics methods allow for the simultaneous modeling of several correlated non-fatal disease processes over time, but there is no clear guidance on the optimal analysis in most settings. An example occurs in diabetes, where it is not known with certainty how microvascular complications of the eyes, kidneys, and nerves co-develop over time. In this article, we propose and contrast two general model frameworks for studying complications (sequential state and parallel trajectory frameworks) and review multivariate methods for their analysis, focusing on multistate and joint modeling. We illustrate these methods in a tutorial format using the long-term follow-up from the Diabetes Control and Complications Trial and Epidemiology of Diabetes Interventions and Complications study public data repository. A formal comparison of prediction error and discrimination is included. Multistate models are particularly advantageous for determining the order and timing of complications, but require discretization of the longitudinal outcomes and possibly a very complex state space process. Intermittent observation of the states must be accounted for, and discretization is a probable disadvantage in this setting. In contrast, joint models can account for variations of continuous biomarkers over time and are particularly designed for modeling complex association structures between the complications and for performing dynamic predictions of an outcome of interest to inform clinical decisions (eg, a late-stage complication). We found that both models have helpful features that can better-inform our understanding of the complex trajectories that complications may take and can therefore help with decision making for patients presenting with diabetes complications.

Trends in the survival benefit of repeat kidney transplantation over the past 3 decades

Repeat kidney transplantation (re-KT) is the preferred treatment for patients with graft failure. Changing allocation policies, widening the risk profile of recipients, and improving dialysis care may have altered the survival benefit of a re-KT. We characterized trends in re-KT survival benefit over 3 decades and tested whether it differed by age, race/ethnicity, sex, and panel reactive assay (PRA). By using the Scientific Registry of Transplant Recipient data, we identified 25 419 patients who underwent a re-KT from 1990 to 2019 and 25 419 waitlisted counterfactuals from the same year with the same waitlisted time following graft failure. In the adjusted analysis, a re-KT was associated with a lower risk of death (adjusted hazard ratio [aHR] = 0.63; 95% confidence interval [CI], 0.61-0.65). By using the 1990-1994 era as a reference (aHR = 0.77; 95% CI, 0.69-0.85), incremental improvements in the survival benefit were noted (1995-1999: aHR = 0.72; 95% CI, 0.67-0.78: 2000-2004: aHR = 0.59; 95% CI, 0.55-0.63: 2005-2009: aHR = 0.59; 95% CI, 0.56-0.63: 2010-2014: aHR = 0.57; 95% CI, 0.53-0.62: 2015-2019: aHR = 0.64; 95% CI, 0.57-0.73). The survival benefit of a re-KT was noted in both younger (age = 18-64 years: aHR = 0.63; 95% CI, 0.61-0.65) and older patients (age ≥65 years: aHR = 0.66; 95% CI, 0.58-0.74; Pinteraction = .45). Patients of all races/ethnicities demonstrated similar benefits with a re-KT. However, it varied by the sex of the recipient (female patients: aHR = 0.60; 95% CI, 0.56-0.63: male patients: aHR = 0.66; 95% CI, 0.63-0.68; Pinteraction = .004) and PRA (0-20: aHR = 0.69; 95% CI, 0.65-0.74: 21-80: aHR = 0.61; 95% CI, 0.57-0.66; Pinteraction = .02; >80: aHR = 0.57; 95% CI, 0.53-0.61; Pinteraction< .001). Our findings support the continued practice of a re-KT and efforts to overcome the medical, immunologic, and surgical challenges of a re-KT.

Missing at random: a stochastic process perspective

We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing-data framework, we give a novel characterization of the observed data as a stopping-set sigma algebra. We demonstrate that the usual missingness-at-random conditions are equivalent to requiring particular stochastic processes to be adapted to a set-indexed filtration. These measurability conditions ensure the usual factorization of likelihood ratios. We illustrate how the theory can be extended easily to incorporate explanatory variables, to describe longitudinal data in continuous time, and to admit more general coarsening of observations.

The illness-death model for family studies

Family studies involve the selection of affected individuals from a disease registry who provide right-truncated ages of disease onset. Coarsened disease histories are then obtained from consenting family members, either through examining medical records, retrospective reporting, or clinical examination. Methods for dealing with such biased sampling schemes are available for continuous, binary, and failure time responses, but methods for more complex life history processes are less developed. We consider a simple joint model for clustered illness-death processes which we formulate to study covariate effects on the marginal intensity for disease onset and to study the within-family dependence in disease onset times. We construct likelihoods and composite likelihoods for family data obtained from biased sampling schemes. In settings where the disease is rare and data are insufficient to fit the model of interest, we show how auxiliary data can augment the composite likelihood to facilitate estimation. We apply the proposed methods to analyze data from a family study of psoriatic arthritis carried out at the University of Toronto Psoriatic Arthritis Registry.

The mediating role of extent of resection in the relationship between the tumor characteristics and survival outcome of glioma

The prognostic value of tumor characteristics for glioma has been controversial, partly because of a lack of knowledge about how these associations develop. Extent of resection may be factors that mediate the relationship between tumor characteristics and the hazard of death from glioma.

Patients and Methods: This consecutive study retrospectively included a group of 393 treatment-naive patients with newly, pathologically confirmed glioma between January 2004 and December 2014. Information on patient age, gender, Karnofsky Performance Status (KPS), tumor grade, tumor size, tumor location, presence or absence of contrast enhancement on MRI and extent of tumor resection have all been collected. The discrete-time survival model integrating survival outcomes within structural equation models was employed to develop and evaluate a comprehensive hypothesis regarding the direct and indirect impact of tumor characteristics on the hazard of death from glioma, mediated by the extent of resection.

Results: Except for tumor location, the indirect effects of tumor grade, contrast enhancement, and tumor size on PFS of glioma through extent of resection were found significant in the model.

Conclusion: This study provides a better understanding of the process through which tumor characteristics is associated with hazard of death from glioma.

Ignorability for general longitudinal data

Likelihood factors that can be disregarded for inference are termed ignorable. We demonstrate that close ties exist between ignorability and identification of causal effects by covariate adjustment. A graphical condition, stability, plays a role analogous to that of missingness at random, but is applicable to general longitudinal data. Our formulation of ignorability does not depend on any notion of missing data, so is appealing in situations where missing data may not actually exist. Several examples illustrate how stability may be assessed.

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

Ordinal outcomes collected at multiple follow-up visits are common in clinical trials. Sometimes, one visit is chosen for the primary analysis and the scale is dichotomized amounting to loss of information. Multistate Markov models describe how a process moves between states over time. Here, simulation studies are performed to investigate the type I error and power characteristics of multistate Markov models for panel data with limited non-adjacent state transitions. The results suggest that the multistate Markov models preserve the type I error and adequate power is achieved with modest sample sizes for panel data with limited non-adjacent state transitions.

Comparison of statistical approaches dealing with time-dependent confounding in drug effectiveness studies

In longitudinal studies, if the time-dependent covariates are affected by the past treatment, time-dependent confounding may be present. For a time-to-event response, marginal structural Cox models are frequently used to deal with such confounding. To avoid some of the problems of fitting marginal structural Cox model, the sequential Cox approach has been suggested as an alternative. Although the estimation mechanisms are different, both approaches claim to estimate the causal effect of treatment by appropriately adjusting for time-dependent confounding. We carry out simulation studies to assess the suitability of the sequential Cox approach for analyzing time-to-event data in the presence of a time-dependent covariate that may or may not be a time-dependent confounder. Results from these simulations revealed that the sequential Cox approach is not as effective as marginal structural Cox model in addressing the time-dependent confounding. The sequential Cox approach was also found to be inadequate in the presence of a time-dependent covariate. We propose a modified version of the sequential Cox approach that correctly estimates the treatment effect in both of the above scenarios. All approaches are applied to investigate the impact of beta-interferon treatment in delaying disability progression in the British Columbia Multiple Sclerosis cohort (1995-2008).

Comparison of Statistical Approaches for Dealing With Immortal Time Bias in Drug Effectiveness Studies

In time-to-event analyses of observational studies of drug effectiveness, incorrect handling of the period between cohort entry and first treatment exposure during follow-up may result in immortal time bias. This bias can be eliminated by acknowledging a change in treatment exposure status with time-dependent analyses, such as fitting a time-dependent Cox model. The prescription time-distribution matching (PTDM) method has been proposed as a simpler approach for controlling immortal time bias. Using simulation studies and theoretical quantification of bias, we compared the performance of the PTDM approach with that of the time-dependent Cox model in the presence of immortal time. Both assessments revealed that the PTDM approach did not adequately address immortal time bias. Based on our simulation results, another recently proposed observational data analysis technique, the sequential Cox approach, was found to be more useful than the PTDM approach (Cox: bias = -0.002, mean squared error = 0.025; PTDM: bias = -1.411, mean squared error = 2.011). We applied these approaches to investigate the association of β-interferon treatment with delaying disability progression in a multiple sclerosis cohort in British Columbia, Canada (Long-Term Benefits and Adverse Effects of Beta-Interferon for Multiple Sclerosis (BeAMS) Study, 1995-2008).

Mechanisms and mediation in survival analysis: towards an integrated analytical framework

BACKGROUND

A wide-ranging debate has taken place in recent years on mediation analysis and causal modelling, raising profound theoretical, philosophical and methodological questions. The authors build on the results of these discussions to work towards an integrated approach to the analysis of research questions that situate survival outcomes in relation to complex causal pathways with multiple mediators. The background to this contribution is the increasingly urgent need for policy-relevant research on the nature of inequalities in health and healthcare.

METHODS

The authors begin by summarising debates on causal inference, mediated effects and statistical models, showing that these three strands of research have powerful synergies. They review a range of approaches which seek to extend existing survival models to obtain valid estimates of mediation effects. They then argue for an alternative strategy, which involves integrating survival outcomes within Structural Equation Models via the discrete-time survival model. This approach can provide an integrated framework for studying mediation effects in relation to survival outcomes, an issue of great relevance in applied health research. The authors provide an example of how these techniques can be used to explore whether the social class position of patients has a significant indirect effect on the hazard of death from colon cancer.

RESULTS

The results suggest that the indirect effects of social class on survival are substantial and negative (-0.23 overall). In addition to the substantial direct effect of this variable (-0.60), its indirect effects account for more than one quarter of the total effect. The two main pathways for this indirect effect, via emergency admission (-0.12), on the one hand, and hospital caseload, on the other, (-0.10) are of similar size.

CONCLUSIONS

The discrete-time survival model provides an attractive way of integrating time-to-event data within the field of Structural Equation Modelling. The authors demonstrate the efficacy of this approach in identifying complex causal pathways that mediate the effects of a socio-economic baseline covariate on the hazard of death from colon cancer. The results show that this approach has the potential to shed light on a class of research questions which is of particular relevance in health research.

A longitudinal, observational study with many repeated measures demonstrated improved precision of individual survival curves using Bayesian joint modeling of disability and survival

BACKGROUND/STUDY CONTEXT: It has not been previously demonstrated whether Bayesian joint modeling (BJM) of disability and survival can, under certain conditions, improve precision of individual survival curves.

METHODS

A longitudinal, observational study wherein 754 initially nondisabled community-dwelling adults in greater New Haven, Connecticut, were observed on a monthly basis for over 10 years.

RESULTS

In this study, BJM exploited many monthly observations to demonstrate, relative to a separate survival model with adjustment, improved precision of individual survival curves, permitting detection of significant differences between survival curves of two similar individuals. The gain in precision was lost when using only those observations from intervals of 6, 9, or 12 months.

CONCLUSION

When there are many repeated measures, BJM of longitudinal functional disability and interval-censored survival can potentially increase the precision of individual survival curves relative to those from a separate survival model. This may facilitate the identification of significant differences between individual survival curves, a useful result usually precluded by the large variability inherent to individual-level estimates from stand-alone survival models.

Accounting for individual differences and timing of events: estimating the effect of treatment on criminal convictions in heroin users

Background

The reduction of crime is an important outcome of opioid maintenance treatment (OMT). Criminal intensity and treatment regimes vary among OMT patients, but this is rarely adjusted for in statistical analyses, which tend to focus on cohort incidence rates and rate ratios. The purpose of this work was to estimate the relationship between treatment and criminal convictions among OMT patients, adjusting for individual covariate information and timing of events, fitting time-to-event regression models of increasing complexity.

Methods

National criminal records were cross linked with treatment data on 3221 patients starting OMT in Norway 1997–2003. In addition to calculating cohort incidence rates, criminal convictions was modelled as a recurrent event dependent variable, and treatment a time-dependent covariate, in Cox proportional hazards, Aalen’s additive hazards, and semi-parametric additive hazards regression models. Both fixed and dynamic covariates were included.

Results

During OMT, the number of days with criminal convictions for the cohort as a whole was 61% lower than when not in treatment. OMT was associated with reduced number of days with criminal convictions in all time-to-event regression models, but the hazard ratio (95% CI) was strongly attenuated when adjusting for covariates; from 0.40 (0.35, 0.45) in a univariate model to 0.79 (0.72, 0.87) in a fully adjusted model. The hazard was lower for females and decreasing with older age, while increasing with high numbers of criminal convictions prior to application to OMT (all p < 0.001). The strongest predictors were level of criminal activity prior to entering into OMT, and having a recent criminal conviction (both p < 0.001). The effect of several predictors was significantly time-varying with their effects diminishing over time.

Conclusions

Analyzing complex observational data regarding to fixed factors only overlooks important temporal information, and naïve cohort level incidence rates might result in biased estimates of the effect of interventions. Applying time-to-event regression models, properly adjusting for individual covariate information and timing of various events, allows for more precise and reliable effect estimates, as well as painting a more nuanced picture that can aid health care professionals and policy makers.

[Causal analysis approaches in epidemiology]

Epidemiological research is mostly based on observational studies. Whether such studies can provide evidence of causation remains discussed. Several causal analysis methods have been developed in epidemiology. This paper aims at presenting an overview of these methods: graphical models, path analysis and its extensions, and models based on the counterfactual approach, with a special emphasis on marginal structural models. Graphical approaches have been developed to allow synthetic representations of supposed causal relationships in a given problem. They serve as qualitative support in the study of causal relationships. The sufficient-component cause model has been developed to deal with the issue of multicausality raised by the emergence of chronic multifactorial diseases. Directed acyclic graphs are mostly used as a visual tool to identify possible confounding sources in a study. Structural equations models, the main extension of path analysis, combine a system of equations and a path diagram, representing a set of possible causal relationships. They allow quantifying direct and indirect effects in a general model in which several relationships can be tested simultaneously. Dynamic path analysis further takes into account the role of time. The counterfactual approach defines causality by comparing the observed event and the counterfactual event (the event that would have been observed if, contrary to the fact, the subject had received a different exposure than the one he actually received). This theoretical approach has shown limits of traditional methods to address some causality questions. In particular, in longitudinal studies, when there is time-varying confounding, classical methods (regressions) may be biased. Marginal structural models have been developed to address this issue. In conclusion, "causal models", though they were developed partly independently, are based on equivalent logical foundations. A crucial step in the application of these models is the formulation of causal hypotheses, which will be a basis for all methodological choices. Beyond this step, statistical analysis tools recently developed offer new possibilities to delineate complex relationships, in particular in life course epidemiology.

Hospital-acquired infections--appropriate statistical treatment is urgently needed!

Research on hospital-acquired infections (HAIs) requires the highest methodological standards to minimize the risk of bias and to avoid misleading interpretation. There are two major issues related specifically to studies in this area, namely the timing of infection and the occurrence of so-called competing risks, which deserve special attention. Just as a patient who acquires a serious infection during hospital admission needs appropriate antibiotic treatment, data being collected in studies on hospital-acquired infections need appropriate statistical analysis. We illustrate the urgent need for appropriate statistical treatment of hospital-acquired infections with some examples from recently conducted studies.The considerations presented are relevant for investigations on risk factors for HAIs as well as for outcome studies.

Dropout in crossover and longitudinal studies: Is complete case so bad?

We discuss inference for longitudinal clinical trials subject to possibly informative dropout. A selection of available methods is reviewed for the simple case of trials with two timepoints. Using data from two such clinical trials, each with two treatments, we demonstrate that different analysis methods can at times lead to quite different conclusions from the same data. We investigate properties of complete-case estimators for the type of trials considered, with emphasis on interpretation and meaning of parameters. We contrast longitudinal and crossover designs and argue that for crossover studies there are often good reasons to prefer a complete case analysis. More generally, we suggest that there is merit in an approach in which no untestable assumptions are made. Such an approach would combine a dropout analysis, an analysis of complete-case data only, and a careful statement of justified conclusions.