Nonlinear and time-dependent effects of sparsely measured continuous time-varying covariates in time-to-event analysis

Temporal effect of imatinib adherence on time to remission in chronic myeloid leukemia patients

INTRODUCTION

Adherence to imatinib in chronic myeloid leukemia (CML) patients is estimated to be as low as 70% despite its clinical benefit, and our understanding of the impact of nonadherence in this population is limited. This study presents a novel application of the Alternating Conditional Estimation (ACE) algorithm in newly diagnosed CML patients to map the full dose-response curve (DRC) and determine how the strength of this curve varies over time.

METHODS

We applied the ACE algorithm alongside a backward elimination procedure to detect the presence of time dependence and nonlinearity in the relationship between imatinib adherence and time-to-remission. An extended Cox model allowing for the flexible modeling of identified effects via unpenalized B-splines was subsequently fit and assessed.

RESULTS

The substantial improvement in model fit associated with the extended Cox approach suggests that traditional Cox proportional hazards model assumptions do not hold in this setting. Results indicate that the DRC for imatinib is non-linearly increasing, with an attenuated effect above a 74% adherence rate. The strength of this effect on remission varied over time and was strongest in the initial months of treatment, reaching a peak around 90 days post-initiation (log hazard ratio: 2.12, 95% confidence interval: 1.47 to 2.66).

CONCLUSION

Most patients that achieved remission did so by 4 months (120 days) with consistently high adherence, suggesting that this could be a critical time and duration for realizing treatment benefit and patient monitoring. Findings regarding the relationship between adherence and remission can additionally help guide the design of future studies.

Adapting SIMEX to correct for bias due to interval-censored outcomes in survival analysis with time-varying exposure

Many clinical and epidemiological applications of survival analysis focus on interval-censored events that can be ascertained only at discrete times of clinic visits. This implies that the values of time-varying covariates are not correctly aligned with the true, unknown event times, inducing a bias in the estimated associations. To address this issue, we adapted the simulation-extrapolation (SIMEX) methodology, based on assessing how the estimates change with the artificially increased time between clinic visits. We propose diagnostics to choose the extrapolating function. In simulations, the SIMEX-corrected estimates reduced considerably the bias to the null and generally yielded a better bias/variance trade-off than conventional estimates. In a real-life pharmacoepidemiological application, the proposed method increased by 27% the excess hazard of the estimated association between a time-varying exposure, representing the 2-year cumulative duration of past use of a hypertensive medication, and the hazard of nonmelanoma skin cancer (interval-censored events). These simulation-based and real-life results suggest that the proposed SIMEX-based correction may help improve the accuracy of estimated associations between time-varying exposures and the hazard of interval-censored events in large cohort studies where the events are recorded only at relatively sparse times of clinic visits/assessments. However, these advantages may be less certain for smaller studies and/or weak associations.

Simulation extrapolation method for measurement error: A review

Measurement error is pervasive in statistics due to the non-availability of authentic data. The reasons for measurement error mainly relate to cost, convenience, and human error. Measurement error can result in non-negligible bias due to attenuated estimates, reduced power of statistical tests, and lower coverage probabilities of the coefficient estimators in a regression model. Several methods have been proposed to correct for measurement error, all of which can be grouped into two broad categories based on the underlying model-functional and structural. Functional models provide flexibility and robustness to estimators by placing minimal or no assumptions on the distribution of the mismeasured covariate or by treating them as a fixed entity, as opposed to a structural model which treats the underlying mismeasured covariates as random with a specified structure. The simulation extrapolation method is one method that is used for the partial correction of measurement error in both structural and functional models. Reviews of measurement error correction techniques are available in the literature. However, none of the previously conducted reviews has exclusively focused on simulation extrapolation and its application in continuous measurement error models, despite its widespread use and ease of application. We attempt to close this gap in the literature by highlighting its development over the past two and a half decades.

Using fractional polynomials and restricted cubic splines to model non-proportional hazards or time-varying covariate effects in the Cox regression model

The Cox proportional hazards model is used extensively in clinical and epidemiological research. A key assumption of this model is that of proportional hazards. A variable satisfies the proportional hazards assumption if the effect of that variable on the hazard function is constant over time. When the proportional hazards assumption is violated for a given variable, a common approach is to modify the model so that the regression coefficient associated with the given variable is assumed to be a linear function of time (or of log‐time), rather than being constant or fixed. However, this is an unnecessarily restrictive assumption. We describe two different methods to allow a regression coefficient, and thus the hazard ratio, in a Cox model to vary as a flexible function of time. These methods use either fractional polynomials or restricted cubic splines to model the log‐hazard ratio as a function of time. We illustrate the utility of these methods using data on 12 705 patients who presented to a hospital emergency department with a primary diagnosis of heart failure. We used a Cox model to assess the association between elevated cardiac troponin at presentation and the hazard of death after adjustment for an extensive set of covariates. SAS code for implementing the restricted cubic spline approach is provided, while an existing Stata function allows for the use of fractional polynomials.

Nurse staffing practices and adverse events in acute care hospitals: The research protocol of a multisite patient-level longitudinal study

Aims

We describe an innovative research protocol to: (a) examine patient‐level longitudinal associations between nurse staffing practices and the risk of adverse events in acute care hospitals and; (b) determine possible thresholds for safe nurse staffing.

Design

A dynamic cohort of adult medical, surgical and intensive care unit patients admitted to 16 hospitals in Quebec (Canada) between January 2015–December 2019.

Methods

Patients in the cohort will be followed from admission until 30‐day postdischarge to assess exposure to selected nurse staffing practices in relation to the subsequent occurrence of adverse events. Five staffing practices will be measured for each shift of an hospitalization episode, using electronic payroll data, with the following time‐varying indicators: (a) nursing worked hours per patient; (b) skill mix; (c) overtime use; (d) education mix and; and (e) experience. Four high‐impact adverse events, presumably associated with nurse staffing practices, will be measured from electronic health record data retrieved at the participating sites: (a) failure‐to‐rescue; (b) in‐hospital falls; (c) hospital‐acquired pneumonia and; and (d) venous thromboembolism. To examine the associations between the selected nurse staffing exposures and the risk of each adverse event, separate multivariable Cox proportional hazards frailty regression models will be fitted, while adjusting for patient, nursing unit and hospital characteristics, and for clustering. To assess for possible staffing thresholds, flexible non‐linear spline functions will be fitted. Funding for the study began in October 2019 and research ethics/institutional approval was granted in February 2020.

Discussion

To our knowledge, this study is the first multisite patient‐level longitudinal investigation of the associations between common nurse staffing practices and the risk of adverse events. It is hoped that our results will assist hospital managers in making the most effective use of the scarce nursing resources and in identifying staffing practices that minimize the occurrence of adverse events.