Selecting the Optimal Transformation of a Continuous Covariate in Cox's Regression: Implications for Hypothesis Testing

Negative binomial mixed models for analyzing longitudinal CD4 count data

It is of great interest for a biomedical analyst or an investigator to correctly model the CD4 cell count or disease biomarkers of a patient in the presence of covariates or factors determining the disease progression over time. The Poisson mixed-effects models (PMM) can be an appropriate choice for repeated count data. However, this model is not realistic because of the restriction that the mean and variance are equal. Therefore, the PMM is replaced by the negative binomial mixed-effects model (NBMM). The later model effectively manages the over-dispersion of the longitudinal data. We evaluate and compare the proposed models and their application to the number of CD4 cells of HIV-Infected patients recruited in the CAPRISA 002 Acute Infection Study. The results display that the NBMM has appropriate properties and outperforms the PMM in terms of handling over-dispersion of the data. Multiple imputation techniques are also used to handle missing values in the dataset to get valid inferences for parameter estimates. In addition, the results imply that the effect of baseline BMI, HAART initiation, baseline viral load, and the number of sexual partners were significantly associated with the patient's CD4 count in both fitted models. Comparison, discussion, and conclusion of the results of the fitted models complete the study.

Using flexible methods to determine risk factors for ventilator-associated pneumonia in the Netherlands

Seven hospitals participated in the Dutch national surveillance for ventilator-associated pneumonia (VAP) and its risk factors. We analysed time-independent and time-dependent risk factors for VAP using the standard Cox regression and the flexible Weighted Cumulative Effects method (WCE) that evaluates both current and past exposures. The prospective surveillance of intensive care patients aged ≥16 years and ventilated ≥48 hours resulted in the inclusion of 940 primary ventilation periods, comprising 7872 ventilation days. The average VAP incidence density was 10.3/1000 ventilation days. Independent risk factors were age (16–40 years at increased risk: HR 2.42 95% confidence interval 1.07–5.50), COPD (HR 0.19 [0.04–0.78]), current sedation score (higher scores at increased risk), current selective oropharyngeal decontamination (HR 0.19 [0.04–0.91]), jet nebulizer (WCE, decreased risk), intravenous antibiotics for selective decontamination of the digestive tract (ivSDD, WCE, decreased risk), and intravenous antibiotics not for SDD (WCE, decreased risk). The protective effect of ivSDD was afforded for 24 days with a delay of 3 days. For some time-dependent variables, the WCE model was preferable over standard Cox proportional hazard regression. The WCE method can furthermore increase insight into the active time frame and possible delay herein of a time-dependent risk factor.

Competing risks modeling of cumulative effects of time-varying drug exposures

An accurate assessment of drug safety or effectiveness in pharmaco-epidemiology requires defining an etiologically correct time-varying exposure model, which specifies how previous drug use affects the hazard of the event of interest. An additional challenge is to account for the multitude of mutually exclusive events that may be associated with the use of a given drug. To simultaneously address both challenges, we develop, and validate in simulations, a new approach that combines flexible modeling of the cumulative effects of time-varying exposures with competing risks methodology to separate the effects of the same drug exposure on different outcomes. To account for the dosage, duration and timing of past exposures, we rely on a spline-based weighted cumulative exposure modeling. We also propose likelihood ratio tests to test if the cumulative effects of past exposure on the hazards of the competing events are the same or different. Simulation results indicate that the estimated event-specific weight functions are reasonably accurate, and that the proposed tests have acceptable type I error rate and power. In real-life application, the proposed method indicated that recent use of antihypertensive drugs may reduce the risk of stroke but has no effect on the hazard of coronary heart disease events.

Using Multiple Pharmacovigilance Models Improves the Timeliness of Signal Detection in Simulated Prospective Surveillance

INTRODUCTION

Prospective pharmacovigilance aims to rapidly detect safety concerns related to medical products. The exposure model selected for pharmacovigilance impacts the timeliness of signal detection. However, in most real-life pharmacovigilance studies, little is known about which model correctly represents the association and there is no evidence to guide the selection of an exposure model. Different exposure models reflect different aspects of exposure history, and their relevance varies across studies. Therefore, one potential solution is to apply several alternative exposure models simultaneously, with each model assuming a different exposure-risk association, and then combine the model results.

METHODS

We simulated alternative clinically plausible associations between time-varying drug exposure and the hazard of an adverse event. Prospective surveillance was conducted on the simulated data by estimating parametric and semi-parametric exposure-risk models at multiple times during follow-up. For each model separately, and using combined evidence from different subsets of models, we compared the time to signal detection.

RESULTS

Timely detection across the simulated associations was obtained by fitting a set of pharmacovigilance models. This set included alternative parametric models that assumed different exposure-risk associations and flexible models that made no assumptions regarding the form/shape of the association. Times to detection generated using a simple combination of evidence from multiple models were comparable to those observed under the ideal, but unrealistic, scenario where pharmacovigilance relied on the single 'true' model used for data generation.

CONCLUSIONS

Simulation results indicate that, if the true model is not known, an association can be detected in a more timely manner by first fitting a carefully selected set of exposure-risk models and then generating a signal as soon as any of the models considered yields a test statistic value below a predetermined testing threshold.

Modeling exposure-lag-response associations with distributed lag non-linear models

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure-lag-response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others.

Flexible modeling improves assessment of prognostic value of C-reactive protein in advanced non-small cell lung cancer

Background:

C-reactive protein (CRP) is gaining credibility as a prognostic factor in different cancers. Cox's proportional hazard (PH) model is usually used to assess prognostic factors. However, this model imposes a priori assumptions, which are rarely tested, that (1) the hazard ratio associated with each prognostic factor remains constant across the follow-up (PH assumption) and (2) the relationship between a continuous predictor and the logarithm of the mortality hazard is linear (linearity assumption).

Methods:

We tested these two assumptions of the Cox's PH model for CRP, using a flexible statistical model, while adjusting for other known prognostic factors, in a cohort of 269 patients newly diagnosed with non-small cell lung cancer (NSCLC).

Results:

In the Cox's PH model, high CRP increased the risk of death (HR=1.11 per each doubling of CRP value, 95% CI: 1.03–1.20, P=0.008). However, both the PH assumption (P=0.033) and the linearity assumption (P=0.015) were rejected for CRP, measured at the initiation of chemotherapy, which kept its prognostic value for approximately 18 months.

Conclusion:

Our analysis shows that flexible modeling provides new insights regarding the value of CRP as a prognostic factor in NSCLC and that Cox's PH model underestimates early risks associated with high CRP.

Flexible modeling of the cumulative effects of time-dependent exposures on the hazard

Many epidemiological studies assess the effects of time-dependent exposures, where both the exposure status and its intensity vary over time. One example that attracts public attention concerns pharmacoepidemiological studies of the adverse effects of medications. The analysis of such studies poses challenges for modeling the impact of complex time-dependent drug exposure, especially given the uncertainty about the way effects cumulate over time and about the etiological relevance of doses taken in different time periods. We present a flexible method for modeling cumulative effects of time-varying exposures, weighted by recency, represented by time-dependent covariates in the Cox proportional hazards model. The function that assigns weights to doses taken in the past is estimated using cubic regression splines. We validated the method in simulations and applied it to re-assess the association between exposure to a psychotropic drug and fall-related injuries in the elderly.