Estimating the distribution of lag in the effect of short-term exposures and interventions: adaptation of a non-parametric regression spline model

The Application of Lag Times in Cancer Pharmacoepidemiology: A Narrative Review

With the increasing utilization of medications worldwide, coupled with the increasing availability of long-term data, there is a growing opportunity and need for robust studies evaluating drug-cancer associations. One methodology of importance in such studies is the application of lag times. In this review, we discuss the main reasons for using lag times. Namely, we discuss the typically long latency period of cancer concerning both tumor promoter and initiator effects and outline why cancer latency is a key consideration when choosing a lag time. We also discuss how the use of lag times can help reduce protopathic and detection bias. Finally, we present practical advice for implementing lag periods. In general, we recommend that researchers consider the information that generated the hypothesis as well as clinical and biological knowledge to inform lag period selection. In addition, given that latency periods are usually unknown, we also advocate that researchers examine multiple lag periods in sensitivity analyses as well as duration analyses and flexible modeling approaches.

New-user and prevalent-user designs and the definition of study time origin in pharmacoepidemiology: A review of reporting practices

BACKGROUND

Guidance reports for observational comparative effectiveness and drug safety research recommend implementing a new-user design whenever possible, since it reduces the risk of selection bias in exposure effect estimation compared to a prevalent-user design. The uptake of this guidance has not been studied extensively.

METHODS

We reviewed 89 observational effectiveness and safety cohort studies published in six pharmacoepidemiological journals in 2018 and 2019. We developed an extraction tool to assess how frequently new-user and prevalent-user designs were reported to be implemented. For studies that implemented a new-user design in both treatment arms, we extracted information about the extent to which the moment of meeting eligibility criteria, treatment initiation, and start of follow-up were reported to be aligned.

RESULTS

Of the 89 studies included, 40% reported implementing a new-user design for both the study exposure arm and the comparator arm, while 13% reported implementing a prevalent-user design in both arms. The moment of meeting eligibility criteria, treatment initiation, and start of follow-up were reported to be aligned in both treatment arms in 53% of studies that reported implementing a new-user design. We provided examples of studies that minimized the risk of introducing bias due to unclear definition of time origin in unexposed participants, immortal time, or a time lag.

CONCLUSIONS

Almost half of the included studies reported implementing a new-user design. Implications of misalignment of study design origin were difficult to assess because it would require explicit reporting of the target estimand in original studies. We recommend that the choice for a particular study time origin is explicitly motivated to enable assessment of validity of the study.

Flexible Modeling of the Association Between Cumulative Exposure to Low-Dose Ionizing Radiation From Cardiac Procedures and Risk of Cancer in Adults With Congenital Heart Disease

Adults with congenital heart disease are increasingly being exposed to low-dose ionizing radiation (LDIR) from cardiac procedures. In a recent study, Cohen et al. (Circulation. 2018;137(13):1334-1345) reported an association between increased LDIR exposure and cancer incidence but did not explore temporal relationships. Yet, the impact of past exposures probably accumulates over years, and its strength may depend on the amount of time elapsed since exposure. Furthermore, LDIR procedures performed shortly before a cancer diagnosis may have been ordered because of early symptoms of cancer, raising concerns about reversal causality bias. To address these challenges, we combined flexible modeling of cumulative exposures with competing-risks methodology to estimate separate associations of time-varying LDIR exposure with cancer incidence and all-cause mortality. Among 24,833 patients from the Quebec Congenital Heart Disease Database, 602 had incident cancer and 500 died during a follow-up period of up to 15 years (1995-2010). Initial results suggested a strong association of cancer incidence with very recent LDIR exposures, likely reflecting reverse causality bias. When exposure was lagged by 2 years, an increased cumulative LDIR dose from the previous 2-6 years was associated with increased cancer incidence, with a stronger association for women. These results illustrate the importance of accurate modeling of temporal relationships between time-varying exposures and health outcomes.

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.

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.

Segmented relationships to model erosion of regression effect in Cox regression

In this article we propose a parsimonious parameterisation to model the so-called erosion of the covariate effect in the Cox model, namely a covariate effect approaching to zero as the follow-up time increases. The proposed parameterisation is based on the segmented relationship where proper constraints are set to accomodate for the erosion. Relevant hypothesis testing is discussed. The approach is illustrated on two historical datasets in the survival analysis literature, and some simulation studies are presented to show how the proposed framework leads to a test for a global effect with good power as compared with alternative procedures. Finally, possible generalisations are also presented for future research.

Generating survival times to simulate Cox proportional hazards models

Simulation studies present an important statistical tool to investigate the performance, properties and adequacy of statistical models in pre-specified situations. One of the most important statistical models in medical research is the proportional hazards model of Cox. In this paper, techniques to generate survival times for simulation studies regarding Cox proportional hazards models are presented. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived, which is useful in simulation studies. It is shown how the exponential, the Weibull and the Gompertz distribution can be applied to generate appropriate survival times for simulation studies. Additionally, the general relation between hazard and survival time can be used to develop own distributions for special situations and to handle flexibly parameterized proportional hazards models. The use of distributions other than the exponential distribution is indispensable to investigate the characteristics of the Cox proportional hazards model, especially in non-standard situations, where the partial likelihood depends on the baseline hazard. A simulation study investigating the effect of measurement errors in the German Uranium Miners Cohort Study is considered to illustrate the proposed simulation techniques and to emphasize the importance of a careful modelling of the baseline hazard in Cox models.