The weighted cumulative exposure method and its application to pharmacoepidemiology: A narrative review

PURPOSE

The weighted cumulative exposure (WCE) method has been used in a number of fields including pharmacoepidemiology where it can account for intensity, duration and timing of exposures on the risk of an outcome. The method uses a data driven approach with flexible cubic B-splines to assign weights to past doses and select an aetiologically appropriate time window. Predictions of risk are possible for common exposure patterns encountered in real-world studies. The purpose of this study was to describe applications of the WCE method to pharmacoepidemiology and assess the strengths and limitations of the method.

METHOD

A literature search was undertaken to find studies applying the WCE method to the study of medicines. Articles published in PubMed using the search term 'weighted cumulative exposure' and articles citing Sylvestre et al. (2009) in Google Scholar or Scopus up to March 2023 were subsequently reviewed. Articles were selected based on title and review of abstracts.

RESULTS

Seventeen clinical applications using the data-driven WCE method with flexible cubic splines were identified in the review. These included 3 case-control studies and 14 cohort studies, of which 12 were analysed with Cox proportional hazards models and 2 with logistic regression. Thirteen studies used time windows of 1 year or longer. Of 11 studies which compared conventional models with the WCE method, 10 (91%) studies found a better fit with WCE models while one had an equivalent fit. The freely available 'WCE' software package has facilitated the applications of the WCE method with flexible cubic splines.

CONCLUSIONS

The WCE method allows additional insights into the effect of cumulative exposure on outcomes, including the timing and intensity (dose) of the exposure on the risk. The flexibility of the method is particularly well suited to studies with long-term exposures that vary over time or where the current risk of an event is affected by how far the exposure is in the past, which is difficult to model with conventional definitions of exposure. Interpretation of the results can be more complex than for conventional models and would be facilitated by a standardised reporting framework.

Importance of accounting for timing of time-varying exposures in association studies: Hydrochlorothiazide and non-melanoma skin cancer

PURPOSE

Hydrochlorothiazide (HCTZ), a widely prescribed antihypertensive drug with photosensitising properties, has been linked with non-melanoma skin cancer (NMSC) risk. However, previous analyses did not fully explore if and how the impact of past HCTZ exposures accumulates with prolonged use and/or depends on time elapsed since exposures. Therefore, we used different models to more comprehensively assess how NMSC risk vary with HCTZ exposure, and explore how the results may depend on modeling strategies.

METHODS

We used different parametric models with alternative time-varying exposure metrics, and the flexible weighted cumulative exposure model (WCE) to estimate associations between HCTZ exposures and NMSC risk in a population-based cohort of HCTZ users over 65 years old, in the province of Ontario, Canada.

RESULTS

Among 3844 HCTZ users, 273 developed NMSC during up to 8 years of follow-up. In parametric models, based on all exposures, increased duration of past HCTZ use was associated with an increase of NMSC risk but cumulative dose showed no systematic association. Yet, WCE results suggested that only exposures taken 2.5-4 years in the past were associated with the current NMSC hazard. This finding led us to re-define the parametric models, which also confirmed that any HCTZ dose taken outside this time-window were not systematically associated with NMSC incidence.

CONCLUSIONS

Our analyses illustrate how flexible modeling may yield new insights into complex temporal relationships between a time-varying drug exposure and risks of adverse events. Duration and recency of antihypertensive agents exposures must be taken into account in evaluating risk and benefits.

Dopamine agonists and risk of lung cancer in patients with restless legs syndrome

PURPOSE

To examine the association between long-term use of dopamine agonists (DAs) and the risk of lung cancer in patients with restless legs syndrome (RLS).

METHODS

We conducted a retrospective cohort study using Optum Clinformatics® database. We included adults ≥40 years diagnosed with RLS during the study period (1/2006-12/2016). Follow-up started with the first RLS diagnosis and ended on the earliest of: incident diagnosis of lung cancer, end of enrollment in the database or end of the study period. The exposure of interest was cumulative duration of DAs use, measured in a time-varying manner. We constructed a multivariable Cox regression model to estimate HRs and 95% CIs for the association between lung cancer and cumulative durations of DA use, adjusting for potential confounding variables.

RESULTS

We identified 295 042 patients with a diagnosis of RLS. The mean age of the cohort was 62.9; 66.6% were women and 82.3% were white. The prevalence of any DA exposure was 40.3%. Compared to the reference group (no use and ≤1 year), the crude HRs for lung cancer were 1.16 (95% CI 0.99-1.36) and 1.14 (95% CI 0.86-1.51) for 1-3 years and >3 years of cumulative DA use, respectively. The adjusted HR for lung cancer was 1.05 (95% CI 0.88-1.25) for 1-3 years and 1.02 (95% CI 0.76-1.37) for >3 years of cumulative DA use, respectively.

CONCLUSIONS

At typical doses for the clinical management of RLS, long-term DA use was not associated with risk of lung cancer.

Comparison of cohort and nested case-control designs for estimating the effect of time-varying drug exposure on the risk of adverse event in the presence of ties

Cohort and nested case-control (NCC) designs are frequently used in pharmacoepidemiology to assess the associations of drug exposure that can vary over time with the risk of an adverse event. Although it is typically expected that estimates from NCC analyses are similar to those from the full cohort analysis, with moderate loss of precision, only few studies have actually compared their respective performance for estimating the effects of time-varying exposures (TVE). We used simulations to compare the properties of the resulting estimators of these designs for both time-invariant exposure and TVE. We varied exposure prevalence, proportion of subjects experiencing the event, hazard ratio, and control-to-case ratio and considered matching on confounders. Using both designs, we also estimated the real-world associations of time-invariant ever use of menopausal hormone therapy (MHT) at baseline and updated, time-varying MHT use with breast cancer incidence. In all simulated scenarios, the cohort-based estimates had small relative bias and greater precision than the NCC design. NCC estimates displayed bias to the null that decreased with a greater number of controls per case. This bias markedly increased with higher proportion of events. Bias was seen with Breslow's and Efron's approximations for handling tied event times but was greatly reduced with the exact method or when NCC analyses were matched on confounders. When analyzing the MHT-breast cancer association, differences between the two designs were consistent with simulated data. Once ties were taken correctly into account, NCC estimates were very similar to those of the full cohort analysis.

Time-varying exposure analysis of the relationship between sustained natural dentition and cognitive decline

AIM

Tooth loss and cognitive decline progress over time and influence each other. This study estimated the impact of sustaining natural dentition on cognitive function in U.S. adults, accounting for the fact that dental and cognitive statuses change over time.

MATERIALS AND METHODS

Data from adults aged ≥51 years who participated in five waves of the Health and Retirement Study from 2004 to 2016 (n = 10,953) were analysed. The impact of retaining some natural teeth from 2006 to 2012 on cognitive function score (0-27) and cognitive impairment (defined as having a cognitive function score of <12) in 2016 was evaluated using the doubly robust targeted maximum likelihood estimation method by considering both time-invariant and time-varying confounders, including cognitive function at baseline and during follow-up.

RESULTS

Respondents with some natural teeth between 2006 and 2012 had a 0.40 point (95% confidence interval [CI]: 0.10-0.71) higher cognitive function score and 3.27 percentage point (95% CI: 0.11-6.66) lower cognitive impairment prevalence in 2016 than those with complete tooth loss.

CONCLUSIONS

Considering past cognitive function assessed at multiple time points, sustained natural dentition was associated with better cognitive function.

Dynamic network connectivity influences the spread of a sub-lineage of porcine reproductive and respiratory syndrome virus

Swine production in the United States is characterized by dynamic farm contacts through animal movements; such movements shape the risk of disease occurrence on farms. Pig movements have been linked to the spread of a virulent porcine reproductive and respiratory syndrome virus (PRRSV), RFLP type 1-7-4, herein denoted as phylogenetic sub-lineage 1A [L1A]. This study aimed to quantify the contribution of pig movements to the risk of L1A occurrence on farms in the United States. Farms were defined as L1A-positive in a given 6-month period if at least one L1A sequence was recovered from the farm. Temporal network autocorrelation modelling was performed using data on animal movements and 1,761 PRRSV ORF5 sequences linked to 494 farms from a dense pig production area in the United States between 2014 and 2017. A farm's current and past exposure to L1A and other PRRSV variants was assessed through its primary and secondary contacts in the animal movement network. Primary and secondary contacts with an L1A-positive farm increased the likelihood of L1A occurrence on a farm by 19% (p = .04) and 23% (p = .03), respectively. While the risk posed by primary contacts with PRRS-positive farms is unsurprising, the observation that secondary contacts also increase the likelihood of infection is novel. Risk of L1A occurrence on a farm also increased by 3.0% (p = .01) for every additional outgoing shipment, possibly due to biosecurity breaches during loading and transporting pigs from the farm. Finally, use of vaccines or field virus inoculation on sow farms one year prior reduced the risk of L1A occurrence in downstream farms by 36% (p = .04), suggesting that control measures that reduce viral circulation and enhance immunological protection in sow farms have a carry-over effect on L1A occurrence in downstream farms. Therefore, coordinated disease management interventions between farms connected via animal movements may be more effective than individual farm-based interventions.

Statistical Analysis of Clinical COVID-19 Data: A Concise Overview of Lessons Learned, Common Errors and How to Avoid Them

By definition, in-hospital patient data are restricted to the time between hospital admission and discharge (alive or dead). For hospitalised cases of COVID-19, a number of events during hospitalization are of interest regarding the influence of risk factors on the likelihood of experiencing these events. The same is true for predicting times from hospital admission of COVID-19 patients to intensive care or from start of ventilation (invasive or non-invasive) to extubation. This logical restriction of the data to the period of hospitalisation is associated with a substantial risk that inappropriate methods are used for analysis. Here, we briefly discuss the most common types of bias which can occur when analysing in-hospital COVID-19 data.

Understanding Marginal Structural Models for Time-Varying Exposures: Pitfalls and Tips

Epidemiologists are increasingly encountering complex longitudinal data, in which exposures and their confounders vary during follow-up. When a prior exposure affects the confounders of the subsequent exposures, estimating the effects of the time-varying exposures requires special statistical techniques, possibly with structural (ie, counterfactual) models for targeted effects, even if all confounders are accurately measured. Among the methods used to estimate such effects, which can be cast as a marginal structural model in a straightforward way, one popular approach is inverse probability weighting. Despite the seemingly intuitive theory and easy-to-implement software, misunderstandings (or "pitfalls") remain. For example, one may mistakenly equate marginal structural models with inverse probability weighting, failing to distinguish a marginal structural model encoding the causal parameters of interest from a nuisance model for exposure probability, and thereby failing to separate the problems of variable selection and model specification for these distinct models. Assuming the causal parameters of interest are identified given the study design and measurements, we provide a step-by-step illustration of generalized computation of standardization (called the g-formula) and inverse probability weighting, as well as the specification of marginal structural models, particularly for time-varying exposures. We use a novel hypothetical example, which allows us access to typically hidden potential outcomes. This illustration provides steppingstones (or "tips") to understand more concretely the estimation of the effects of complex time-varying exposures.

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.

Methods for time-varying exposure related problems in pharmacoepidemiology: An overview

Purpose

Lack of control for time‐varying exposures can lead to substantial bias in estimates of treatment effects. The aim of this study is to provide an overview and guidance on some of the available methodologies used to address problems related to time‐varying exposure and confounding in pharmacoepidemiology and other observational studies. The methods are explored from a conceptual rather than an analytical perspective.

Methods

The methods described in this study have been identified exploring the literature concerning to the time‐varying exposure concept and basing the search on four fundamental pharmacoepidemiological problems, construction of treatment episodes, time‐varying confounders, cumulative exposure and latency, and treatment switching.

Results

A correct treatment episodes construction is fundamental to avoid bias in treatment effect estimates. Several methods exist to address time‐varying covariates, but the complexity of the most advanced approaches—eg, marginal structural models or structural nested failure time models—and the lack of user‐friendly statistical packages have prevented broader adoption of these methods. Consequently, simpler methods are most commonly used, including, for example, methods without any adjustment strategy and models with time‐varying covariates. The magnitude of exposure needs to be considered and properly modelled.

Conclusions

Further research on the application and implementation of the most complex methods is needed. Because different methods can lead to substantial differences in the treatment effect estimates, the application of several methods and comparison of the results is recommended. Treatment episodes estimation and exposure quantification are key parts in the estimation of treatment effects or associations of interest.

The importance of considering competing treatment affecting prognosis in the evaluation of therapy in trials: the example of renal transplantation in hemodialysis trials

Background

During the follow-up in a randomized controlled trial (RCT), participants may receive additional (non-randomly allocated) treatment that affects the outcome. Typically such additional treatment is not taken into account in evaluation of the results. Two pivotal trials of the effects of hemodiafiltration (HDF) versus hemodialysis (HD) on mortality in patients with end-stage renal disease reported differing results. We set out to evaluate to what extent methods to take other treatments (i.e. renal transplantation) into account may explain the difference in findings between RCTs. This is illustrated using a clinical example of two RCTs estimating the effect of HDF versus HD on mortality.

Methods

Using individual patient data from the Estudio de Supervivencia de Hemodiafiltración On-Line (ESHOL; n  =  902) and The Dutch CONvective TRAnsport STudy (CONTRAST; n  = 714) trials, five methods for estimating the effect of HDF versus HD on all-cause mortality were compared: intention-to-treat (ITT) analysis (i.e. not taking renal transplantation into account), per protocol exclusion (PP excl ; exclusion of patients who receive transplantation), PP cens (censoring patients at the time of transplantation), transplantation-adjusted (TA) analysis and an extension of the TA analysis (TA ext ) with additional adjustment for variables related to both the risk of receiving a transplant and the risk of an outcome (transplantation-outcome confounders). Cox proportional hazards models were applied.

Results

Unadjusted ITT analysis of all-cause mortality led to differing results between CONTRAST and ESHOL: hazard ratio (HR) 0.95 (95% CI 0.75-1.20) and HR 0.76 (95% CI 0.59-0.97), respectively; difference between 5 and 24% risk reductions. Similar differences between the two trials were observed for the other unadjusted analytical methods (PP cens, PP excl , TA) The HRs of HDF versus HD treatment became more similar after adding transplantation as a time-varying covariate and including transplantation-outcome confounders: HR 0.89 (95% CI 0.69-1.13) in CONTRAST and HR 0.80 (95% CI 0.62-1.02) in ESHOL.

Conclusions

The apparent differences in estimated treatment effects between two dialysis trials were to a large extent attributable to differences in applied methodology for taking renal transplantation into account in their final analyses. Our results exemplify the necessity of careful consideration of the treatment effect of interest when estimating the therapeutic effect in RCTs in which participants may receive additional treatments.

Mendelian randomization analysis of a time-varying exposure for binary disease outcomes using functional data analysis methods

A Mendelian randomization (MR) analysis is performed to analyze the causal effect of an exposure variable on a disease outcome in observational studies, by using genetic variants that affect the disease outcome only through the exposure variable. This method has recently gained popularity among epidemiologists given the success of genetic association studies. Many exposure variables of interest in epidemiological studies are time varying, for example, body mass index (BMI). Although longitudinal data have been collected in many cohort studies, current MR studies only use one measurement of a time-varying exposure variable, which cannot adequately capture the long-term time-varying information. We propose using the functional principal component analysis method to recover the underlying individual trajectory of the time-varying exposure from the sparsely and irregularly observed longitudinal data, and then conduct MR analysis using the recovered curves. We further propose two MR analysis methods. The first assumes a cumulative effect of the time-varying exposure variable on the disease risk, while the second assumes a time-varying genetic effect and employs functional regression models. We focus on statistical testing for a causal effect. Our simulation studies mimicking the real data show that the proposed functional data analysis based methods incorporating longitudinal data have substantial power gains compared to standard MR analysis using only one measurement. We used the Framingham Heart Study data to demonstrate the promising performance of the new methods as well as inconsistent results produced by the standard MR analysis that relies on a single measurement of the exposure at some arbitrary time point.

Quantifying risk over the life course - latency, age-related susceptibility, and other time-varying exposure metrics

Identification of the latency period and age-related susceptibility, if any, is an important aspect of assessing risks of environmental, nutritional, and occupational exposures. We consider estimation and inference for latency and age-related susceptibility in relative risk and excess risk models. We focus on likelihood-based methods for point and interval estimation of the latency period and age-related windows of susceptibility coupled with several commonly considered exposure metrics. The method is illustrated in a study of the timing of the effects of constituents of air pollution on mortality in the Nurses' Health Study. Copyright © 2016 John Wiley & Sons, Ltd.

Effect on child cognitive function of increasing household expenditure in Indonesia: application of a marginal structural model and simulation of a cash transfer programme

BACKGROUND

Parental investments in children are an important determinant of human capability formation. We investigated the causal effect of household expenditure on Indonesian children's cognitive function between 2000 and 2007. We also investigated the effect of change in mean cognitive function from a simulation of a hypothetical cash transfer intervention.

METHODS

A longitudinal analysis using data from the Indonesian Family Life Survey (IFLS) was conducted including 6136 children aged 7 to 14 years in 2000 and still alive in 2007. We used the inverse probability of treatment weighting of a marginal structural model to estimate the causal effect of household expenditure on children's cognitive function.

RESULTS

Cumulative household expenditure was positively associated with cognitive function z-score. From the marginal structural model, a 74534 rupiah/month (about US$9) increase in household expenditure resulted in a 0.03 increase in cognitive function z-score [β=0.32, 95% confidence interval (CI) 0.30-0.35] Based on our simulations, among children in the poorest households in 2000 an additional ≈ US$6-10 of cash transfer resulted in a 0.01 unit increase in cognitive function z-score, equivalent to about 6% increase from the mean z-score prior to cash transfer. In contrast, children in the poorest household in 2007 did not benefit from an additional ≈ US$10 cash transfer. We found no overall effect of cash transfers at the total population level.

CONCLUSIONS

Greater household expenditure had a small causal effect on children's cognitive function. Although cash transfer interventions had a positive effect for poor children, this effect was quite small. Multi-faceted interventions that combine nutrition, cash transfer, improved living conditions and women's education are required to benefit children's cognitive development in Indonesia.

Time-varying effect moderation using the structural nested mean model: estimation using inverse-weighted regression with residuals

This article considers the problem of examining time-varying causal effect moderation using observational, longitudinal data in which treatment, candidate moderators, and possible confounders are time varying. The structural nested mean model (SNMM) is used to specify the moderated time-varying causal effects of interest in a conditional mean model for a continuous response given time-varying treatments and moderators. We present an easy-to-use estimator of the SNMM that combines an existing regression-with-residuals (RR) approach with an inverse-probability-of-treatment weighting (IPTW) strategy. The RR approach has been shown to identify the moderated time-varying causal effects if the time-varying moderators are also the sole time-varying confounders. The proposed IPTW+RR approach provides estimators of the moderated time-varying causal effects in the SNMM in the presence of an additional, auxiliary set of known and measured time-varying confounders. We use a small simulation experiment to compare IPTW+RR versus the traditional regression approach and to compare small and large sample properties of asymptotic versus bootstrap estimators of the standard errors for the IPTW+RR approach. This article clarifies the distinction between time-varying moderators and time-varying confounders. We illustrate the methodology in a case study to assess if time-varying substance use moderates treatment effects on future substance use.

Estimating the effects of time-varying exposures in observational studies using Cox models with stabilized weights adjustment

PURPOSE

Assessing the safety and effectiveness of medical products with observational electronic medical record data is challenging when the treatment is time-varying. The objective of this paper is to develop a Cox model stratified by event times with stabilized weights (SWs) adjustment to examine the effect of time-varying treatment in observational studies.

METHODS

Time-varying SWs are calculated at unique event times and are used in a Cox model stratified by event times to estimate the effect of time-varying treatment. We applied this method in examining the effect of an antiplatelet agent, clopidogrel, on events, including bleeding, myocardial infarction, and death after a drug-eluting stent was implanted in coronary artery. Clopidogrel use may change over time on the basis of patients' behavior (e.g., non-adherence) and physicians' recommendations (e.g., end of duration of therapy). We also compared the results with those from a Cox model for counting processes adjusting for all covariates used in creating SWs.

RESULTS

We demonstrate that the (i) results from the stratified Cox model without SWs adjustment and the Cox model for counting processes without covariate adjustment are identical in analyzing the clopidogrel data; and (ii) the effects of clopidogrel on bleeding, myocardial infarction, and death are larger in the stratified Cox model with SWs adjustment compared with those from the Cox model for counting processes with covariate adjustment.

CONCLUSIONS

The Cox model stratified by event times with time-varying SWs adjustment is useful in estimating the effect of time-varying treatments in observational studies while balancing for known confounders.