Flexible Marginal Structural Models for Estimating the Cumulative Effect of a Time-Dependent Treatment on the Hazard: Reassessing the Cardiovascular Risks of Didanosine Treatment in the Swiss HIV Cohort Study

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.

Marginal structural models with latent class growth analysis of treatment trajectories: Statins for primary prevention among older adults

Latent class growth analysis is increasingly proposed as a solution to summarize the observed longitudinal treatment into a few distinct groups. When latent class growth analysis is combined with standard approaches like Cox proportional hazards models, confounding bias is not properly addressed because of time-varying covariates that have a double role of confounders and mediators. We propose to use latent class growth analysis to classify individuals into a few latent classes based on their medication adherence pattern, then choose a working marginal structural model that relates the outcome to these groups. The parameter of interest is defined as a projection of the true marginal structural model onto the chosen working model. Simulation studies are used to illustrate our approach and compare it with unadjusted, baseline covariates adjusted, time-varying covariates adjusted, and inverse probability of trajectory groups weighted adjusted models. Our proposed approach yielded estimators with little or no bias and appropriate coverage of confidence intervals in these simulations. We applied our latent class growth analysis and marginal structural model approach to a database comprising information on 52,790 individuals from the province of Quebec, Canada, aged more than 65 and who were statin initiators to estimate the effect of statin-usage trajectories on a first cardiovascular event.

Comparison of Different Modeling Approaches for Prescription Opioid Use and Its Association With Adverse Events

Previous research linking opioid prescribing to adverse drug events has failed to properly account for the time-varying nature of opioid exposure. This study aimed to explore how the risk of opioid-related emergency department visits, readmissions, or deaths (composite outcome) varies with opioid dose and duration, comparing different novel modeling techniques. A prospective cohort of 1,511 hospitalized patients discharged from 2 McGill-affiliated hospitals in Montreal, 2014-2016, was followed from the first postdischarge opioid dispensation until 1 year after discharge. Marginal structural Cox proportional hazards models and their flexible extensions were used to explore the association between time-varying opioid use and the composite outcome. Weighted cumulative exposure models assessed cumulative effects of past use and explored how its impact depends on the recency of exposure. The patient mean age was 69.6 (standard deviation = 14.9) years; 57.7% were male. In marginal structural model analyses, current opioid use was associated with a 71% increase in the hazard of opioid-related adverse events (adjusted hazard ratio = 1.71, 95% confidence interval: 1.21, 2.43). The weighted cumulative exposure results suggested that the risk cumulates over the previous 50 days of opioid consumption. Flexible modeling techniques helped assess how the risk of opioid-related adverse events may be associated with time-varying opioid exposures while accounting for nonlinear relationships and the recency of past use.

A competing risks regression model for the association between time-varying opioid exposure and risk of overdose

In the opioid research, predicting the risk of overdose or other adverse outcomes from opioid prescription patterns can help health professionals identify high-risk individuals. Challenges may arise in modeling the exposure-time-response association if the intensity, duration, and timing of exposure vary among subjects, and if exposures have a cumulative or latency effect on the risk. Further challenges may arise when the data involve competing risks, where subjects may fail from one of multiple events and failure from one precludes the risk of experiencing others. In this study, we proposed a competing risks regression model via subdistribution hazards to directly estimate the association between longitudinal patterns of opioid exposure and cumulative incidence of opioid overdose. The model incorporated weighted cumulative effects of the exposure and used penalized splines in the partial likelihood equation to estimate the weights flexibly. The proposed model is able to distinguish different opioid prescription patterns even though these patterns have the same overall intensity during the study period. Performance of the model was evaluated through simulation.

Evaluating Montréal's harm reduction interventions for people who inject drugs: protocol for observational study and cost-effectiveness analysis

INTRODUCTION

The main harm reduction interventions for people who inject drugs (PWID) are supervised injection facilities, needle and syringe programmes and opioid agonist treatment. Current evidence supporting their implementation and operation underestimates their usefulness by excluding skin, soft tissue and vascular infections (SSTVIs) and anoxic/toxicity-related brain injury from cost-effectiveness analyses (CEA). Our goal is to conduct a comprehensive CEA of harm reduction interventions in a setting with a large, dispersed, heterogeneous population of PWID, and include prevention of SSTVIs and anoxic/toxicity-related brain injury as measures of benefit in addition to HIV, hepatitis C and overdose morbidity and mortalities averted.

METHODS AND ANALYSIS

This protocol describes how we will develop an open, retrospective cohort of adult PWID living in Québec between 1 January 2009 and 31 December 2020 using administrative health record data. By complementing this data with non-linkable paramedic dispatch records, regional monthly needle and syringe dispensation counts and repeated cross-sectional biobehavioural surveys, we will estimate the hazards of occurrence and the impact of Montréal's harm reduction interventions on the incidence of drug-use-related injuries, infections and deaths. We will synthesise results from our empirical analyses with published evidence to simulate infections and injuries in a hypothetical population of PWID in Montréal under different intervention scenarios including current levels of use and scale-up, and assess the cost-effectiveness of each intervention from the public healthcare payer's perspective.

ETHICS AND DISSEMINATION

This study was approved by McGill University's Institutional Review Board (Study Number: A08-E53-19B). We will work with community partners to disseminate results to the public and scientific community via scientific conferences, a publicly accessible report, op-ed articles and open access peer-reviewed journals.

Impact of time-varying cumulative bevacizumab exposures on survival: re-analysis of data from randomized clinical trial in patients with metastatic colo-rectal cancer

Background

As cancer treatment, biotherapies can be as effective as chemotherapy while reducing the risk of secondary effects, so that they can be taken over longer periods than conventional chemotherapy. Thus, some trials aimed at assessing the benefit of maintaining biotherapies during chemotherapy-free intervals (CFI). For example, the recent PRODIGE9 trial assessed the effect of maintaining bevacizumab during CFI in metastatic colorectal cancer (mCRC) patients. However, its analysis was hindered by a small difference of exposure to the treatment between the randomized groups and by a large proportion of early drop outs, leading to a potentially unbalanced distribution of confounding factors among the trial completers. To address these limitations, we re-analyzed the PRODIGE9 data to assess the effects of different exposure metrics on all-cause mortality of patients with mCRC using methods originally developed for observational studies.

Methods

To account for the actual patterns of drug use by individual patients and for possible cumulative effects, we used five alternative time-varying exposure metrics: (i) cumulative dose, (ii) quantiles of the cumulative dose, (iii) standardized cumulative dose, (iv) Theoretical Blood Concentration (TBC), and (v) Weighted Cumulative Exposure (WCE). The last two metrics account for the timing of drug use. Treatment effects were estimated using adjusted Hazard Ratio from multivariable Cox proportional hazards models.

Results

After excluding 112 patients who died during the induction period, we analyzed data on 382 patients, among whom 320 (83.8%) died. All time-varying exposures improved substantially the model’s fit to data, relative to using only the time-invariant randomization group. All exposures indicated a protective effect for higher cumulative bevacizumab doses. The best-fitting WCE and TBC models accounted for both the cumulative effects and the different impact of doses taken at different times.

Conclusions

All time-varying analyses, regardless of the exposure metric used, consistently suggested protective effects of higher cumulative bevacizumab doses. However, the results may partly reflect the presence of a confusion bias. Complementing the main ITT analysis of maintenance trials with an analysis of potential cumulative effects of treatment actually taken can provide new insights, but the results must be interpreted with caution because they do not benefit from the randomization.

Trial registration

clinicaltrials.gov, NCT00952029. Registered 8 August 2009.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-020-01202-9.

Evaluating the intended and unintended consequences of opioid-prescribing interventions on primary care in British Columbia, Canada: protocol for a retrospective population-based cohort study

INTRODUCTION

Between 2015 and 2018, there were over 40 000 opioid-related overdose events and 4551 deaths among residents in British Columbia (BC). During this time the province mobilised a variety of policy levers to encourage physicians to expand access to opioid agonist treatment and the College of Physicians and Surgeons of British Columbia (CPSBC) released a practice standard establishing legally enforceable minimum thresholds of professional behaviour in the hopes of curtailing overdose events. Our goal is to conduct a comprehensive investigation of the intended and unintended consequences of these policy changes. Specifically, we aim to understand the effects of these measures on physician prescribing behaviours, identify physician characteristics associated with uptake of the new measures, and measure the effects of the policy changes on patients' access to quality primary care.

METHODS AND ANALYSIS

This is a population-level, retrospective cohort study of all BC primary care physicians who prescribed any opioid medication for opioid-use disorder or chronic non-cancer pain during the study period, and their patients. The study period is 1 January 2013-31 December 2018, with a 1-year wash-in period (1 January 2012-31 December 2012) to exclude patients who initiated long-term opioid treatment prior to our study period or whose pain type (ie, 'chronic non-cancer', 'acute', 'cancer or palliative', or 'other') cannot be confirmed. The project combines five administrative health datasets under the authority of the BC Ministry of Health, with the CPSBC's Physician Registry, BC Cancer Agency's Cancer Registry and Vital Statistics' Mortality data. We will create measures of prescribing concordance, access, continuity, and comprehensiveness to assess primary care delivery and quality at both the physician and patient level. We will use generalised estimating equations, interrupted time series, mixed effects models, and funnel plots to identify factors related to changes in prescribing and evaluate the impact of the changes to prescribing policies. Results will be reported using appropriate Enhancing the QUAlity and Transparency Of health Research guidelines (eg, STrengthening the Reporting of OBservational studies in Epidemiology).

ETHICS AND DISSEMINATION

This study has been approved by McGill University's Institutional Review Board (#A11-M55-19A), and the University of British Columbia's Research Ethics Board (#H19-03537). We will disseminate results via a combination of open access peer-reviewed journal publications, conferences, lay summaries and OpEds.

Modeling of cumulative effects of time-varying drug exposures on within-subject changes in a continuous outcome

An accurate assessment of the safety or effectiveness of drugs in pharmaco-epidemiological studies requires defining an etiologically correct time-varying exposure model, which specifies how previous drug use affects the outcome of interest. To address this issue, we develop, and validate in simulations, a new approach for flexible modeling of the cumulative effects of time-varying exposures on repeated measures of a continuous response variable, such as a quantitative surrogate outcome, or a biomarker. Specifically, we extend the linear mixed effects modeling to estimate how past and recent drug exposure affects the way individual values of the outcome change throughout the follow-up. To account for the dosage, duration and timing of past exposures, we rely on a flexible weighted cumulative exposure methodology to model the cumulative effects of past drug use, as the weighted sum of past doses. Weights, modeled with unpenalized cubic regression B-splines, reflect the relative importance of doses taken at different times in the past. In simulations, we evaluate the performance of the model under different assumptions concerning (i) the shape of the weight function, (ii) the sample size, (iii) the number of the longitudinal observations and (iv) the intra-individual variance. Results demonstrate the accuracy of our estimates of the weight function and of the between- and within-patients variances, and good correlation between the observed and predicted longitudinal changes in the outcome. We then apply the proposed method to re-assess the association between time-varying glucocorticoid exposure and weight gain in people living with rheumatoid arthritis.

Penalized estimation of complex, non-linear exposure-lag-response associations

We propose a novel approach for the flexible modeling of complex exposure-lag-response associations in time-to-event data, where multiple past exposures within a defined time window are cumulatively associated with the hazard. Our method allows for the estimation of a wide variety of effects, including potentially smooth and smoothly time-varying effects as well as cumulative effects with leads and lags, taking advantage of the inference methods that have recently been developed for generalized additive mixed models. We apply our method to data from a large observational study of intensive care patients in order to analyze the association of both the timing and the amount of artificial nutrition with the short term survival of critically ill patients. We evaluate the properties of the proposed method by performing extensive simulation studies and provide a systematic comparison with related approaches.

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.

Use of digoxin in atrial fibrillation: One step further in the mortality controversy from the AFFIRM study

BACKGROUND

Whether there is a causal association between digoxin and mortality among patients with atrial fibrillation (AF), with or without congestive heart failure (HF), has been controversial; in particular, two prior analyses of data from the Atrial Fibrillation Follow-up Investigation of Rhythm Management (AFFIRM) trial have yielded conflicting results. We sought to investigate how digoxin impacts mortality, in the full AFFIRM cohort and for various subgroups, by applying marginal structural modeling (MSM) to AFFIRM data.

METHODS

MSM is a newer statistical approach, which estimates causal association in the absence of randomization. MSM more effectively accounts for time-varying treatment and mitigates potential biases, in contrast to the two statistical approaches used in prior analyses of the AFFIRM data.

RESULTS

Among 4,060 patients in AFFIRM, 660 (16.3%) died during follow-up. Digoxin was associated with significantly higher mortality in the full cohort (estimated hazard ratio [HR] 1.33, 95% confidence interval [CI] 1.11-1.60, P  =  0.002) and in 3,121 patients without HF (HR 1.36, 95% CI 1.07-1.72, P  =  0.011). There was a trend toward higher mortality with digoxin in 939 patients with HF (HR 1.29, 95% CI 0.96-1.72, P  =  0.090). Associations were nonsignificant in 463 patients with HF and left ventricular ejection fraction (EF) ≥40% and in 155 patients with EF ≤30%.

CONCLUSIONS

Digoxin is associated with significantly increased mortality among AFFIRM patients collectively, as determined by MSM statistical methodology. However, the impact of digoxin among AFFIRM patients with coexisting HF is inconclusive.

Performance of the marginal structural cox model for estimating individual and joined effects of treatments given in combination

BACKGROUND

The Marginal Structural Cox Model (Cox-MSM), an alternative approach to handle time-dependent confounder, was introduced for survival analysis and applied to estimate the joint causal effect of two time-dependent nonrandomized treatments on survival among HIV-positive subjects. Nevertheless, Cox-MSM performance in the case of multiple treatments has not been fully explored under different degree of time-dependent confounding for treatments or in case of interaction between treatments. We aimed to evaluate and compare the performance of the marginal structural Cox model (Cox-MSM) to the standard Cox model in estimating the treatment effect in the case of multiple treatments under different scenarios of time-dependent confounding and when an interaction between treatment effects is present.

METHODS

We specified a Cox-MSM with two treatments including an interaction term for situations where an adverse event might be caused by two treatments taken simultaneously but not by each treatment taken alone. We simulated longitudinal data with two treatments and a time-dependent confounder affected by one or the two treatments. To fit the Cox-MSM, we used the inverse probability weighting method. We illustrated the method to evaluate the specific effect of protease inhibitors combined (or not) to other antiretroviral medications on the anal cancer risk in HIV-infected individuals, with CD4 cell count as time-dependent confounder.

RESULTS

Overall, Cox-MSM performed better than the standard Cox model. Furthermore, we showed that estimates were unbiased when an interaction term was included in the model.

CONCLUSION

Cox-MSM may be used for accurately estimating causal individual and joined treatment effects from a combination therapy in presence of time-dependent confounding provided that an interaction term is estimated.

Modeling the causal effect of treatment initiation time on survival: Application to HIV/TB co-infection

The timing of antiretroviral therapy (ART) initiation for HIV and tuberculosis (TB) co-infected patients needs to be considered carefully. CD4 cell count can be used to guide decision making about when to initiate ART. Evidence from recent randomized trials and observational studies generally supports early initiation but does not provide information about effects of initiation time on a continuous scale. In this article, we develop and apply a highly flexible structural proportional hazards model for characterizing the effect of treatment initiation time on a survival distribution. The model can be fitted using a weighted partial likelihood score function. Construction of both the score function and the weights must accommodate censoring of the treatment initiation time, the outcome, or both. The methods are applied to data on 4903 individuals with HIV/TB co-infection, derived from electronic health records in a large HIV care program in Kenya. We use a model formulation that flexibly captures the joint effects of ART initiation time and ART duration using natural cubic splines. The model is used to generate survival curves corresponding to specific treatment initiation times; and to identify optimal times for ART initiation for subgroups defined by CD4 count at time of TB diagnosis. Our findings potentially provide 'higher resolution' information about the relationship between ART timing and mortality, and about the differential effect of ART timing within CD4 subgroups.

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.

Adjustment for time-dependent unmeasured confounders in marginal structural Cox models using validation sample data

Large databases used in observational studies of drug safety often lack information on important confounders. The resulting unmeasured confounding bias may be avoided by using additional confounder information, frequently available in smaller clinical “validation samples”. Yet, no existing method that uses such validation samples is able to deal with unmeasured time-varying variables acting as both confounders and possible mediators of the treatment effect. We propose and compare alternative methods which control for confounders measured only in a validation sample within marginal structural Cox models. Each method corrects the time-varying inverse probability of treatment weights for all subject-by-time observations using either regression calibration of the propensity score, or multiple imputation of unmeasured confounders. Two proposed methods rely on martingale residuals from a Cox model that includes only confounders fully measured in the large database, to correct inverse probability of treatment weight for imputed values of unmeasured confounders. Simulation demonstrates that martingale residual-based methods systematically reduce confounding bias over naïve methods, with multiple imputation including the martingale residual yielding, on average, the best overall accuracy. We apply martingale residual-based imputation to re-assess the potential risk of drug-induced hypoglycemia in diabetic patients, where an important laboratory test is repeatedly measured only in a small sub-cohort.

Estimating inverse probability weights using super learner when weight-model specification is unknown in a marginal structural Cox model context

Correct specification of the inverse probability weighting (IPW) model is necessary for consistent inference from a marginal structural Cox model (MSCM). In practical applications, researchers are typically unaware of the true specification of the weight model. Nonetheless, IPWs are commonly estimated using parametric models, such as the main-effects logistic regression model. In practice, assumptions underlying such models may not hold and data-adaptive statistical learning methods may provide an alternative. Many candidate statistical learning approaches are available in the literature. However, the optimal approach for a given dataset is impossible to predict. Super learner (SL) has been proposed as a tool for selecting an optimal learner from a set of candidates using cross-validation. In this study, we evaluate the usefulness of a SL in estimating IPW in four different MSCM simulation scenarios, in which we varied the specification of the true weight model specification (linear and/or additive). Our simulations show that, in the presence of weight model misspecification, with a rich and diverse set of candidate algorithms, SL can generally offer a better alternative to the commonly used statistical learning approaches in terms of MSE as well as the coverage probabilities of the estimated effect in an MSCM. The findings from the simulation studies guided the application of the MSCM in a multiple sclerosis cohort from British Columbia, Canada (1995-2008), to estimate the impact of beta-interferon treatment in delaying disability progression. Copyright © 2017 John Wiley & Sons, Ltd.

Dynamic models for estimating the effect of HAART on CD4 in observational studies: Application to the Aquitaine Cohort and the Swiss HIV Cohort Study

Highly active antiretroviral therapy (HAART) has proved efficient in increasing CD4 counts in many randomized clinical trials. Because randomized trials have some limitations (e.g., short duration, highly selected subjects), it is interesting to assess the effect of treatments using observational studies. This is challenging because treatment is started preferentially in subjects with severe conditions. This general problem had been treated using Marginal Structural Models (MSM) relying on the counterfactual formulation. Another approach to causality is based on dynamical models. We present three discrete-time dynamic models based on linear increments models (LIM): the first one based on one difference equation for CD4 counts, the second with an equilibrium point, and the third based on a system of two difference equations, which allows jointly modeling CD4 counts and viral load. We also consider continuous-time models based on ordinary differential equations with non-linear mixed effects (ODE-NLME). These mechanistic models allow incorporating biological knowledge when available, which leads to increased statistical evidence for detecting treatment effect. Because inference in ODE-NLME is numerically challenging and requires specific methods and softwares, LIM are a valuable intermediary option in terms of consistency, precision, and complexity. We compare the different approaches in simulation and in illustration on the ANRS CO3 Aquitaine Cohort and the Swiss HIV Cohort Study.

Martingale residual-based method to control for confounders measured only in a validation sample in time-to-event analysis

Unmeasured confounding remains an important problem in observational studies, including pharmacoepidemiological studies of large administrative databases. Several recently developed methods utilize smaller validation samples, with information on additional confounders, to control for confounders unmeasured in the main, larger database. However, up-to-date applications of these methods to survival analyses seem to be limited to propensity score calibration, which relies on a strong surrogacy assumption. We propose a new method, specifically designed for time-to-event analyses, which uses martingale residuals, in addition to measured covariates, to enhance imputation of the unmeasured confounders in the main database. The method is applicable for analyses with both time-invariant data and time-varying exposure/confounders. In simulations, our method consistently eliminated bias because of unmeasured confounding, regardless of surrogacy violation and other relevant design parameters, and almost always yielded lower mean squared errors than other methods applicable for survival analyses, outperforming propensity score calibration in several scenarios. We apply the method to a real-life pharmacoepidemiological database study of the association between glucocorticoid therapy and risk of type II diabetes mellitus in patients with rheumatoid arthritis, with additional potential confounders available in an external validation sample. Compared with conventional analyses, which adjust only for confounders measured in the main database, our estimates suggest a considerably weaker association. Copyright © 2016 John Wiley & Sons, Ltd.

The missing cause approach to unmeasured confounding in pharmacoepidemiology

Unmeasured confounding is a major threat to the validity of pharmacoepidemiological studies of medication safety and effectiveness. We propose a new method for detecting and reducing the impact of unobserved confounding in large observational database studies. The method uses assumptions similar to the prescribing preference-based instrumental variable (IV) approach. Our method relies on the new 'missing cause' principle, according to which the impact of unmeasured confounding by (contra-)indication may be detected by assessing discrepancies between the following: (i) treatment actually received by individual patients and (ii) treatment that they would be expected to receive based on the observed data. Specifically, we use the treatment-by-discrepancy interaction to test for the presence of unmeasured confounding and correct the treatment effect estimate for the resulting bias. Under standard IV assumptions, we first proved that unmeasured confounding induces a spurious treatment-by-discrepancy interaction in risk difference models for binary outcomes and then simulated large pharmacoepidemiological studies with unmeasured confounding. In simulations, our estimates had four to six times smaller bias than conventional treatment effect estimates, adjusted only for measured confounders, and much smaller variance inflation than unbiased but very unstable IV estimates, resulting in uniformly lowest root mean square errors. The much lower variance of our estimates, relative to IV estimates, was also observed in an application comparing gastrointestinal safety of two classes of anti-inflammatory drugs. In conclusion, our missing cause-based method may complement other methods and enhance accuracy of analyses of large pharmacoepidemiological studies.

Effect of Cumulating Exposure to Abacavir on the Risk of Cardiovascular Disease Events in Patients From the Swiss HIV Cohort Study

BACKGROUND

Patients with HIV exposed to the antiretroviral drug abacavir may have an increased risk of cardiovascular disease (CVD). There is concern that this association arises because of a channeling bias. Even if exposure is a risk, it is not clear how that risk changes as exposure cumulates.

METHODS

We assess the effect of exposure to abacavir on the risk of CVD events in the Swiss HIV Cohort Study. We use a new marginal structural Cox model to estimate the effect of abacavir as a flexible function of past exposures while accounting for risk factors that potentially lie on a causal pathway between exposure to abacavir and CVD.

RESULTS

A total of 11,856 patients were followed for a median of 6.6 years; 365 patients had a CVD event (4.6 events per 1000 patient-years). In a conventional Cox model, recent--but not cumulative--exposure to abacavir increased the risk of a CVD event. In the new marginal structural Cox model, continued exposure to abacavir during the past 4 years increased the risk of a CVD event (hazard ratio = 2.06; 95% confidence interval: 1.43 to 2.98). The estimated function for the effect of past exposures suggests that exposure during the past 6-36 months caused the greatest increase in risk.

CONCLUSIONS

Abacavir increases the risk of a CVD event: the effect of exposure is not immediate, rather the risk increases as exposure cumulates over the past few years. This gradual increase in risk is not consistent with a rapidly acting mechanism, such as acute inflammation.

Semiparametric adjusted exposure-response curves

Exposure-response curves are central to understanding how continuous exposures relate to health outcomes. Common methods to plot such curves include the use of crude and adjusted regression, with the exposure specified using fractional polynomials or regression splines. These approaches are subject to important limitations. In this article, we illustrate the use of semiparametric marginally adjusted exposure-response curves obtained via inverse probability weighting. We explore the relation between interpregnancy interval and preterm birth in a cohort of over 720,000 live births in Quebec between 1989 and 2008. We include online supplementary material showing how mixed modeling routines in standard software packages can be used to implement the procedure, and how pointwise bootstrap confidence intervals can be obtained.