Optimal probability weights for estimating causal effects of time‐varying treatments with marginal structural Cox models

AbstractMarginal structural models (MSM) with inverse probability weighting (IPW) are used to estimate causal effects of time-varying treatments, but can result in erratic finite-sample performance when there is low overlap in covariate distributions across different treatment patterns. Modifications to IPW which target the average treatment effect (ATE) estimand either introduce bias or rely on unverifiable parametric assumptions and extrapolation. This paper extends an alternate estimand, the ATE on the overlap population (ATO) which is estimated on a sub-population with a reasonable probability of receiving alternate treatment patterns in time-varying treatment settings. To estimate the ATO within an MSM framework, this paper extends a stochastic pruning method based on the posterior predictive treatment assignment (PPTA) (Zigler, C. M., and M. Cefalu. 2017. “Posterior Predictive Treatment Assignment for Estimating Causal Effects with Limited Overlap.” eprint arXiv:1710.08749.) as well as a weighting analog (Li, F., K. L. Morgan, and A. M. Zaslavsky. 2018. “Balancing Covariates via Propensity Score Weighting.” Journal of the American Statistical Association 113: 390–400, https://doi.org/10.1080/01621459.2016.1260466.) to the time-varying treatment setting. Simulations demonstrate the performance of these extensions compared against IPW and stabilized weighting with regard to bias, efficiency, and coverage. Finally, an analysis using these methods is performed on Medicare beneficiaries residing across 18,480 ZIP codes in the U.S. to evaluate the effect of coal-fired power plant emissions exposure on ischemic heart disease (IHD) hospitalization, accounting for seasonal patterns that lead to change in treatment over time.

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Does biologic therapy impact the development of PsA among patients with psoriasis?

Annals of the Rheumatic Diseases ◽

10.1136/annrheumdis-2021-220761 ◽

2021 ◽

Vol 81 (1) ◽

pp. 80-86

Author(s):

Elana Meer ◽

Joseph F Merola ◽

Robert Fitzsimmons ◽

Thorvardur Jon Love ◽

Shiyu Wang ◽

...

Keyword(s):

Cohort Study ◽

Propensity Score ◽

Retrospective Cohort Study ◽

Retrospective Cohort ◽

Oral Therapy ◽

Biologic Therapy ◽

Therapy Group ◽

Time Varying ◽

Confounding By Indication ◽

Cox Models

ObjectiveTo examine the association of biologic therapy use for psoriasis with incident psoriatic arthritis (PsA) diagnosis.MethodsA retrospective cohort study was conducted in the OptumInsights Electronic Health Record Database between 2006 and 2017 among patients with psoriasis between the ages of 16 and 90 initiating a therapy for psoriasis (oral, biologic or phototherapy). The incidence of PsA was calculated within each therapy group. Multivariable Cox models were used to calculate the HR for biologic versus oral or phototherapy using biologics as a time-varying exposure and next in a propensity score-matched cohort.ResultsAmong 1 93 709 patients with psoriasis without PsA, 14 569 biologic and 20 321 cumulative oral therapy and phototherapy initiations were identified. Mean age was lower among biologic initiators compared with oral/phototherapy initiators (45.9 vs 49.8). The incidence of PsA regardless of therapy exposure was 9.75 per 1000 person-years compared with 77.26 among biologic users, 61.99 among oral therapy users, 26.11 among phototherapy users and 5.85 among those without a prescription for one of the target therapies. Using a multivariable adjustment approach with time-varying exposure, adjusted HR (95% CI) for biologic users was 4.48 (4.23 to 4.75) compared with oral or phototherapy users. After propensity score matching, the HR (95% CI) was 2.14 (2.00 to 2.28).ConclusionsIn this retrospective cohort study, biologic use was associated with the development of PsA among patients with psoriasis. This may be related to confounding by indication and protopathic bias. Prospective studies are needed to address this important question.

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Estimation of the causal effects of time-varying exposures

Chapman & Hall/CRC Handbooks of Modern Statistical Methods - Longitudinal Data Analysis ◽

10.1201/9781420011579.ch23 ◽

2008 ◽

pp. 553-599 ◽

Cited By ~ 48

Author(s):

James Robins ◽

Miguel Hernan

Keyword(s):

Causal Effects ◽

Time Varying

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A fast routine for fitting Cox models with time varying effects of the covariates

Computer Methods and Programs in Biomedicine ◽

10.1016/j.cmpb.2005.11.006 ◽

2006 ◽

Vol 81 (2) ◽

pp. 154-161 ◽

Cited By ~ 11

Author(s):

Aris Perperoglou ◽

Saskia le Cessie ◽

Hans C. van Houwelingen

Keyword(s):

Time Varying ◽

Cox Models

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Association of changes in circulating cell-free plasma DNA (cfDNA) and circulating tumor cells (CTC) during treatment with clinical outcome from olaparib in castration-resistant prostate cancer (CRPC): Exploratory analyses from the TOPARP-A trial.

Journal of Clinical Oncology ◽

10.1200/jco.2017.35.6_suppl.141 ◽

2017 ◽

Vol 35 (6_suppl) ◽

pp. 141-141 ◽

Cited By ~ 1

Author(s):

Joaquin Mateo ◽

Helen Mossop ◽

Jane Goodall ◽

David Lorente ◽

Nuria Porta ◽

...

Keyword(s):

Progression Free Survival ◽

P Value ◽

Time Varying ◽

Castration Resistant Prostate Cancer ◽

Plasma Dna ◽

Cox Models ◽

Castration Resistant ◽

Treatment Switch ◽

Response Biomarkers ◽

Time Varying Covariates

141 Background: Response biomarkers are needed to optimize treatment switch decisions in CRPC patients. CTC and cfDNA may have clinical utility as response biomarkers; we studied them during olaparib treatment in a phase II trial in CRCP (Mateo et al NEJM 2015). Methods: CTC were enumerated using CellSearch (Jannsen Diagnostics) and cfDNA was extracted with the QIASymphony circulating DNA kit (Qiagen) from blood samples taken at baseline, 4- and 8-weeks (wk) of therapy. Radiological progression-free survival (rPFS) was defined as time from starting treatment to progression by RECIST 1.1, bone scan (PCWG2) or death. Overall survival (OS) was defined as time from starting treatment to death. CTC changes were categorized based on conversion from ≥ 5 to < 5 CTC/7.5ml blood and on ≥ 30% decline (Lorente et al Eur Urol 2016). cfDNA changes were evaluated as percentage change from baseline (continuous and binary). The prognostic value of CTC and cfDNA changes were assessed by Landmark analysis and Cox models with time-varying covariates; p-value < 0.01 were considered significant to account for multiple tests. Results: Overall, 13/47 (28%) and 16/42 (38%) evaluable patients had a CTC conversion at 4- and 8-wk respectively. A CTC conversion after 4-wk of olaparib associated with longer rPFS (median 8.9 vs 2.7 months [m], p = 0.001); a similar association was found at 8-wk. A 30% CTC decline at 4-wk also associated with longer rPFS (median 4.4 vs 2.6 m, p = 0.004). CTC conversion as a time-varying covariate associated with longer OS (HR 0.26, 95%CI 0.14-0.50, p < 0.001). Median baseline cfDNA was 31.6 ng/ml (IQR 19.4-57.1); 46 and 42 patients were evaluable for cfDNA changes at 4- and 8-wk. Percentage changes in cfDNA at 4- and 8- wk associated with rPFS (HR 1.01 and 1.005; p = 0.005 and 0.002 respectively) but association with OS was not significant. cfDNA declines ≥ 50% at 8- wk associated with longer rPFS (median 8.9 vs 2.7 m, p = 0.007) and OS (17.0 vs 10.1 m, p = 0.004). Conclusions: Decreases in CTC counts and cfDNA concentration associate with improved outcome from olaparib (rPFS, OS) in the TOPARP-A trial. Clinical trial information: NCT01682772.

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An association between time-varying serum alkaline phosphatase concentrations and mortality rate in patients undergoing peritoneal dialysis: a five-year cohort study

Scientific Reports ◽

10.1038/srep43314 ◽

2017 ◽

Vol 7 (1) ◽

Cited By ~ 7

Author(s):

Ying Liu ◽

Jin-Gang Zhu ◽

Ben-Chung Cheng ◽

Shang-Chih Liao ◽

Chih-Hsiung Lee ◽

...

Keyword(s):

Cardiovascular Disease ◽

Alkaline Phosphatase ◽

Peritoneal Dialysis ◽

Serum Alkaline Phosphatase ◽

Urine Volume ◽

Time Dependent ◽

Time Varying ◽

Cox Models ◽

Death Risk ◽

The Relationship

Abstract The relationship between serum alkaline phosphatase (ALP) concentrations and mortality in peritoneal dialysis (PD) patients is rarely reported. We enrolled 667 PD patients in one PD centre in Taiwan to retrospectively examine the association between three ALP concentrations (baseline, time-averaged, time-dependent) and mortality over a 5-year period (2011–2015). Baseline data collection included demographics, clinical, and laboratory parameters. Multivariable-adjusted Cox models were used to analyse the association. Four ALP quartiles were defined at the baseline: ≤62, 63–82, 83–118, and ≥119 U/L. Of 667 patients, 65 patients died, of which 8 patients died due to cardiovascular disease. Females were predominant in the higher ALP quartiles, and 24-h urine volume was significantly proportionately decreased in the higher ALP quartiles. ALP quartiles expressed by the three models were not associated with all-cause or cardiovascular mortalities after adjusting for demographics, liver function, bone metabolism, mortality, hemoglobin, and 24-h urine volume. In conclusion, ALP concentrations were not associated with death risk in PD patients over the 5-year period.

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11. Identification and Estimation of Causal Effects with Time-Varying Treatments and Time-Varying Outcomes

Sociological Methodology ◽

10.1111/j.1467-9531.2007.00185.x ◽

2007 ◽

Vol 37 (1) ◽

pp. 393-434 ◽

Cited By ~ 19

Author(s):

Jennie E. Brand ◽

Yu Xie

Keyword(s):

Employment Status ◽

Causal Effect ◽

Causal Effects ◽

Potential Outcomes ◽

Time Varying ◽

Potential Outcome ◽

Units Of Analysis ◽

Wisconsin Longitudinal Study ◽

Time Periods ◽

Causal Variable

We develop an approach to identifying and estimating causal effects in longitudinal settings with time-varying treatments and time-varying outcomes. The classic potential outcome approach to causal inference generally involves two time periods: units of analysis are exposed to one of two possible values of the causal variable, treatment or control, at a given point in time, and values for an outcome are assessed some time subsequent to exposure. In this paper, we develop a potential outcome approach for longitudinal situations in which both exposure to treatment and the effects of treatment are time-varying. In this longitudinal setting, the research interest centers not on only two potential outcomes, but on a whole matrix of potential outcomes, requiring a complicated conceptualization of many potential counterfactuals. Motivated by sociological applications, we develop a simplification scheme—a weighted composite causal effect that allows identification and estimation of effects with a number of possible solutions. Our approach is illustrated via an analysis of the effects of disability on subsequent employment status using panel data from the Wisconsin Longitudinal Study.

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Causal inference under over-simplified longitudinal causal models

The International Journal of Biostatistics ◽

10.1515/ijb-2020-0081 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Lola Étiévant ◽

Vivian Viallon

Keyword(s):

Causal Inference ◽

Causal Effect ◽

Sufficient Conditions ◽

Repeated Measurements ◽

Causal Models ◽

Causal Effects ◽

Sensitivity Analyses ◽

Time Varying ◽

Weighted Averages

Abstract Many causal models of interest in epidemiology involve longitudinal exposures, confounders and mediators. However, repeated measurements are not always available or used in practice, leading analysts to overlook the time-varying nature of exposures and work under over-simplified causal models. Our objective is to assess whether – and how – causal effects identified under such misspecified causal models relates to true causal effects of interest. We derive sufficient conditions ensuring that the quantities estimated in practice under over-simplified causal models can be expressed as weighted averages of longitudinal causal effects of interest. Unsurprisingly, these sufficient conditions are very restrictive, and our results state that the quantities estimated in practice should be interpreted with caution in general, as they usually do not relate to any longitudinal causal effect of interest. Our simulations further illustrate that the bias between the quantities estimated in practice and the weighted averages of longitudinal causal effects of interest can be substantial. Overall, our results confirm the need for repeated measurements to conduct proper analyses and/or the development of sensitivity analyses when they are not available.

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Gformula: Estimating Causal Effects in the Presence of Time-Varying Confounding or Mediation using the G-Computation Formula

The Stata Journal Promoting communications on statistics and Stata ◽

10.1177/1536867x1201100401 ◽

2011 ◽

Vol 11 (4) ◽

pp. 479-517 ◽

Cited By ~ 61

Author(s):

Rhian M. Daniel ◽

Bianca L. De Stavola ◽

Simon N. Cousens

Keyword(s):

Indirect Effects ◽