Surrogate markers for time-varying treatments and outcomes.

BACKGROUND: A surrogate marker is a variable commonly used in clinical trials to guide treatment decisions when the outcome of ultimate interest is not available. A good surrogate marker is one where the treatment effect on the surrogate is a strong predictor of the effect of treatment on the outcome. We review the situation when there is one treatment delivered at baseline, one surrogate measured at one later time point, and one ultimate outcome of interest and discuss new issues arising when variables are time-varying. METHODS: Most of the literature on surrogate markers has only considered simple settings with one treatment, one surrogate, and one outcome of interest at a fixed time point. However, more complicated time-varying settings are common in practice. In this article, we describe the unique challenges in two settings, time-varying treatments and time-varying surrogates, while relating the ideas back to the causal-effects and causal-association paradigms. CONCLUSION: In addition to discussing and extending popular notions of surrogacy to time-varying settings, we give examples illustrating that one can be misled by not taking into account time-varying information about the surrogate or treatment. We hope this article has provided some motivation for future work on estimation and inference in such settings.

Optimal restricted estimation for more efficient longitudinal causal inference.

Efficient semiparametric estimation of longitudinal causal effects is often analytically or computationally intractable. We propose a novel restricted estimation approach for increasing efficiency, which can be used with other techniques, is straightforward to implement, and requires no additional modeling assumptions.

Association of kidney disease outcomes with risk factors for CKD: findings from the Chronic Renal Insufficiency Cohort (CRIC) study.

BACKGROUND: Various indicators of progression of chronic kidney disease (CKD) have been used as outcomes in clinical research studies. The effect of using varying measures on the association of risk factors with CKD progression has not been well characterized. STUDY DESIGN: Prospective cohort study. SETTING & PARTICIPANTS: The Chronic Renal Insufficiency Cohort (CRIC) Study (N=3,939) enrolled men and women with mild to moderate CKD, 48% of whom had diabetes and 42% were self-reported black race. PREDICTORS: Age, race, sex, diabetes, baseline estimated glomerular filtration rate (eGFR), proteinuria, and other established CKD risk factors. OUTCOMES: Death, end-stage renal disease (ESRD), and eGFR events, including: (1) eGFR halving, (2) eGFR<15mL/min/1.73m(2), (3) eGFR halving and <15mL/min/1.73m(2), (4) eGFR decrease of 20mL/min/1.73m(2), (5) eGFR halving or decrease of 20mL/min/1.73m(2), and (6) eGFR decrease of 25% and change in CKD stage. RESULTS: Mean entry eGFR was 44.9mL/min/1.73m(2). Annual rates of death, ESRD, and eGFR halving were 2.5%, 4.0%, and 6.1%, respectively, during an average follow-up of 5.4 years. Associations between risk factors and ESRD and eGFR events were similar across different definitions. However, these associations were substantially different from those with death. HRs for ESRD, eGFR halving, and death in the highest compared to the lowest proteinuria category were 11.83 (95% CI, 8.40-16.65), 11.19 (95% CI, 8.53-14.68), and 1.47 (95% CI, 1.10-1.96), respectively. LIMITATIONS: Participants may not be representative of the entire CKD population. CONCLUSIONS: Using ESRD or eGFR events, but not death, in the definition of kidney disease outcomes is appropriate in follow-up studies to identify risk factors for CKD progression.

DNA methylation profile associated with rapid decline in kidney function: findings from the CRIC study.

BACKGROUND: Epigenetic mechanisms may be important in the progression of chronic kidney disease (CKD). METHODS: We studied the genome-wide DNA methylation pattern associated with rapid loss of kidney function using the Infinium HumanMethylation 450 K BeadChip in 40 Chronic Renal Insufficiency (CRIC) study participants (n = 3939) with the highest and lowest rates of decline in estimated glomerular filtration rate. RESULTS: The mean eGFR slope was 2.2 (1.4) and -5.1 (1.2) mL/min/1.73 m(2) in the stable kidney function group and the rapid progression group, respectively. CpG islands in NPHP4, IQSEC1 and TCF3 were hypermethylated to a larger extent in subjects with stable kidney function (P-values of 7.8E-05 to 9.5E-05). These genes are involved in pathways known to promote the epithelial to mesenchymal transition and renal fibrosis. Other CKD-related genes that were differentially methylated are NOS3, NFKBIL2, CLU, NFKBIB, TGFB3 and TGFBI, which are involved in oxidative stress and inflammatory pathways (P-values of 4.5E-03 to 0.046). Pathway analysis using Ingenuity Pathway Analysis showed that gene networks related to cell signaling, carbohydrate metabolism and human behavior are epigenetically regulated in CKD. CONCLUSIONS: Epigenetic modifications may be important in determining the rate of loss of kidney function in patients with established CKD.

Covariance adjustment on propensity parameters for continuous treatment in linear models.

Propensity scores are widely used to control for confounding when estimating the effect of a binary treatment in observational studies. They have been generalized to ordinal and continuous treatments in the recent literature. Following the definition of propensity function and its parameterizations (called the propensity parameter in this paper) proposed by Imai and van Dyk, we explore sufficient conditions for selecting propensity parameters to control for confounding for continuous treatments in the context of regression-based adjustment in linear models. Typically, investigators make parametric assumptions about the form of the dose-response function for a continuous treatment. Such assumptions often allow the analyst to use only a subset of the propensity parameters to control confounding. When the treatment is the only predictor in the structural, that is, causal model, it is sufficient to adjust only for the propensity parameters that characterize the expectation of the treatment variable or its functional form. When the structural model includes selected baseline covariates other than the treatment variable, those baseline covariates, in addition to the propensity parameters, must also be adjusted in the model. We demonstrate these points with an example estimating the dose-response relationship for the effect of erythropoietin on hematocrit level in patients with end-stage renal disease.

Tom Ten Have's contributions to causal inference and biostatistics: review and future research directions.

Tom Ten Have made many contributions to causal inference and biostatistics before his untimely death. This paper reviews Tom's contributions and discusses potential related future research directions. We focus on Tom's contributions to longitudinal/repeated measures categorical data analysis and particularly his contributions to causal inference. Tom's work on causal inference was primarily in the areas of estimating the effect of receiving treatment in randomized trials with nonadherence and mediation analysis. A related area to mediation analysis he was working on at the time of his death was posttreatment effect modification with applications to designing adaptive treatment strategies.

Bias due to coarsening of time intervals in the inference for the effectiveness of colorectal cancer screening.

BACKGROUND: Observational studies are frequently used to estimate the comparative effectiveness of different colorectal cancer (CRC) screening methods due to the practical limitations and time needed to conduct large clinical trials. However, time-varying confounders, e.g. polyp detection in the last screening, can bias statistical results. Recently, generalized methods, or G-methods, have been used for the analysis of observational studies of CRC screening, given their ability to account for such time-varying confounders. Discretization, or the process of converting continuous functions into discrete counterparts, is required for G-methods when the treatment and outcomes are assessed at a continuous scale. DEVELOPMENT: This paper evaluates the interplay between time-varying confounding and discretization, which can induce bias in assessing screening effectiveness. We investigate this bias in evaluating the effect of different CRC screening methods that differ from each other in typical screening frequency. APPLICATION: First, using theory, we establish the direction of the bias. Then, we use simulations of hypothetical settings to study the bias magnitude for varying levels of discretization, frequency of screening and length of the study period. We develop a method to assess possible bias due to coarsening in simulated situations. CONCLUSIONS: The proposed method can inform future studies of screening effectiveness, especially for CRC, by determining the choice of interval lengths where data are discretized to minimize bias due to coarsening while balancing computational costs.

Exploring the effect of erythropoietin on mortality using USRDS data.

PURPOSE: Erythropoietin (EPO) improves measures of quality of life and reduces transfusions. Clinical trials have reported higher mortality associated with higher hemoglobin targets in varied clinical settings, making difficult the selection of erythropoiesis stimulation strategies in end-stage kidney disease. Observational studies distinguishing an effect of EPO from underlying conditions are challenging, but promise insights relevant to real-world settings. METHODS: Using data from the United States Renal Data System, we performed a retrospective cohort study of hemodialysis patients treated between 2000 and 2004. 409 364 Medicare insured patients receiving hemodialysis therapy as of January 2000 or who began dialysis after January 2000 and survived >6 months were studied. We examined the association of EPO dose in any given month with death over subsequent follow-up. RESULTS: Within each hematocrit group (<30%, 30%­< 33%, 33%­< 36%, 36%­< 39% and >39%), the hazard ratios comparing the 80th percentile to the median EPO dose were 0.88 (95% CI: [0.87­0.90]), 0.94 ([0.93­0.94]), 0.98 ([0.98­0.99]), 1.06 ([1.05­1.06]) and 1.08 ([1.07­1.09]), respectively. Within the highest hematocrit group, the association of a high EPO dose with elevated mortality was attenuated over time. Among patients with malignancy or indications of EPO resistance, the association of higher EPO dose with lower mortality was attenuated when hematocrit was low, while its association with higher mortality was stronger when hematocrit was high. CONCLUSIONS: These analyses demonstrate a complex relationship between EPO dosing and mortality, suggesting a possible beneficial effect among severely anemic hemodialysis patients, but possible harm when administered to individuals with higher hematocrit levels.

Estimating GFR among participants in the Chronic Renal Insufficiency Cohort (CRIC) Study.

BACKGROUND: Glomerular filtration rate (GFR) is considered the best measure of kidney function, but repeated assessment is not feasible in most research studies. STUDY DESIGN: Cross-sectional study of 1,433 participants in the Chronic Renal Insufficiency Cohort (CRIC) Study (ie, the GFR subcohort) to derive an internal GFR estimating equation using a split-sample approach. SETTING & PARTICIPANTS: Adults from 7 US metropolitan areas with mild to moderate chronic kidney disease; 48% had diabetes and 37% were black. INDEX TEST: CRIC GFR estimating equation. REFERENCE TEST OR OUTCOME: Urinary (125)I-iothalamate clearance testing (measured GFR [mGFR]). OTHER MEASUREMENTS: Laboratory measures, including serum creatinine and cystatin C, and anthropometrics. RESULTS: In the validation data set, the model that included serum creatinine level, serum cystatin C level, age, sex, and race was the most parsimonious and similarly predictive of mGFR compared with a model additionally including bioelectrical impedance analysis phase angle, CRIC clinical center, and 24-hour urinary creatinine excretion. Specifically, root mean square errors for the separate models were 0.207 versus 0.202, respectively. Performance of the CRIC GFR estimating equation was most accurate for the subgroups of younger participants, men, nonblacks, non-Hispanics, those without diabetes, those with body mass index <30 kg/m(2), those with higher 24-hour urine creatinine excretion, those with lower high-sensitivity C-reactive protein levels, and those with higher mGFRs. LIMITATIONS: Urinary clearance of (125)I-iothalamate is an imperfect measure of true GFR; cystatin C level is not standardized to certified reference material; lack of external validation; small sample sizes limit analyses of subgroup-specific predictors. CONCLUSIONS: The CRIC GFR estimating equation predicts mGFR accurately in the CRIC cohort using serum creatinine and cystatin C levels, age, sex, and race. Its performance was best in younger and healthier participants.

Carotid plaque, carotid intima-media thickness, and coronary calcification equally discriminate prevalent cardiovascular disease in kidney disease.

BACKGROUND: Despite the significant morbidity and mortality attributable to cardiovascular disease (CVD), risk stratification remains an important challenge in the chronic kidney disease (CKD) population. We examined the discriminative ability of noninvasive measures of atherosclerosis, including carotid intima-media thickness (cIMT), carotid plaque, coronary artery calcification (CAC) and ascending and descending thoracic aorta calcification (TCAC), and Framingham risk score (FRS) to predict self-reported prevalent CVD. METHODS AND RESULTS: Participants were enrolled in the cIMT ancillary study of the Chronic Renal Insufficiency Cohort (CRIC) study and also had all of the above measures within an 18-month period. CVD was present in 21% of study participants. C-statistics were used to ascertain the discriminatory power of each measure of atherosclerosis. The study population (n = 220) was 64% male; 51% black and 45% white. The proportion of individuals with estimated glomerular filtration rate ≥60, 45-59, 30-44, and <30 ml/min/1.73 m(2) was 21, 41, 28, and 11%, respectively. In multivariable analyses adjusting for demographic factors, we failed to find a difference between CAC, carotid plaque, and cIMT as predictors of self-reported prevalent CVD (C-statistic 0.70, 95% CI: 0.62-0.78; C-statistic 0.68, 95% CI: 0.60-0.75, and C-statistic 0.64, CI: 0.56-0.72, respectively). CAC was statistically better than FRS. FRS was the weakest discriminator of self-reported prevalent CVD (C-statistic 0.58). CONCLUSIONS: There was a significant burden of atherosclerosis among individuals with CKD, ascertained by several different imaging modalities. We were unable to find a difference in the ability of CAC, carotid plaque, and cIMT to predict self-reported prevalent CVD.

Urinary sodium is a potent correlate of proteinuria: lessons from the chronic renal insufficiency cohort study.

BACKGROUND: While higher blood pressure is known to increase proteinuria, whether increased dietary sodium as estimated from 24-hour urinary excretion correlates with increased proteinuria in patients with chronic kidney disease (CKD) is not well studied. METHODS: We measured 24-hour urinary sodium, potassium and protein excretion in 3,680 participants in the Chronic Renal Insufficiency Cohort study, to determine the relationship between urinary sodium and potassium and urinary protein excretion in patients with CKD. We stratified our data based on the presence or absence of diabetes given the absence of any data on this relationship and evidence that diabetics had greater urinary protein excretion at nearly every level of urinary sodium excretion. Multiple linear regressions were used with a stepwise inclusion of covariates such as systolic blood pressure, demographics, hemoglobin A1c and type of antihypertensive medications to evaluate the relationship between urinary electrolyte excretion and proteinuria. RESULTS: Our data demonstrated that urinary sodium (+1 SD above the mean), as a univariate variable, explained 12% of the variation in proteinuria (ß = 0.29, p < 0.0001), with rising urinary sodium excretion associated with increasing proteinuria. The significance of that relationship was only partially attenuated with adjustment for demographic and clinical factors and the addition of 24-hour urinary potassium to the model (ß = 0.13, R(2) = 0.35, p < 0.0001). CONCLUSIONS: An understanding of the relationship between these clinical factors and dietary sodium may allow a more tailored approach for dietary salt restriction in patients with CKD.

G-estimation and artificial censoring: problems, challenges, and applications.

In principle, G-estimation is an attractive approach for dealing with confounding by variables affected by treatment. It has rarely been applied for estimation of the effects of treatment on failure-time outcomes. Part of this is due to artificial censoring, an analytic device which considers some subjects who actually were observed to fail as if they were censored. Artificial censoring leads to a lack of smoothness in the estimating function, which can pose problems in variance estimation and in optimization. It also can lead to failure to have solutions to the usual estimating functions, which then raises questions about the appropriate criteria for optimization. To improve performance of the optimization procedures, we consider approaches for reducing the amount of artificial censoring, propose the substitution of smooth for indicator functions, and propose the use of estimating functions scaled to a measure of the information in the data; we evaluate performance of these approaches using simulation. We also consider appropriate optimization criteria in the presence of information loss due to artificial censoring. We motivate and illustrate our approaches using observational data on the effect of erythropoietin on mortality among subjects on hemodialysis.

Subtle issues in model specification and estimation of marginal structural models.

We review the concept of time-dependent confounding by using the example in paper "Comparative effectiveness of individual angiotensin receptor blockers on risk of mortality in patients with chronic heart failure" by Desai et al. and illustrate how to adjust for it by using inverse probability of treatment weighting through a simulated example. We discuss a few subtle issues that arise in specification of the model for treatment required to fit marginal structural models (MSMs) and in specification of the structural model for the outcome. We discuss the differences between the effects estimated in MSMs and intention-to-treat effects estimated in randomized trials, followed by an outline of some limitations of MSMs.

Effects of adjusting for instrumental variables on bias and precision of effect estimates.

Recent theoretical studies have shown that conditioning on an instrumental variable (IV), a variable that is associated with exposure but not associated with outcome except through exposure, can increase both bias and variance of exposure effect estimates. Although these findings have obvious implications in cases of known IVs, their meaning remains unclear in the more common scenario where investigators are uncertain whether a measured covariate meets the criteria for an IV or rather a confounder. The authors present results from two simulation studies designed to provide insight into the problem of conditioning on potential IVs in routine epidemiologic practice. The simulations explored the effects of conditioning on IVs, near-IVs (predictors of exposure that are weakly associated with outcome), and confounders on the bias and variance of a binary exposure effect estimate. The results indicate that effect estimates which are conditional on a perfect IV or near-IV may have larger bias and variance than the unconditional estimate. However, in most scenarios considered, the increases in error due to conditioning were small compared with the total estimation error. In these cases, minimizing unmeasured confounding should be the priority when selecting variables for adjustment, even at the risk of conditioning on IVs.

CAUSAL INFERENCE FOR CONTINUOUS-TIME PROCESSES WHEN COVARIATES ARE OBSERVED ONLY AT DISCRETE TIMES.

Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumptions that guarantee the consistency of discrete-time g-estimation. In more general cases, when those assumptions are violated, we propose a controlling-the-future method that performs at least as well as g-estimation in most scenarios and which provides consistent estimation in some cases where g-estimation is severely inconsistent. We apply the methods discussed in this paper to simulated data, as well as to a data set collected following a massive flood in Bangladesh, estimating the effect of diarrhea on children's height. Results from different methods are compared in both simulation and the real application.

HLA-A amino acid polymorphism and delayed kidney allograft function.

Delayed allograft function (DGF) is a common adverse event in postrenal transplantation. The etiology of DGF is thought to include both nonimmunologic (donor age, cold ischemia time, and recipient race) and immunologic factors. We examined the association of DGF with amino acid mismatches at 66 variable sites of the HLA-A molecule in a prospective cohort study of 697 renal transplant recipients of deceased donors. Using a multivariate logistic regression model adjusted for nonimmunologic risk factors, we show that combinations of a few amino acid mismatches at crucial sites of HLA-A molecules were associated with DGF. In Caucasian recipients, a mismatch at position 62, 95, or 163, all known to be functionally important within the antigen recognition site, was associated with an increased risk for DGF. Furthermore, a decreased risk for DGF was associated with a mismatch at HLA-A family-specific sites (149, 184, 193, or 246), indicating that evolutionary features of HLA-A polymorphism separating HLA-A families and lineages among donor-recipient pairs may correlate with the magnitude of alloreactivity influencing the development of DGF. These findings suggest that amino acid polymorphisms at functionally important positions at the antigen recognition site of the HLA-A molecule have a significant influence on DGF.

Visual Acuity Outcome over Time in Non-Infectious Uveitis.

Introduction: We evaluated visual acuity (VA) over 5 years in a subspecialty noninfectious uveitis population.Methods: Retrospective data from 5,530 noninfectious uveitis patients with anterior, intermediate, posterior or panuveitis were abstracted by expert reviewers. Mean VA was calculated using inverse probability of censoring weighting to account for losses to follow-up.Results: Patients were a median of 41 years old, 65% female, and 73% white. Initial mean VA was worse among panuveitis (20/84) than posterior (20/64), intermediate (20/47), and anterior (20/37) uveitides. On average, mean VA improved by 0.62, 0.51, 0.37, and 0.26 logMAR-equivalent lines over 2 years, respectively (each P < .001), then remained stable, except posterior uveitis mean VA worsened to initial levels.Conclusion: Mean VA of uveitic eyes improved and, typically, improvement was sustained under uveitis subspecialty care. Because VA tends to improve under tertiary care, mean VA change appears a better outcome for clinical studies than time-to-loss of VA.

Design and analysis of multiple events case-control studies.

In case-control research where there are multiple case groups, standard analyses fail to make use of all available information. Multiple events case-control (MECC) studies provide a new approach to sampling from a cohort and are useful when it is desired to study multiple types of events in the cohort. In this design, subjects in the cohort who develop any event of interest are sampled, as well as a fraction of the remaining subjects. We show that a simple case-control analysis of data arising from MECC studies is biased and develop three general estimating-equation-based approaches to analyzing data from these studies. We conduct simulation studies to compare the efficiency of the various MECC analyses with each other and with the corresponding conventional analyses. It is shown that the gain in efficiency by using the new design is substantial in many situations. We demonstrate the application of our approach to a nested case-control study of the effect of oral sodium phosphate use on chronic kidney injury with multiple case definitions.

Factors other than glomerular filtration rate affect serum cystatin C levels.

Cystatin C is an endogenous glomerular filtration marker hence its serum level is affected by the glomerular filtration rate (GFR). To study what other factors might affect it blood level we performed a cross-sectional analysis of 3418 patients which included a pooled dataset of clinical trial participants and a clinical population with chronic kidney disease. The serum cystatin C and creatinine levels were related to clinical and biochemical parameters and errors-in-variables models were used to account for errors in GFR measurements. The GFR was measured as the urinary clearance of 125I-iothalamate and 51Cr-EDTA. Cystatin C was determined at a single laboratory while creatinine was standardized to reference methods and these were 2.1+/-1.1 mg/dL and 1.8+/-0.8 mg/L, respectively. After adjustment for GFR, cystatin C was 4.3% lower for every 20 years of age, 9.2% lower for female gender but only 1.9% lower in blacks. Diabetes was associated with 8.5% higher levels of cystatin C and 3.9% lower levels of creatinine. Higher C-reactive protein and white blood cell count and lower serum albumin were associated with higher levels of cystatin C and lower levels of creatinine. Adjustment for age, gender and race had a greater effect on the association of factors with creatinine than cystatin C. Hence, we found that cystatin C is affected by factors other than GFR which should be considered when the GFR is estimated using serum levels of cystatin C.

Physician characteristics and knowledge of CKD management.

BACKGROUND: Many studies suggest that chronic kidney disease (CKD) care is suboptimal in the United States. However, it is not known whether knowledge of CKD management in primary care physicians (PCPs) might have an important role in the suboptimal care and whether PCP characteristics are associated with having adequate knowledge. STUDY DESIGN: Cross-sectional study. SETTING & PARTICIPANTS: Self-administered questionnaire sent to a random sample of 1,550 US PCPs in February 2007. PREDICTOR OR FACTOR: PCP characteristics, including age, sex, degree (MD versus DO), primary specialty, board certification, patient volume, percentage of time in patient care spent in the inpatient versus outpatient setting, and number of patients referred to nephrologists in a month. OUTCOMES & MEASUREMENTS: Regression analyses of the association between physician characteristics and overall physician knowledge of CKD management, as well as individual subdomains of CKD knowledge related to recognition of CKD and management of hypertension in the setting of CKD. RESULTS: 470 of 1,453 (32.4%) eligible PCPs returned a completed survey. PCPs show significant variation in their ability to recognize CKD stages 2 to 4, but most have appropriate blood pressure goals in patients with CKD and are knowledgeable of the role of angiotensin-converting enzyme inhibitors in managing proteinuria. For each 10-year increase in age, the odds of showing satisfactory knowledge of CKD management decreased by 26% (odds ratio, 0.74; 95% confidence interval, 0.60 to 0.92). PCPs with the primary specialty of internal medicine had a more than 3-fold greater odds of showing a satisfactory level of knowledge compared with family practice specialists (odds ratio, 3.40; 95% confidence interval, 2.17 to 5.32). LIMITATIONS: The study findings are limited by the potential presence of nonresponse bias, information bias, and results suggesting there are multiple knowledge subdomains that perhaps are not additive. CONCLUSION: There is need to improve CKD knowledge in PCPs, especially regarding recognition of CKD at an early stage.