The HEMO Study was a fifteen-center randomized clinical trial of the effects of hemodialysis dose and membrane flux on mortality and morbidity in patients undergoing chronic dialysis
. Patients in this study were randomized to either standard or high dose (eKt/V of 1.05 vs. 1.45, respectively) and to either high or low flux membranes (beta-2 microglobulin clearance of <10 ml/min or >20 ml/min, respectively). Enrollment in the HEMO Study began in March 1995 and ended in October 2000 with a total of 1846 patients enrolled in the study. Patient eligibility criteria have been described previously
. The primary endpoint was all-cause mortality
. The Institutional Review Boards at the 15 institutions approved the study protocol and written informed consent was obtained from all study participants.
Demographic information and clinical history were collected through review of medical records and self-reported questionnaires. The race of the respondent was assessed by self-report and categorized as African-American or non-African American include those self-identified as white, Asian, Native American or ‘other’. Clinical data including laboratory measurements were obtained using standardized protocols. Comorbidity was assessed at baseline using the Index of Coexistent Disease (ICED) calculated without using the diabetes score
[6, 11, 12]. The ICED aggregates the presence and severity of 19 medical conditions and 11 physical impairments into 2 summary indices: the Index of Disease Severity (IDS) and the Index of Physical Impairment (IPI)
. Diabetes was defined using the ICED classification as present if the patient had been previously diagnosed with diabetes, had been prescribed a diabetic diet, was receiving insulin or oral hypoglycemic agents or had been previously admitted to the hospital for hyperglycemia or ketoacidosis.
Classification of cause-specific mortality in HEMO
The duration of follow-up monitoring ranged from 0.003 to 6.639 yr, depending on the time of randomization. The mean actual follow-up duration was 2.84 yr. The determination of cause-specific mortality in the HEMO Study has been previously described
[6, 7, 9]. Briefly, causes of deaths were independently reviewed by two clinicians blinded to the intervention assignments. The members assigned one primary and up to three secondary causes of death based on their clinical judgment from the narrative description of the death, hospital discharges, laboratories, and study data. When agreement could not be reached, the case was adjudicated by the full Outcome Review Committee. The cause-specific infectious, cardiac, and cardiovascular deaths were selected since these are the most common etiologies of death among hemodialysis patients. The four cardiac causes of death were: (1) Ischemic Heart Disease; (2) congestive heart failure; (3) arrhythmias, and (4) other heart diseases. The categorization of cardiovascular deaths included cardiac, cerebrovascular and vascular causes of death.
Covariates for all-cause and cause-specific mortality
In order to account for residual confounding on mortality we adjusted our survival analyses for the following baseline patient characteristics that have been found to be associated with the mortality of ESRD patients in previous studies. 1) Demographic: age, gender, race and body mass index (BMI) 2) Dialysis Related Factors: Duration of ESRD (also known as “vintage”), residual renal function (absent or present based on a residual urine output of less than 200 ml/day) and dialysis access. Dialysis access was defined as dialysis catheter vs. all other (Arteriovenous Fistula (AVF), grafts or other) 3) Laboratory tests: calcium (mg/dL), phosphorus (mg/dL), serum total cholesterol (mg/dl), and serum albumin (g/dl) 4) Comorbidity: ICED score (computed without the diabetes related questions). Since these data were collected in the setting of a randomized trial, we included treatment assignment as covariates (dialysis dose and membrane flux).
In this secondary analysis of the HEMO study data, baseline demographic, socioeconomic and laboratory variables were summarized as mean(standard deviation) for normally distributed continuous variables and as percentages for categorical variables. Skewed continuous variables were summarized using the median ± inter-quartile range. Differences in summary statistics were tested, 1) for the normally distributed variables using a two sided t-test 2) for skewed continuous variables using a rank sum test, and 3) for categorical variables using a chi-square test. To understand the relationship between outcome and the predictors of interest, both the Cox-TVC and Gray’s models were fit to the data. All-cause and cause-specific mortality analyses for cardiovascular, cardiac, and infectious diseases included the following variables in addition to the diabetes variables: age, race, BMI, years of dialysis, Kt/V, flux, dialysis access, ICED, systolic and diastolic blood pressure, smoking, calcium, phosphorus, and serum albumin.
Cox’s time dependent covariate
model. The Cox proportional hazards model depends on the assumption of a constant hazard over time. That means the hazard in the diabetic group is a constant proportion of the hazard in the non-diabetic group. If a time varying covariate is used in a Cox model then proportional hazard assumption violates. While this assumption holds in many different applications, the model can provide misleading results when the hazard function changes over time. To accommodate this possibility, the standard Cox proportional hazards regression model can be extended to fit a model with time varying covariates
[7, 9]. In Cox-TVC model the values of the covariate may vary over time. For example, diabetic status of an individual may vary over time whereas race is constant over time. We fit single predictor Cox-PH models for each of the variables considered for analysis and tested the proportional hazards assumption. For diabetes, a variable that does not satisfy the proportional hazards assumption, we created a time-varying covariate that included diabetes status by time. We assessed the influence of including other covariate by time interactions in the model and found that there was very little influence in the interpretation of the risk associated with diabetes. Therefore, the more parsimonious model using the diabetes status by time covariate was examined. The final multivariable Cox-TVC model was fit using a significance level of 0.15 as a cutoff for inclusion in the model, with the exception of the variables for study interventions and diastolic blood pressure.
Gray’s time varying coefficient
model. The use of time varying covariate in the Cox model involves the choice of complex functional form of the covariate and requires deep biologic insight. It also may lead to potential bias, and does not lead to prediction for the individual survival experience as does the usual Cox model with fixed covariate values
. The statistical formulation of Gray’s model is very similar to the Cox proportional hazards model with the hazard function being a more general version of the function used to fit Cox’s model. For Gray’s model, the regression coefficients differ across set time intervals allowing for the inclusion of non-proportional hazards and providing a better description of the change in risk over time. During each time interval, the rise is assumed to be constant; i.e., the proportionality of hazards is assumed to hold within but not between successive intervals. Assuming that the recorded survival times divided into c + 1 time intervals
where the last interval includes the largest observed time. Then the hazard function for the Gray’s model is given by
, for t lies between
. Based on Gray’s model, there will be
associated with each covariate. Gray’s model relies on a flexible spline model to include these changes over time, requiring the specification of the number of time intervals needed to fit the model. The model output then includes a regression coefficient for each of the time intervals, a test of the overall statistical significance of the regression coefficients, and a test of proportionality through a test of the equality of the coefficients over time. The models presented here have been fit using 10 time intervals, so that each interval contains approximately the same number of mortality events
. We examined both single predictor Gray’s models as well as models that included multiple predictors. As with the Cox regression models, we used a significance level of 0.15 as inclusion criteria for any variables considered for modeling. The statistical formulation and technical details for Gray’s model can be found in
[8, 9]. We used Stata 10 and R software for fitting the Cox-TVC model and Gray’s model respectively.