Kidney Failure and the Federal Government (1991) / Chapter Skim
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Appendix D: Survival Analysis Methods for the End-Stage Renal Disease (ESRD) Program of Medicare
Appendix D: Survival Analysis Methods for the End-Stage Renal Disease (ESRD) Program of Medicare
Pages 353-400
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From page 353... ...
The first focus is a critical review of methods of survival analysis for Medicare ESRD data, including methods used in the past by HCFA and the USRDS, methods that have been proposed by other members of the renal community, and methods that are potentially useful for future analyses. The second focus is a review of the results of international comparisons of mortality rates with the objective of determining what conclusions can be drawn from such comparisons.
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From page 354... ...
Interpretation of the results of mortality analyses is complicated by the variety of analytical methods and types of numerical summaries that can be reported. Analytical methods include adjusted and unadjusted results, cross-tabulations and multiple regression models, parametric and nonparametric methods, Cox models and logistic regression models, and other methods discussed below.
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From page 355... ...
GENERAL ISSUES IN SURVIVAL ANALYSIS Overview Survival analysis of ESRD patient data can help to identify factors, such as etiology, that are related to differences in patient mortality. For example, a comparison of the one-year survival proportions for diabetic and nondiabetic patients shows that mortality rates differ by etiology.
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From page 356... ...
Identification of the Study Population What is the death rate among ESRD patients? The death rate among untreated ESRD patients is very high; with no kidney function, they will surely die within days.
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From page 357... ...
Different definitions distinguishing between reduced kidney function and ESRD could also have a substantial effect on reported death rates among the ESRD population. Thus, any evaluation of mortality rates among ESRD patients must identify which patient population is being considered.
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From page 358... ...
, then the high death rate among diabetic ESRD patients and the higher prevalence of diabetes among CAPD patients would cause unadjusted death rates to be higher among CAPD patients than among CH patients. Comparison of crude (unadjusted for patient characteristics)
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From page 359... ...
Interpreting Standard Errors for Population Data When there is no sampling error because a statistic is reported for all ESRD patients, how should the standard error be interpreted? The standard error does not reflect uncertainty about the specific population being described, since the statistic precisely summarizes the experience of the whole population.
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From page 360... ...
D.22) indicates that, even in two stable populations with identical death rates, a difference in survival proportions bigger than 4.3 percent would be likely to occur frequently just by chance.
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From page 361... ...
Analysis of Provider Versus Patient Suppose that the annual death rate is 15 percent at institution A and 25 percent at institution B that the difference is significant (P <.001)
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From page 362... ...
Another, less important, cause of the apparent discrepancy can be illustrated by the analogies of death rates to compound interest rates and of death proportions to simple interest rates. The proportion of individuals, P
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From page 363... ...
Extrapolations and projections of trends are very susceptible to error. Accuracy of Counts The counts of incident ESRD patients reported by the USRDS for 1987 (USRDS, 1989, pp.
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From page 364... ...
Patient Characteristics Related to Mortality Several patient characteristics that are, or might be, related to mortality rates among ESRD patients are discussed below. For many of these characteristics, there are difficulties in the appropriate interpretation of their effects on mortality, and these issues are briefly discussed.
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From page 365... ...
Unfortunately, treatment patterns as well as patient characteristics have changed over the years, and both could affect patient outcomes. Some of the changes, such as the availability of transplantation therapy and the aging of the treated ESRD patient population, are documented in the data and can be adjusted for through statistical analysis.
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From page 366... ...
However, there are likely to be other patient characteristics that have changed over the years that are also associated with mortality but which have not been recorded in the Medicare data base. If such characteristics are not recorded in the data base and accounted for in statistical analyses, then their effects would appear as an unexplained general trend in mortality rates over the years.
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From page 367... ...
Current year of therapy is relevant because it is likely to reflect national norms of treatment practice. Race For dialyzed patients, mortality rates are generally lower among black ESRD patients than among white ESRD patients for a given age and diagnosis.
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From page 368... ...
Medical History The medical histories of ESRD patients may have a substantial effect on their subsequent mortality rates. The important aspects of medical histories are only partially measured by the etiology of ESRD; they also include medical events and health practices for which there are little data in the Medicare data base.
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From page 369... ...
For example, the frequency of hospitalization prior to the start of a therapy is a measure of the morbidity experienced by the patient and should be adjusted for, if possible, when comparing therapies because it is likely related to subsequent mortality rates. In contrast, the frequency of hospitalization after the start of therapy may well be a result of the inadequacy of the therapy and should itself be analyzed as a patient outcome, but not as a predictor of patient outcomes.
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From page 370... ...
If the data are available at the provider level, including them in the national data base or in a sample from it may not be difficult or expensive. Multivariable Methods The examples in the previous sections of this paper have shown that it is important to adjust for differences in patient characteristics when comparing patient survival for several treatment groups of ESRD patients.
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From page 371... ...
Modeling is based on the principal of "synthesize and approximate." A statistical model approximates the relationship between patient outcomes and patient characteristics using an equation. Since outcomes vary from patient to patient, individual patient outcomes cannot be predicted precisely with an equation.
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From page 372... ...
Modeling In survival analysis, a model is an equation that relates the numerical values of a set of patient characteristics to the numerical value of a summary mortality measure for the corresponding group of patients. A hypothetical model for death rates, htt)
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From page 373... ...
Then the estimated annual death rates for black patients and white patients of age 60 are 0.230 i= exp (-1.95 + 0.008 · 60 + 01]
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From page 374... ...
Definitions of patient characteristics cannot be based on the future events for the patients. At any time, the death rates for a group can be modeled in terms of the complete history of the group up to that time, but should not be allowed to depend upon future events.
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From page 375... ...
Note that the comparison groups are defined in terms of what has already taken place. It is inappropriate to compare mortality rates among patients who do not switch treatment modalities in the future to rates among patients who do switch sometime in the future.
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From page 376... ...
For example, regression coefficients in a statistical model can summarize the relationship between death rates and patient characteristics. In addition to parameters that characterize the pattern of mortality in a single population, other parameters measure the difference in mortality for two populations.
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From page 377... ...
In order to compare death proportions based on different types of time intervals, it is sometimes possible to compute death rates that correspond to each of the proportions and then to compare the death rates to each other. Death Rates The death rate is approximately equal to the fraction dying during an interval of time divided by the length of the interval.
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From page 378... ...
Continuing with the numerical values in the example, the cumulative hazard for death during a 6-month interval would be approximately 0.06, which can be computed as 0.01 6 if the calculations are based on months or as 0.12 · 0.5 if the calculations are based on years. The cumulative hazard is used to relate death rates to death proportions, as discussed below.
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From page 379... ...
An extension of the Kaplan-Meier estimator based on the Cox model (discussed below) can be used to estimate adjusted survival curves.
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From page 380... ...
Instead of reporting the individual mortality summaries for each of several groups, comparative statistics can be used to summarize just the sizes of the differences between the individual mortality summaries. Important examples include relative death rates (from a Cox or other proportional hazards regression model)
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From page 381... ...
All of these regression models allow multiple patient characteristics to be empirically related to mortality. Since the Cox model is the most widely used method of analysis for survival data and since it has many of the features of other methods, the interpretation of results from the Cox model is discussed in detail here.
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From page 382... ...
For example, in order to estimate the ratio of death rates for diabetic and nondiabetic patients who are of the same age, both diabetes and age would be included in the Cox model. The resulting coefficient for the diabetes variable estimates the log of the adjusted death rate ratio.
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From page 383... ...
Both yield estimates of relative death rates. The major difference between them is that Poisson regression models yield direct estimates of death rates whereas Cox models yield direct estimates of survival curves.
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From page 384... ...
The death rates calculated by this equation agree closely with the observed death rates shown in Table 1, although the agreement is far from perfect. The equation implies that the death rates among black ESRD patients increase by a factor of 1.0358 [=exp(0.035181]
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From page 385... ...
385 Poisson regression models are appropriate for estimating statistical models for death rates using data from a registry such as the USRDS. In its simplest form, this methodology is descriptive; moveover, it can yield estimates of the death rate for any specific combination of patient characteristics.
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From page 386... ...
However, instead of yielding estimates of death rates, as with the Poisson regression models, the Cox models yield estimates of relative death rates and of the survival function, i.e., the fraction surviving at various times since entry into study. The Cox model was designed primarily to estimate relative death rates.
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From page 387... ...
Moreover, it can be used to evaluate the effect of changing treatment modalities and other time-dependent factors, such as patient age, calendar year, and time since first ESRD therapy. The results of analysis include estimates of relative death rates and survival curves.
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From page 388... ...
Both yield summaries of overall mortality; the Poisson regression model yields estimates of death rates whereas the Cox model yields estimates of the survival function. The Poisson regression model requires that the data be grouped into relatively short periods of follow-up time, whereas the Cox model allows the followup interval for each patient to be arbitrarily long.
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From page 389... ...
The effect of year of current therapy on dialysis mortality rates can be estimated with either Poisson or Cox regression models. A unified analysis would account for the simultaneous effect on death rates of year of first therapy, year of current therapy, patient age, and other patient characterist~cs.
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From page 390... ...
However, the exponential model is known to be a poor approximator of the long-term survival pattern for people because death rates rise with age. Further, the death rate among ESRD patients tends to decrease with the number of years since first ESRD therapy.
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From page 391... ...
It is not as easy to use the Weibull model with time-varying patient characteristics as it is to use the Cox or Poisson regression models, because the standard statistical packages have not been extended to allow time-dependent covariates with the Weibull model. One danger in the use of this model, or any other parametric model, is that the model can be estimated on the basis of a short period of patient follow-up and then extrapolated to yield estimates of long-term survival.
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From page 392... ...
Further, a patient is potentially in each of several prevalent cohorts in such a classification. Analysis can be performed either with Poisson regression models or with a Cox model using time-dependent covariates or strata.
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From page 393... ...
The rates published in the USRDS Annual Data Report are currently limited to the prevalent cohort of ESRD patients at the start of 1988. If continued for successive years, these rates will be useful for comparing death rates in small study groups to the expected rates based on national data.
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From page 394... ...
For example, ESRD patients with an etiology of AIDS may have much higher mortality rates than do patients with other etiologies. However, therapy for ESRD may prove to be just as useful in extending the lifetime of ESRD AIDS patients relative to expected lifetimes among non-ESRD AIDS patients, as it is for diabetic ESRD patients relative to non-ESRD diabetic patients.
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From page 395... ...
Most of the limitations of international comparisons described below were recognized and acknowledged by Held report but are reviewed here in more detail. The results in the Held report are intriguing and give some indication that ESRD mortality rates are substantially lower in other nations than they are in the United States.
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From page 396... ...
However, death rates adjusted for age, race, sex, and primary diagnosis have been relatively stable during the same period (USRDS, 1990, Tables E.53, E.55, and E.571. Post hoc adjustments to international comparisons of mortality rates can also be made for known patient characteristics, such as age and etiology, but such adjustments are likely to be less accurate than would be a unified analysis of the combined data from several nations.
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From page 397... ...
Other recent analyses (Wolfe et al., 1990) have shown that the difference between the mortality rates of blacks and whites is most substantial for diabetic patients and hypertensive patients, indicating that the impact of these two etiologies can vary substantially across different groups of patients.
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From page 398... ...
Patient Follow-up Ascertainment of mortality status by the ESRD data system is largely complete because of the computer links to the Social Security System. Although patients with long-lived transplants may be temporarily lost to the Medicare data collection system, their deaths are recorded when they occur so that overall mortality rates can be accurately estimated.
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From page 399... ...
(19901. Further study of differential mortality rates in the populations of diabetics and hypertensives from various nations may also be useful.
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From page 400... ...
1990. Annual Data Report.
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