Database

We used 1991–1999 Medicare claims data for control subjects from the Surveillance, Epidemiology, and End Results (SEER)-Medicare database.^{16} Control subjects were individuals in the annual 5% random sample of Medicare beneficiaries who lived in SEER program areas and had no cancers reported to the SEER program during the study years. Individuals in SEER areas are generally comparable to the U.S. population, though somewhat more urban and more likely to be foreign-born.^{17} Medicare claims were obtained from Medicare Provider Analysis and Review (MedPAR, Part A claims), Carrier Claims (physician/supplier Part B bills) and Outpatient Claims (institutional outpatient Part B bills). When this study began, the SEER program included 5 state registries (Connecticut, Hawaii, Iowa, New Mexico, and Utah) and 7 county-based registries (Atlanta, Detroit, rural Georgia, Los Angeles, San Francisco, San Jose, and Seattle/Puget Sound) in 4 other states. Medicare data include patient sociodemographic characteristics, enrollment dates, health maintenance organization (HMO) membership, date of death, if applicable, and, for fee-for-service beneficiaries, billed claims that include the diagnoses for care provided in hospitals, physician offices, and clinics.

Study Population

We randomly selected 50,000 individuals ages 66 or older and enrolled in Parts A and B fee-for-service Medicare for a full calendar year at any time between 1991 and 1999. All 50,000 individuals had at least 1 year of comorbidity data and were included in the study. Comorbidity was measured in subsequent calendar years if an individual had a full 12 months of enrollment in Parts A and B fee-for-service Medicare in that year. The sample sizes for each year varied depending on the availability of comorbidity data—from 31,058 to 37,227. Nearly 10% of the original sample of 50,000 contributed only 1 year of comorbidity data or had at least 1 year of missing data prior to death or the end of the study period. To ensure that our results represented a population with longitudinal data, we created a subsample in which each individual had at least 2 consecutive years of comorbidity data and no subsequent missing years of comorbidity data. This subsample contained 44,016 individuals.

Measurement of Comorbidity

The primary independent variable of interest in this study is comorbidity. The Romano adaptation of the Charlson weighted comorbidity index was used to calculate annual comorbidity scores for each year between 1991 and 1999 in which a study subject was enrolled for all 12 months in fee for service Medicare parts A and B.^{4} We chose the Charlson index because it is widely used by health services researchers, is available in the public domain, and permits calculation of rolling comorbidity scores.^{18} Baldwinet al. demonstrated that the Charlson index, Adjusted Clinical Groups (ACGs), and Diagnostic Cost Groups (DxCGs) were essentially equivalent in their ability to predict mortality and treatment type in colon cancer patients.^{19} The Charlson index consists of 19 comorbid conditions weighted according to the degree to which they predicted mortality among an inpatient cohort, then summed to produce an index score. These conditions included, in order of frequency during the middle year of the study (1995), diabetes (8.2%), chronic pulmonary disease (6.7%), congestive heart failure (6.0%), cerebrovascular disease (3.9%), peripheral vascular disease (3.7%), dementia (2.5%), diabetes with chronic complications (1.7%), prior myocardial infarction (1.5%), peptic ulcer (1.1%), connective tissue disease (1.1%), renal disease (0.9%), acute myocardial infarction (0.8%), hemiplegia or paraplegia (0.3%), mild liver disease (0.2%), moderate or severe liver disease (0.1%), and AIDS (0.03%). Romano adapted this index for use with administrative claims by identifying the ICD-9-CM codes corresponding to the measure’s comorbid conditions. The index has been further adapted to incorporate outpatient as well as inpatient-only diagnoses.^{3} Because we were using a non-cancer control population from the SEER-Medicare claims database, we excluded “any tumor,” “metastatic solid tumor,” “lymphoma,” and “leukemia” from the calculation of the Romano-Charlson index score as these likely represented rule out diagnoses or cancers diagnosed prior to living in a SEER registry area. A comorbid condition was identified if its corresponding ICD-9-CM codes appeared more than once in the Carrier (physician/supplier) and Outpatient claims at least 31 days apart, or appeared at least once in the MedPAR (inpatient) claims. Comorbidity rates calculated using this “rule-out” algorithm were more comparable to national estimates for selected conditions, and corresponded more closely with hospital record review than rates calculated without claims restrictions.^{20}

We calculated 2 Romano-Charlson annual comorbidity scores—one using only the claims data from the prior year, the other as a “rolling” comorbidity score in which chronic medical conditions (except peptic ulcer disease, counted as a comorbidity only in the years it was diagnosed) were considered ongoing once identified. In the rolling comorbidity definition, a patient with a diagnosis of diabetes in 1992 was considered to have this diabetes diagnosis in each ensuing year regardless of whether the diagnosis reappeared in the claims data. In this study, 33.7% of subjects had at least one rolling comorbidity score that differed from the standard prior year comorbidity scores.

General Modeling Approach

The study’s outcome of interest is all cause death. The day, month, and year of each individual’s death was available between January 1,1992, and December 31, 2000. We used Cox regression models with time to death through December 31, 2000 as the dependent variable to examine the influence of various comorbidity measures. Age, gender, and race/ethnicity were included as potential confounding variables. Age was treated as a time-dependent continuous variable. Race/ethnicity, available from Medicare files, was categorized as African American, Asian, Caucasian, Hispanic, or Other.

Modeling Longitudinal Comorbidity Measures

We developed 11 approaches to incorporating comorbidity as a covariate in our survival analysis. They include the following measures for a subject in year t:

- Baseline comorbidity: the time independent comorbidity score in the year prior to the first observation year.
- Prior year’s comorbidity: the time dependent comorbidity score in year (t−1).
- Prior year’s rolling comorbidity: the time dependent rolling comorbidity score in year (t−1).
- Baseline and prior year’s comorbidity: the time independent baseline comorbidity score and the time dependent comorbidity score in year (t−1).
- Baseline and prior year’s rolling comorbidity: the time independent baseline comorbidity score and the time dependent rolling comorbidity score in year (t−1).
In (A), all observation years for each subject can be included in the models because each subject had an initial year of comorbidity data. In (B) – (E), subjects’ observation years were dropped if their comorbidity measures were missing in the prior year due to lack of eligibility in fee for service parts A and B Medicare. In models (F) – (G), described below, missing data were imputed with the most recent available mean comorbidity score. In models (H) – (I), missing data were imputed using the most recent available comorbidity or rolling comorbidity scores using the last observation carry forward (LOCF) method. In models (J) – (K), missing data were imputed using the regression calibration (RC) imputation method.^{21} The RC method has been shown to perform well with missing data and measurement error if the relative hazard parameter for the missing covariate is not large^{22}^{,}^{23}, which is the case in our application. The RC estimator assumes that data are missing at random, namely that the missing data probability is a function of the observed data.

- Mean comorbidity: a time dependent function of the average of the available comorbidity scores before year t.
- Baseline and mean comorbidity: the baseline comorbidity score and the average of the available comorbidity scores before year t.
- Baseline and the most recent comorbidity: the baseline comorbidity score and the comorbidity score in most recent year for which a comorbidity score was available.
- Baseline and the most recent rolling comorbidity: the baseline comorbidity score and the rolling comorbidity score in the most recent year a comorbidity score was available.
- Baseline and prior year comorbidity with RC imputation: the baseline comorbidity score and the comorbidity score from the prior year, or, if prior year comorbidity score is missing, imputation of the missing prior year comorbidity score using its conditional expectation given observed covariates and the last observed comorbidity.
- Baseline and prior year rolling comorbidity with RC imputation: the baseline comorbidity score and the rolling comorbidity score from the prior year, or, if prior year rolling comorbidity score is missing, imputation of the missing prior year rolling comorbidity score using its conditional expectation given observed covariates and the last observed rolling comorbidity.

Relative Hazard Function

We developed the following **relative hazard** functions for modeling and comparing our longitudinal comorbidity measures. For subject *i* = 1, …, 50,000, let the longitudinal comorbidity be denoted by *S*_{i}(*t*). Let the first year of a subject *i* be denoted by *t*_{i0}, at which a subject is selected into the study cohort. More than 50% of the study subjects had 1991 as their first year. The baseline comorbidity for subject *i* is *S*_{i}(*t*_{i0}), which is available for the entire cohort of 50,000 subjects. Let *X*_{i} be the vector of age, gender and race/ethnicity for subject *i*. The Cox proportional hazards function consists of a baseline hazard function and a relative hazard function. When we visually examined the Kaplan-Meyer survival curves for different subgroups, there was no clear violation of the proportional hazards model assumption. However, given the very large study population, the assumption violation was statistically significant. To ensure that the proportional hazards model is used appropriately, we included interactions ofall the covariates with time in our models. For the 11 comorbidity modeling approaches above, their main difference is the relative hazard function. Model (A)’s simple model for the relative hazard function is

The second comorbidity model, (B), is based on the following relative hazard function:

The relative hazard function for model (C) is similar to (B) above, but with the comorbidity score at year (*t*−1) being replaced by the rolling comorbidity score at year (*t*−1). The relative hazard function for models (D) and (E) can be expressed similarly to (B) and (C) with the addition of baseline comorbidity. Some subjects may have missing comorbidity scores in certain years, and under (B) – (E), the relative hazard parameters are estimated based on available comorbidity scores only, with no imputation of data. The relative hazard functions for models (F) to (K) are variations on the above noted functions, though models (F) – **(G)** use mean rather than prior year comorbidity scores. For instance, the relative hazard function for model **(G)** can be written as

where

_{i}(

*t*−1) is the average of available comorbidity scores between years

*t*_{i0} and year (

*t*−1). An important difference between (B) to (E) versus (F) to (G) is that the former does not include year

*t* in the survival analysis if the comorbidity score at year (

*t*−

*1*) is not available, while the latter includes year t in the survival analysis even if some prior comorbidity scores in year (

*t*−

*1*) are missing by using the average of the available comorbidity scores before time

*t*.

We consider models (H) and (I) as modified approaches to models (D) and (E) by imputing missing data using the LOCF method. Similarly, models (J) and (K) are modified approaches to models (D) and (E) by imputing missing data using the RC method. They are important and practical models in dealing with incomplete longitudinal data.

Analysis

We first calculated summary statistics to describe the demographic characteristics, mean comorbidity scores, and mean number of observation years for our study population. We computed annual death rates for our annual cohorts, stratified by presence or absence of baseline comorbidity. We then used Cox regression analysis to assess the contribution of each comorbidity measure to predicting survival after controlling for age, gender, and race/ethnicity. The likelihood ratio test and the Akaike Information Criterion (AIC) were used to evaluate the overall goodness of fit of the Cox regression models with different comorbidity measures. The AIC allows descriptive comparison of non-nested models, and accounts for the number of covariates in the model. Models with larger likelihood ratio scores and smaller AIC scores were considered to have better fit. As the p-values for all the models were ≤ 0.0001, they did not provide useful information for assessing model fit. We conducted the Cox regression analysis on our original study sample, and the subsample with individuals continuously enrolled in fee-for-service parts A and B Medicare and with at least 2 consecutive years of comorbidity. Using the many years of longitudinal comorbidity measures in our large study cohort, we found that baseline comorbidity does not fully predict the most recent available comorbidity. Although each individual in our study may have many comorbidity measures, there were at most 2 comorbidity measures used to predict survival for each observation year in the estimating procedure.