Early prediction of median survival among a large AIDS surveillance cohort

Since the beginning of the AIDS epidemic, the prediction of trends in survival after an AIDS diagnosis has been important for planning health care services and for monitoring the impact of the epidemic. Temporal associations between improved survival following the introduction of expanded treatment options provide population-based evidence that there may be beneficial treatment effects long before these hypotheses can be tested formally. In a time when health care resources are limited and health priorities must be established, it is crucial to project the short-term mortality after AIDS for future planning of health care resources [1].

Temporal trends and improvements in survival with AIDS were reported early in the epidemic even before the introduction of advances in therapy [2]. Shortly after the introduction of zidovudine therapy, temporal trends in survival were (eventually) noted using surveillance data [3]. Other registry-based studies investigated the relationship between survival following an AIDS diagnosis and calendar date of diagnosis [4, 5]. These studies consistently showed marked improvements in AIDS survival after the introduction of zidovudine therapy and Pneumocystis carinii pneumonia prophylaxis. More recently, the introduction of highly active antiretroviral therapy (HAART) has renewed the idea of examining trends in survival after an AIDS diagnosis in order to study both the short- and long-term effects of these new drugs on HIV-related morbidity and mortality.

In this study, a new approach was implemented to predict AIDS survival and test its accuracy using AIDS surveillance data. The purpose of this study was: (1) to determine the earliest quantile (such as 0.10, 0.15, or 0.20) of the survival distribution that can be used to predict accurately a cohort's subsequently observed median survival, and (2) to estimate the survival quantiles using the Inverse Probability of Censoring Weighted (IPCW) estimator [6] in order to improve the prediction methodology in the common situation with registry data in which death is subject to delays in reporting [7].

For cohorts of individuals who have recently been diagnosed with AIDS, data exist for "early" survival quantiles (such as the 0.10, 0.15, 0.20 quantiles, etc.) but many years of additional observation must elapse before later quantiles, such as the median (0.50 quantile) can be estimated with accuracy. Assuming a linear relationship between the early survival quantile and the median survival, an early prediction of the median value for a cohort's eventual survival distribution is compared to the actual or true median value for the cohort. If the predicted median is accurate, then early estimation of AIDS survival is possible and will be of great benefit to health care planners developing strategies and financing for the health care needs of these patients. Additionally, such an accurate, early prediction methodology could be extended to other large, population-based surveillance systems where survival prediction is a major goal.

For cohorts of individuals who have been diagnosed recently with AIDS, data exist relatively soon after diagnosis for estimating "early" survival quantiles (such as the 0.10, 0.15, 0.20 quantiles, etc.) but many years of additional observation must elapse before later quantiles can be estimated accurately. The purpose of this study was to determine if median survival could be predicted accurately using earlier quantiles of survival distributions provided by AIDS surveillance data. Our approach for predicting median survival consisted of two components: (1) the estimation of quantiles of the survival distribution using the IPCW estimator, and (2) the use of a linear model to reflect the relationship between the early quantile and the later quantile. The utility of such an approach would allow early information to predict later unobserved survival patterns in order to accurately identify changes in population-based survival years before such changes are observed. If accurate estimation could be achieved, this approach could offer a method for researchers to estimate the expected survival distribution after AIDS diagnosis (or after many conditions for which surveillance databases are maintained such as cancer). This approach enables accurate predictions of changes in survival among HIV-infected individuals like that observed in 1987 [3–5, 12] and more notably with the advent of the use of highly active antiretroviral therapies [13–16].

The class of IPCW estimators has been developed in order to improve more traditional techniques in situations where these techniques may lead to biased estimates of survival. IPCW estimators have been applied to many types of survival problems such as correcting for non-compliance and dependent censoring in the examination of a beneficial treatment effect on survival [17] and non-parametric survival estimation when death is reported with delay [11], as in this study.

In this study, the 0.15 quantile of the survival distribution predicted accurately the median survival for cohorts diagnosed before the third quarter of 1993. In addition, the 0.15 quantile of the survival distributions predicted accurately the median survival in the short-term for two cohorts (933 and 934) for which a median estimate could not be estimated at the time of analysis (December 31, 1996). By using traditional methods (i.e., the K-M estimator) and without the use of our methodology, at least six months of additional follow-up would be required to observe any median survival estimate for the 933 cohort and at least 45 months until the predicted median of 34 months (as predicted by our methodology) would be observed for this cohort. This demonstrated that our methodology not only provides an accurate estimate of median survival, but an estimate of median survival long before traditional approaches would allow.

The results of this study suggest that our methodology yields an accurate prediction of median survival for cohorts diagnosed at least three years earlier than the date when the prediction is made. For example, the difference between the predicted and the true median survival was ≤ 6 months for the cohorts 933 and 934 but greater than 6 months for the cohorts 941 and 941 using data as of December 31, 1996. The "true" median estimate (using data as of December 31, 2001) according to the IPCW estimator for the 942 cohort was estimated to be 80 months. This may indeed be an early estimate of the median survival for this cohort and, as more data for this cohort becomes available, this median estimate may decrease over time like that observed with the K-M estimator (Additional File 1). This early estimate would greatly affect our assessment of the accuracy of our predictions since we are using this estimate as the "true" median survival. As a result, if one applies this methodology now in the second quarter of 2006, we could only expect to be able to predict with accuracy the median survival for cohorts that were diagnosed in the second quarter of 2003 or earlier. This methodology would not appear to work for cohorts diagnosed later than the second quarter of 2003.

The ability of the method, however, to accurately predict median survival in the short-term based on historical data is greatly influenced by three factors: (1) the variability of the estimates of the various quantiles of the survival distribution, (2) the assumption that the relation between the early quantile and the later quantile (median) can be represented by a linear model, and (3) this relation will remain the same in the short-term.

The estimates of the various quantiles of the survival distribution are affected greatly by two sources of bias: delays in diagnosis and delays in death reports. The fact that patients who were in HARS as of a particular date of analysis were included in the study sample obviously excluded those who were diagnosed before this date of analysis but were reported sometime after. Delays in diagnosis affect the estimates of survival by introducing additional individuals into each of the cohorts and, depending on their individual survival times, may affect the observed quantiles of the survival distribution. It is unclear how such individuals would affect the estimates of survival, but this potential for bias was eliminated by only including those who were reported by a fixed data of analysis (e.g., December 31, 1996) in order to mimic the "real world" situation in which only those patients currently entered into a database are available for analysis. This should not detract from the utility of the estimation procedure since the predicted medians were compared with additional data five years after the prediction was made using only those patients who were selected in the original study sample.

In addition, delays in the reporting of death can bias estimates of survival if one assumes that a case is alive if a death date has not been reported. In this study, the use of the IPCW estimator is an attempt to mitigate the potential for bias in estimating survival after an AIDS diagnosis due to reporting delays of death. This estimator adjusts the estimates of survival for a given cohort to account for delays in death reports, provided that the delay of death report distribution is known. The bias introduced by failing to account for delays in death reporting when estimating survival after an AIDS diagnosis has already been established [11].

For simplicity, the prediction method assumed that the early quantile such as the 0.15 quantile, a representation of the "early"' survival experience was linearly related to the median of the survival estimate, the "later survival experience". Higher-dimensional models were explored but did not improve the predictive ability (data not shown). In assuming a linear relationship and extrapolating the observed relationship to the future, an additional assumption made was that this relationship would remain as observed in the past, at least in the short-term. Validation from the more recent cohorts (i.e., the 933 and 934 cohorts) confirms that the linear model accurately predicts median survival in the short-term, but may not perform well for all cohorts (e.g., the 941 and 942 cohorts). Assuming that HAART first became available with the approval of Saquinavir (hard-gel) in December 1995, the 941 and 942 cohorts would have been introduced to HAART earlier after diagnosis (21 months for the 941 cohort and 18 months for the 942 cohort) in comparison to the 933 and 934 cohorts (27 months and 24 months respectively). When comparing survival across different cohorts diagnosed over time, we would expect the later cohorts to demonstrate a shift in survival, thus violating any observed linear relationships between earlier quantiles and later quantiles observed in the past.

This investigation suggests that this approach to survival estimation accurately predicted subsequent survival experience observed in two of these cohorts (the 933 and 934 cohorts). It is notable that the technique did not perform well during a period of rapid increase in AIDS survival that is not unlike the presently observed increases in survival influenced by current advances in therapy. However, the performance of the methodology before the introduction of HAART suggests that this methodology may work well in a time of more gradual improvement in survival with antiretroviral treatment. This technique may also have application in other areas of research (e.g. cancer surveillance) where population changes in survival have been observed and should be validated using additional data.