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PubMed1994

Spline-based tests in survival analysis.

This paper examines a method for testing hypotheses on covariate effects in a proportional hazards model, and also on how effects change over time in regression analysis of survival data. The technique used is very general and can be applied to testing many other aspects of parametric and semiparametric models. The basic idea is to formulate a flexible parametric alternative using fixed knot splines, together with a penalty function that penalizes noisy alternatives more than smooth ones, to focus the power of the tests toward smooth alternatives. The test statistics are the analogs of ordinary likelihood-based statistics, only computed from a penalized likelihood formed by subtracting the penalty function from the ordinary log-likelihood. Large-sample approximations to the distributions are found when the number of knots is held fixed as the sample size increases. Numerical results suggest these approximations may be adequate with moderate sized samples.

Analysis of Variance↗
PubMed1998

Left-truncated data with age as time scale: an alternative for survival analysis in the elderly population.

BACKGROUND: The standard approach for survival analysis of the elderly population is to define the survival time as the elapsed time from entry into the study until death, and to adjust by age using stratification and regression procedures. However, the interest is in the study of the aging process and the risk factors related to it, not in the use of time-on-study as the time scale. Here, we present methods to use age as the time scale and compare inferences and interpretations with those obtained using the standard approach. METHODS: A total of 1,315 individuals aged 65 years or older from the city of Barcelona, Spain, were interviewed in 1986 (baseline). The vital status of the cohort was assessed in October 1994. To illustrate the usefulness of age as time scale (alternative approach) instead of time-on-study in the survival analysis of the elderly population, both methods were used to assess the relationship between baseline functional capacity and mortality. RESULTS: Using the alternative approach, we observed that 50% of the sample died at age 80.6 years; this information could not be estimated with the standard approach. Using age as a covariate in the standard analysis with time-on-study as the time scale and using age as the time scale in the alternative analysis, the association of functional capacity at baseline and mortality was of similar magnitude under both analyses. Nevertheless, using the alternative approach, relative risks were slightly lower, and the adjustment by age was tight and was not subject to the inherent assumptions in regression models of the functional relationship of independent variables with outcome. We illustrated the methods with fixed covariates (i.e., gender) and baseline values of time-dependent covariates (i.e., functional capacity), but we discussed the extension of our methods for the analysis of time-dependent covariates measured at several visits in a cohort study. Methods proposed here are easily implemented with widely available statistical software packages. CONCLUSIONS: Although the use of standard survival analysis generally produces correct estimates, the use of age as time scale is deemed more appropriate for survival analysis of the elderly: Inferences are easier to interpret and final models are simpler. We therefore recommend the use of age as time scale for survival analysis of the elderly population.

Aged↗
PubMed2006

On the use of multi-objective evolutionary algorithms for survival analysis.

This paper proposes and evaluates a multi-objective evolutionary algorithm for survival analysis. One aim of survival analysis is the extraction of models from data that approximate lifetime/failure time distributions. These models can be used to estimate the time that an event takes to happen to an object. To use of multi-objective evolutionary algorithms for survival analysis has several advantages. They can cope with feature interactions, noisy data, and are capable of optimising several objectives. This is important, as model extraction is a multi-objective problem. It has at least two objectives, which are the extraction of accurate and simple models. Accurate models are required to achieve good predictions. Simple models are important to prevent overfitting, improve the transparency of the models, and to save computational resources. Although there is a plethora of evolutionary approaches to extract models for classification and regression, the presented approach is one of the first applied to survival analysis. The approach is evaluated on several artificial datasets and one medical dataset. It is shown that the approach is capable of producing accurate models, even for problems that violate some of the assumptions made by classical approaches.

Algorithms↗
PubMed2005

[Basic concepts in survival analysis].

The present article aims to introduce and explain basic concepts in survival analysis. Most survival analyses use terms such as Kaplan-Meyer, logrank, and censored times, among others. We discuss the background to these terms and their interpretation. We discuss how to produce and interpret survival curves and how to compare them. Finally, we explain some conditions that should be borne in mind when performing a survival analysis.

Humans↗
PubMed1995

Trees and splines in survival analysis.

During the past few years several nonparametric alternatives to the Cox proportional hazards model have appeared in the literature. These methods extend techniques that are well known from regression analysis to the analysis of censored survival data. In this paper we discuss methods based on (partition) trees and (polynomial) splines, analyse two datasets using both Survival Trees and HARE, and compare the strengths and weaknesses of the two methods. One of the strengths of HARE is that its model fitting procedure has an implicit check for proportionality of the underlying hazards model. It also provides an explicit model for the conditional hazards function, which makes it very convenient to obtain graphical summaries. On the other hand, the tree-based methods automatically partition a dataset into groups of cases that are similar in survival history. Results obtained by survival trees and HARE are often complementary. Trees and splines in survival analysis should provide the data analyst with two useful tools when analysing survival data.

Algorithms↗
PubMedDate not supplied

Survival analysis with unreliable endpoints.

There exists a current interest in the application of survival analysis methodology to evaluate differences in latencies of response to psychological or psychopharmacological treatment modalities. However, unreliability in the measurement of treatment responses in such research poses a problem. Two methods of defining the "discrete endpoint" that is required for survival analysis are compared regarding power of tests of significance for differences in survival curves. Discrete endpoints defined by regression equations fitted to all available data for each subject provided greater power when entered into survival analysis than did endpoints dependent only on individual measurements. While this may not surprise statisticians, no examples of the use of regression estimates for survival analysis endpoints have been identified in reports of previous clinical trials nor in discussions concerning potential applications of survival analysis methodology in psychiatric research.

Analysis of Variance↗
PubMed1985

Logistic regression in survival analysis.

Logistic regression has been applied to numerous investigations that examine the relationship between risk factors and various disease events. Recently, the ability to consider the time element of event occurrences by proportional hazards models has meant that logistic regression has played a less important role in the analysis of survival data. This paper, however, shows that when event times are grouped into intervals, logistic regression can be adapted to the analysis of such data by modeling the interval when an event occurs. Furthermore, it is shown that results from such an adaptation will often lead to parameter estimates close to those obtained by the proportional hazards model in the grouped event time setting. An illustration of the application of logistic regression to survival analysis is based on data from the Framingham Heart Study.

Coronary Disease↗
PubMed1993

Cross-validation in survival analysis.

The predictive value of a statistical model is conceptually different from the explained variation. In this paper we construct a measure of the predictive value of the Cox proportional hazards model, computed from the leave-one-out regression coefficients. These coefficients can also be used to calculate a shrinkage factor which can be applied to improve the predictions and that can be used in R2-type measures of the proportion of explained variation. Our methods are illustrated by a study of chemotherapy for advanced ovarian cancer.

Antineoplastic Combined Chemotherapy Protocols↗
PubMed1998

Localized well-differentiated thyroid carcinoma: survival analysis of prognostic factors and (131)I therapy.

BACKGROUND: Recommendations regarding therapeutic use of (131)I for patients with well-differentiated thyroid cancer remain controversial. Between 1969 and 1993, 1171 patients with papillary (including mixed) or follicular thyroid cancer were reported to the New Mexico Tumor Registry. Of these, 1075 cases (77.6% female, median age 41 years) were available for analysis of survival plots and previously recognized risk factors. Extent of operation was documented for 344 patients. METHODS: One hundred twenty-seven (37%) patients underwent postoperative (131)I ablation. Median follow-up was 99 months. A proportional hazards model was constructed using age, gender, stage, histology, and use of radioiodine. The same variables plus extent of operation were examined in the smaller group. RESULTS: Kaplan-Meier survival estimates at 12 years were 96.2% for patients younger than 45 years and 68.6% for those older than 45 years. Age, gender, and histology, but not stage, were important survival variables (P <.05). Adjusting for other risk factors, there was no apparent survival benefit associated with radioiodine following clinically appropriate thyroidectomy. Findings from the small group mirrored those of the large group. CONCLUSIONS: (131)I may not be as efficacious as previously believed for patients with well-differentiated thyroid cancer confined to the neck.

Adenocarcinoma, Follicular↗
PubMed2006

[Survival analysis on liver failure patients treated with an artificial liver support system].

OBJECTIVE: To evaluate the efficacy of artificial liver support system (ALSS) in the treatment of liver failure patients. METHODS: This is a prospective, multi-center, controlled, large sample clinic trial. 518 patients with liver failure from 5 hospitals were studied and followed. All the patients received similar pharmacological manipulation according to one and the same protocol but were divided into an ALSS treatment group and a control group without ALSS treatment. The ALSS treatment procedures included plasma exchange, molecular adsorbent recirculating system (MARS), plasma exchange plus hemofiltration and other combined nonbioartificial methods. The analysis of survival time was computed using the Kaplain-Maier method, and comparison among groups was done using Log-Rank, Breslow and/or the Tarone-Ware test. RESULTS: Survival time of acute liver failure patients was prolonged from 4.0+/-0.2 days to 8.0+/-0.4 days (P=0.004). ALSS was shown to be two times more effective. ALSS increased the survival time of acute on chronic (A on C) liver failure patients from 27.0+/-1.6 days to 39.0+/-4.0 days (P less than 0.01). In addition, it increased the survival time of the patients in the middle and end stage of subacute liver failure and A on C liver failure, but had no significant effects on early stage patients. The survival time of middle stage patients was 38.0+/-17.5 days in the control group vs 66.0+/-18.6 days in the ALSS group (P less than 0.05). The survival time of end stage patients of the control group and the ALSS group was 18.0+/-4.0 days vs 26.0+/-2.5 days (P less than 0.01). CONCLUSIONS: Multi ALSS treatment is more effective than the standard medicinal liver care treatment. Multi-ALSS treatment could increase survival time of patients suffering from acute liver failure or A on C liver failure, especially in their middle and end stages. It is important and necessary to treat these patients with ALSS.

Adolescent↗
PubMed1993

Survival analysis of joint replacements.

Survival analysis is a powerful tool for analysing the results of total joint replacement, but it has major drawbacks when the failure rates are very low. We have reviewed 35 recent survival analyses of joint replacements to assess the magnitude of these problems and make recommendations as to how they may be avoided.

Confidence Intervals↗
PubMed2000

Using survival analysis to study spatial point patterns in geographical epidemiology.

The spatial K-function has become a well accepted method of investigating whether significant clustering can be detected in spatial point patterns. Unlike nearest neighbor-based methods, the K-function approach has the advantage of exploring spatial pattern across a range of spatial scales. However, K-functions still have a number of drawbacks. For instance, although K-functions are based on inter-event distances, they only use a count of the number of point events within successive distance bands. This represents data aggregation and information loss. Secondly, and perhaps more significantly, K-functions are based on a cumulative count of point events with distance. This feature raises the possibility that the investigation of pattern at different scales is compromised by the dependency of any one count to previous counts. This paper proposes a new approach to the analysis of spatial point patterns based upon survival analysis. Although typically used in the temporal domain, there is no reason why survival analysis cannot be applied to any positively-valued, continuous variable as well as time. In this paper, survival analysis is applied to the inter-event distance measures of bivariate spatial point patterns to investigate the 'random labeling' hypothesis. It is shown, through both a controlled data situation and empirical epidemiological applications, that such an approach may be a very useful complement to K-function analysis.

Accidents, Traffic↗
PubMed1998

A comparison of breeding value predictors for longevity using a linear model and survival analysis.

A comparison was made among breeding values of sires for longevity that were obtained by different methods: phenotypic averages of daughters using only uncensored records, BLUP using only uncensored records, survival analysis using only uncensored records, and survival analysis using both censored and uncensored records. Two data files were used: one contained data from small herds, and the other contained data from large herds. The results from both data files were similar. Different methods of predicting breeding values resulted in different rankings of sires. The results obtained using phenotypic averages were weakly correlated (< or = 0.46) with those results obtained using the other methods of prediction. The REML BLUP had strong correlations (< or = -0.91) with the survival analysis predictor if the same data were used, and correlations weakened (< or = -0.60) when censored records were included in the survival analysis. The correlations are negative because the linear method analyzed longevity, and survival analysis measured the risk of being culled, which has an antagonistic relationship with longevity. The results from REML BLUP and survival analysis methods differed mainly because of the different data that were used (uncensored only versus both censored and uncensored).

Aging↗
PubMed1990

Quality adjusted survival analysis.

We present a technique, quality adjusted survival analysis, for the analysis of controlled trials where patients may experience several health states which differ in their quality of life. When the data are censored, a survival analysis of the quality adjusted life years achieved may involve informative censoring, and produce biased estimates. To overcome this, we partition the survival curve; the resulting areas, which represent the mean time in each state, are multiplied by utility weights to provide an unbiased estimate of (restricted) quality adjusted survival. If the appropriate weights are in doubt, the results are best presented as a threshold analysis over the utility weights, allowing individual recommendation to be read from a simple graph. The certainty of the conclusions can be presented as confidence bands on the threshold line. The techniques are illustrated with a re-analysis of a large three-arm trial of adjuvant chemoendocrine therapy for stage II breast cancer in postmenopausal women. This shows that if the value of time spent in toxicity is greater than the time spent in relapse, we can be 95 per cent confident that chemoendocrine therapy is the preferred option.

Breast Neoplasms↗
PubMedDate not supplied

[Age as time-scale: an application to the survival analysis of chronic diseases].

BACKGROUND: Cohort study survival analysis does not take into account the age at which an individual dies, but rather the age throughout which the individual has been included in the follow-up. This study is aimed at assessing the resulting differences in the calculation of the relative risk (RR) when the age is used instead of follow-up as a timescale in the chronic diseases survival analysis. METHODS: The five-year cohort follow-up data for the Catalan Health Interview Survey (COHESCA) is analyzed. Cox models are adjusted to the follow-up time ("standard" approach) and the age ("alternative" approach) as the timescale. The main covariable used is the comorbility index, which is adjusted by demographics, lifestyles and self-perceived health. RESULTS: Among men in the 40-64 age range, using the "standard" approach, no significant increase in the RR of death was found. Among women within the 40-64 age range with a 3-4 score on the index, there was a significant increase in the RR. Among those over age 64, a significant increase in the risk was found for the 3-4 score (RRmen = 2.1 (1.3-2.5); RRwomen = 2.1 (1.2-3.7)) and > = 5 on the index (RRmen = 3.4 (1.7-6.9); RRwomen = 4.0 (2.1-7.7)). Using the "alternative" approach, the RR was 1.0 (0.7-1.4) among men with a score of 1-2, 1.5 (1.0-2.3) for those with a score of 3-4 and 2.6 (1.4-4.9) for those with a score of > = 5. Among women, the RR were respectively 0.8 (0.5-1.2), 1.7 (1.1-2.7) and 2.6 (1.5-4.8). CONCLUSIONS: Both approaches showed an increase in the RR according to the comorbility index. However, in the "alternative" approach, it is adjusted by the confounding effect of age.

Adult↗
PubMed1995

Multiple time scales in survival analysis.

In some problems in survival analysis there may be more than one plausible measure of time for each individual. For example mileage may be a better indication of the age of a car than months. This paper considers the possibility of combining two (or more) time scales measured on each individual into a single scale. A collapsibility condition is proposed for regarding the combined scale as fully informative regarding survival. The resulting model may be regarded as a generalization of the usual accelerated life model that allows time-dependent covariates. Parametric methods for the choice of time scale, for testing the validity of the collapsibility assumption and for parametric inference about the failure distribution along the new scale are discussed. Two examples are used to illustrate the methods, namely Hyde's (1980) Channing House data and a large cohort mortality study of asbestos workers in Quebec.

Aged↗