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Objective: To investigate the use and performance of Weibull distribution in cure models using simulation study.

Methods: Estimation and comparison of cure proportions and survival of the uncured in the age groups of patients diagnosed with colon cancer between 1971 and 1990 obtained from a cancer registry. Assessment of the performance of Weibull distribution in fitting cure models when the underlying assumptions are partly or not satisfied using simulations.

Results: The youngest age group had better survival and higher cure proportion than other age groups when cure models were fitted. The simulation study showed that mixture cure Weibull models produced unbiased estimates of the cure proportions and biased estimates of the median and 90th percentile survival times when fitted to datasets generated from two-component Weibull distribution.

Conclusion: The use of Weibull distribution in mixture cure models to model datasets generated from a two-component Weibull distribution would give unbiased estimates of cure proportions, but would provide biased estimates of the median survival and 90th percentile survival times (that is, time at which 90 percent of diagnosed patients would have died).


Patterns of survival among patients with myeloproliferative neoplasms diagnosed in Sweden from 1973 to 2008: a population-based study.

Abstract: Reported survival in patients with myeloproliferative neoplasms (MPNs) shows great variation. Patients with primary myelofibrosis (PMF) have substantially reduced life expectancy, whereas patients with polycythemia vera (PV) and essential thrombocythemia (ET) have moderately reduced survival in most, but not all, studies. We conducted a large population-based study to establish patterns of survival in more than 9,000 patients with MPNs.We identified 9,384 patients with MPNs (from the Swedish Cancer Register) diagnosed from 1973 to 2008 (divided into four calendar periods) with follow-up to 2009. Relative survival ratios (RSRs) and excess mortality rate ratios were computed as measures of survival.Patient survival was considerably lower in all MPN subtypes compared with expected survival in the general population, reflected in 10-year RSRs of 0.64 (95% CI, 0.62 to 0.67) in patients with PV, 0.68 (95% CI, 0.64 to 0.71) in those with ET, and 0.21 (95% CI, 0.18 to 0.25) in those with PMF. Excess mortality was observed in patients with any MPN subtype during all four calendar periods (P < .001). Survival improved significantly over time (P < .001); however, the improvement was less pronounced after the year 2000 and was confined to patients with PV and ET.We found patients with any MPN subtype to have significantly reduced life expectancy compared with the general population. The improvement over time is most likely explained by better overall clinical management of patients with MPN. The decreased life expectancy even in the most recent calendar period emphasizes the need for new treatment options for these patients.

Pub.: 18 Jul '12, Pinned: 28 Jun '17

Temporal trends in the proportion cured among adults diagnosed with acute myeloid leukaemia in Sweden 1973-2001, a population-based study.

Abstract: Large age-dependent differences in temporal trends in 1- and 5-year relative survival have been observed in patients with acute myeloid leukaemia (AML) in Sweden. This investigation used an alternative approach to studying patient survival that simultaneously estimated the proportion of patients cured from their cancer and the survival of the 'uncured'. We conducted a population-based study including 6439 AML patients aged 19-80 years in Sweden between 1973 and 2001. Mixture cure models were estimated, with age at diagnosis categorised (19-40, 41-60, 61-70 and 71-80) and year of diagnosis modelled using splines. In 1975 the cure proportion was < or =6% in all age groups and the median survival time for 'uncured' patients was <0.5 years. In 2000 the cure proportion was 68% (95% confidence interval 56-77%) in the youngest group, and 32% (25-39%), 8% (3-21%), and 4% (2-8%) in the other groups, respectively. The median survival times for 'uncured' were 0.74 (0.43-1.26), 0.71 (0.53-0.97), 0.69 (0.51-0.95) and 0.37 (0.31-0.44) years, respectively. A dramatic improvement in the cure proportion was seen in younger patients, whereas improvement in older ages was mainly within the survival of the 'uncured'. This novel approach of analysing survival data could be a valuable tool for physicians, patients, health care planners and health economists.

Pub.: 10 Dec '09, Pinned: 26 Jun '17

A simulation study of predictive ability measures in a survival model I: explained variation measures.

Abstract: Measures of predictive ability play an important role in quantifying the clinical significance of prognostic factors. Several measures have been proposed to evaluate the predictive ability of survival models in the last two decades, but no single measure is consistently used. The proposed measures can be classified into the following categories: explained variation, explained randomness, and predictive accuracy. The three categories are conceptually different and are based on different principles. Several new measures have been proposed since Schemper and Stare's study in 1996 on some of the existing measures. This paper is the first of two papers that study the proposed measures systematically by applying a set of criteria that a measure of predictive ability should possess in the context of survival analysis. The present paper focuses on the explained variation category, and part II studies the proposed measures in the other categories. Simulation studies are used to examine the performance of five explained variation measures with respect to these criteria, discussing their strengths and shortcomings. Our simulation studies show that the measures proposed by Kent and O'Quigley, R(PM)(2), and Royston and Sauerbrei, R(D)(2), appear to be the best overall at quantifying predictive ability. However, it should be noted that neither measure is perfect; R(PM)(2) is sensitive to outliers and R(D)(2) to (marked) non-normality of the distribution of the prognostic index. The results show that the other measures perform poorly, primarily because they are adversely affected by censoring.

Pub.: 27 Apr '11, Pinned: 26 Jun '17

Estimating and modelling cure in population-based cancer studies within the framework of flexible parametric survival models.

Abstract: When the mortality among a cancer patient group returns to the same level as in the general population, that is, the patients no longer experience excess mortality, the patients still alive are considered "statistically cured". Cure models can be used to estimate the cure proportion as well as the survival function of the "uncured". One limitation of parametric cure models is that the functional form of the survival of the "uncured" has to be specified. It can sometimes be hard to find a survival function flexible enough to fit the observed data, for example, when there is high excess hazard within a few months from diagnosis, which is common among older age groups. This has led to the exclusion of older age groups in population-based cancer studies using cure models.Here we have extended the flexible parametric survival model to incorporate cure as a special case to estimate the cure proportion and the survival of the "uncured". Flexible parametric survival models use splines to model the underlying hazard function, and therefore no parametric distribution has to be specified.We have compared the fit from standard cure models to our flexible cure model, using data on colon cancer patients in Finland. This new method gives similar results to a standard cure model, when it is reliable, and better fit when the standard cure model gives biased estimates.Cure models within the framework of flexible parametric models enables cure modelling when standard models give biased estimates. These flexible cure models enable inclusion of older age groups and can give stage-specific estimates, which is not always possible from parametric cure models.

Pub.: 24 Jun '11, Pinned: 26 Jun '17

Partitioning of excess mortality in population-based cancer patient survival studies using flexible parametric survival models.

Abstract: Relative survival is commonly used for studying survival of cancer patients as it captures both the direct and indirect contribution of a cancer diagnosis on mortality by comparing the observed survival of the patients to the expected survival in a comparable cancer-free population. However, existing methods do not allow estimation of the impact of isolated conditions (e.g., excess cardiovascular mortality) on the total excess mortality. For this purpose we extend flexible parametric survival models for relative survival, which use restricted cubic splines for the baseline cumulative excess hazard and for any time-dependent effects.In the extended model we partition the excess mortality associated with a diagnosis of cancer through estimating a separate baseline excess hazard function for the outcomes under investigation. This is done by incorporating mutually exclusive background mortality rates, stratified by the underlying causes of death reported in the Swedish population, and by introducing cause of death as a time-dependent effect in the extended model. This approach thereby enables modeling of temporal trends in e.g., excess cardiovascular mortality and remaining cancer excess mortality simultaneously. Furthermore, we illustrate how the results from the proposed model can be used to derive crude probabilities of death due to the component parts, i.e., probabilities estimated in the presence of competing causes of death.The method is illustrated with examples where the total excess mortality experienced by patients diagnosed with breast cancer is partitioned into excess cardiovascular mortality and remaining cancer excess mortality.The proposed method can be used to simultaneously study disease patterns and temporal trends for various causes of cancer-consequent deaths. Such information should be of interest for patients and clinicians as one way of improving prognosis after cancer is through adapting treatment strategies and follow-up of patients towards reducing the excess mortality caused by side effects of the treatment.

Pub.: 26 Jun '12, Pinned: 26 Jun '17

How can we make cancer survival statistics more useful for patients and clinicians: an illustration using localized prostate cancer in Sweden.

Abstract: Studies of cancer patient survival typically report relative survival or cause-specific survival using data from patients diagnosed many years in the past. From a risk-communication perspective, such measures are suboptimal for several reasons; their interpretation is not transparent for non-specialists, competing causes of death are ignored and the estimates are unsuitable to predict the outcome of newly diagnosed patients. In this paper, we discuss the relative merits of recently developed alternatives to traditionally reported measures of cancer patient survival.In a relative survival framework, using a period approach, we estimated probabilities of death in the presence of competing risks. To illustrate the methods, we present estimates of survival among 23,353 initially untreated, or hormonally treated men with intermediate- or high-risk localized prostate cancer using Swedish population-based data.Among all groups of newly diagnosed patients, the probability of dying from prostate cancer, accounting for competing risks, was lower compared to the corresponding estimates where competing risks were ignored. Accounting for competing deaths was particularly important for patients aged more than 70 years at diagnosis in order to avoid overestimating the risk of dying from prostate cancer.We argue that period estimates of survival, accounting for competing risks, provide the tools to communicate the actual risk that cancer patients, diagnosed today, face to die from their disease. Such measures should offer a more useful basis for risk communication between patients and clinicians and we advocate their use as means to answer prognostic questions.

Pub.: 09 Jan '13, Pinned: 26 Jun '17

Estimating the loss in expectation of life due to cancer using flexible parametric survival models.

Abstract: A useful summary measure for survival data is the expectation of life, which is calculated by obtaining the area under a survival curve. The loss in expectation of life due to a certain type of cancer is the difference between the expectation of life in the general population and the expectation of life among the cancer patients. This measure is used little in practice as its estimation generally requires extrapolation of both the expected and observed survival. A parametric distribution can be used for extrapolation of the observed survival, but it is difficult to find a distribution that captures the underlying shape of the survival function after the end of follow-up. In this paper, we base our extrapolation on relative survival, because it is more stable and reliable. Relative survival is defined as the observed survival divided by the expected survival, and the mortality analogue is excess mortality. Approaches have been suggested for extrapolation of relative survival within life-table data, by assuming that the excess mortality has reached zero (statistical cure) or has stabilized to a constant. We propose the use of flexible parametric survival models for relative survival, which enables estimating the loss in expectation of life on individual level data by making these assumptions or by extrapolating the estimated linear trend at the end of follow-up. We have evaluated the extrapolation from this model using data on four types of cancer, and the results agree well with observed data.

Pub.: 17 Sep '13, Pinned: 26 Jun '17

Long-term survival in young and middle-aged Hodgkin lymphoma patients in Sweden 1992-2009-trends in cure proportions by clinical characteristics.

Abstract: Trends in Hodgkin lymphoma (HL) survival among patients treated outside of clinical trials provide real-world benchmark estimates of prognosis and help identify patient subgroups for targeted trials. In a Swedish population-based cohort of 1947 HL patients diagnosed in 1992-2009 at ages 18-59 years, we estimated relative survival (RS), cure proportions (CP), and median survival times using flexible parametric cure models. Overall, the CP was 89% (95% CI: 0.87-0.91) and median survival of the uncured was 4.6 years (95% CI: 3.0-6.3). For patients aged 18-50 years diagnosed after the year 2000, CP was high and stable, whereas for patients of 50-59 years, cure was not reached. The survival of relapse-free patients was similar to that of the general population (RS5-year : 0.99; 95% CI: 0.98-0.99, RS15-year : 0.95; 95% CI: 0.92-0.97). The excess mortality of relapsing patients was 19 times (95% CI: 12-31) that of relapse-free patients. Despite modern treatments, patients with adverse prognostic factors (e.g., advanced stage) still had markedly worse outcomes [CP stage: IIIB 0.82 (95% CI: 0.73-0.89); CP stage: IVB 0.72, (95% CI: 0.60-0.81)] and patients with international prognostic score (IPS) ≥3 had 2.7 times higher excess mortality (95% CI: 1.0-7.0, p = 0.04) than patients with IPS <3. High-risk patients selected for 6-8 courses of BEACOPP (bleomycin, etoposide, doxorubicin, cyclofosphamide, vincristine, procarbazine, prednisone)-chemotherapy had a 15-year relative survival of 87%, (95% CI: 0.80-0.92), whereas the corresponding estimate for patients selected for 6-8 courses of ABVD (doxorubicin, bleomycin, vinblastine, dacarbazine) was 93% (95% CI: 0.88-0.97). These population-based results indicate limited fatal side-effects in the 15-year perspective with contemporary treatments, while the unmet need of effective relapse treatment remains of concern. BEACOPP-chemotherapy was still not sufficient in high-risk HL patients. Am. J. Hematol. 90:1128-1134, 2015. © 2015 Wiley Periodicals, Inc.

Pub.: 09 Sep '15, Pinned: 26 Jun '17

A flexible parametric approach to examining spatial variation in relative survival

Abstract: Most of the few published models used to obtain small-area estimates of relative survival are based on a generalized linear model with piecewise constant hazards under a Bayesian formulation. Limitations of these models include the need to artificially split the time scale, restricted ability to include continuous covariates, and limited predictive capacity. Here, an alternative Bayesian approach is proposed: a spatial flexible parametric relative survival model. This overcomes previous limitations by combining the benefits of flexible parametric models: the smooth, well-fitting baseline hazard functions and predictive ability, with the Bayesian benefits of robust and reliable small-area estimates. Both spatially structured and unstructured frailty components are included. Spatial smoothing is conducted using the intrinsic conditional autoregressive prior. The model was applied to breast, colorectal, and lung cancer data from the Queensland Cancer Registry across 478 geographical areas. Advantages of this approach include the ease of including more realistic complexity, the feasibility of using individual-level input data, and the capacity to conduct overall, cause-specific, and relative survival analysis within the same framework. Spatial flexible parametric survival models have great potential for exploring small-area survival inequalities, and we hope to stimulate further use of these models within wider contexts. Copyright © 2016 John Wiley & Sons, Ltd.

Pub.: 08 Aug '16, Pinned: 26 Jun '17