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Hypertabastic survival model.

Tabatabai MA, Bursac Z, Williams DK, Singh KP - Theor Biol Med Model (2007)

Bottom Line: We then demonstrate the application of the hypertabastic survival model by applying it to data from two motivating studies.The first one demonstrates the proportional hazards version of the model by applying it to a data set from multiple myeloma study.Based on the results from the simulation study and two applications, the proposed model shows to be a flexible and promising alternative to practitioners in this field.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biostatistics, University of Arkansas for Medical Sciences, Little Rock, AR, USA. mtabatabai@cameron.edu

ABSTRACT
A new two-parameter probability distribution called hypertabastic is introduced to model the survival or time-to-event data. A simulation study was carried out to evaluate the performance of the hypertabastic distribution in comparison with popular distributions. We then demonstrate the application of the hypertabastic survival model by applying it to data from two motivating studies. The first one demonstrates the proportional hazards version of the model by applying it to a data set from multiple myeloma study. The second one demonstrates an accelerated failure time version of the model by applying it to data from a randomized study of glioma patients who underwent radiotherapy treatment with and without radiosensitizer misonidazole. Based on the results from the simulation study and two applications, the proposed model shows to be a flexible and promising alternative to practitioners in this field.

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Kaplan-Meier survival curves for glioma brain cancer.
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Figure 5: Kaplan-Meier survival curves for glioma brain cancer.

Mentions: Glioma is a cancer of the brain which begins in glial cells. These cells support the neurons. These cells have a very high rate of growth which can quickly destroy the normal cells. The primary types of glioma cancers are astrocytomas, ependymomas and oligodendrogliomas. Shin et al. [28] studied ways to improve the effectiveness of radiation in the treatment of cerebral malignant astrocytoma. Their study focused on the assessment of the effect of multiple daily fractionated radiation therapy with and without misonidazole. They concluded that the addition of misonidazole did not significantly improve the patients' survival. In this section we apply the hypertabastic accelerated failure time technique to model the survival time of a sample of 30 patients from the randomized trials of radiotherapy with and without the radiosensitizer misinidazole. The data was obtained from the Medical Research Council Working Party (MRC) on misonidazole in gliomas. This data is right censored and has been previously analyzed for the selection of variables by MRC [29]. Survival time was measured in days and the longest survival time was 1098 days. We compared radiotherapy treatment of brain cancer patients with radiosensitizer misonidazole to radiotherapy without misonidazole. Figure 5 shows a Kaplan-Meier plot of the estimated survival curves for both groups. The log-rank, Wilcoxon, and likelihood ratio tests are all non-significant, suggesting no significant difference between survival curves for the two groups. The Kaplan-Meier estimates of median survival time for radiotherapy with misonidazole group is 258.5 days and for the radiotherapy without misonidazole group is 488 days. The overall median survival time for both groups combined is 361 days. Using the Kaplan-Meier estimates of survival function, a plot of log-cumulative hazard function against the logarithm of the survival time for individuals in two groups indicates that the data is coming from a Weibul distribution. Knowing this information led us to evaluate the performance of the hypertabastic model. First, we fit a hypertabastic accelerated failure time model to analyze the brain cancer data. Then the hypertabastic accelerated failure time model is compared with Weibul, log-logistic, log-normal accelerated failure time models and the Cox proportional hazards model. This model incorporates a binary covariate coded as treatment = 1 for the type of radiotherapy with misonidazole, and as treatment = 0 for radiotherapy without misonidazole. The second covariate is the age of the patient. Thus, this model contains two covariates- treatment and age. We use the method of maximum likelihood to maximize hypertabastic accelerated failure time log-likelihood function for right censored data discussed in section 5. Table 3 gives a statistical summary for the glioma data. For instance, the hypertabastic estimated value for the coefficient of the variable radiosensitizer is 0.4387 with a standard error of 0.3437. The Wald and the likelihood ratio statistics associated with this variable are 1.6294 (p = 0.2018) and 1.6254 (p = 0.2023) respectively. Both tests indicate that the effect of individual variable radiosensitizer is non-significant. The estimated accelerator factor is 1.5507 (exponentiated value of parameter 0.4387). This means that after controlling for the age of the patient, the probability of a patient treated with "therapy with radiosensitizer misonidazole" surviving t days equals to the probability of a patient treated with "therapy without radiosensitizer misonidazole" surviving 1.5507 t days. For instance, the hypertabastic accelerated failure time model suggests that for 49 year old patients (median age for all patients under study), the probability of a patient treated with " therapy with radiosensitizer misonidazole " surviving 293 days equals to the probability of a patient treated with" therapy without radiosensitizer misonidazole " surviving 454 days. The Wald statistic for the age covariate is 22.18 (p < 0.0001).


Hypertabastic survival model.

Tabatabai MA, Bursac Z, Williams DK, Singh KP - Theor Biol Med Model (2007)

Kaplan-Meier survival curves for glioma brain cancer.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2169222&req=5

Figure 5: Kaplan-Meier survival curves for glioma brain cancer.
Mentions: Glioma is a cancer of the brain which begins in glial cells. These cells support the neurons. These cells have a very high rate of growth which can quickly destroy the normal cells. The primary types of glioma cancers are astrocytomas, ependymomas and oligodendrogliomas. Shin et al. [28] studied ways to improve the effectiveness of radiation in the treatment of cerebral malignant astrocytoma. Their study focused on the assessment of the effect of multiple daily fractionated radiation therapy with and without misonidazole. They concluded that the addition of misonidazole did not significantly improve the patients' survival. In this section we apply the hypertabastic accelerated failure time technique to model the survival time of a sample of 30 patients from the randomized trials of radiotherapy with and without the radiosensitizer misinidazole. The data was obtained from the Medical Research Council Working Party (MRC) on misonidazole in gliomas. This data is right censored and has been previously analyzed for the selection of variables by MRC [29]. Survival time was measured in days and the longest survival time was 1098 days. We compared radiotherapy treatment of brain cancer patients with radiosensitizer misonidazole to radiotherapy without misonidazole. Figure 5 shows a Kaplan-Meier plot of the estimated survival curves for both groups. The log-rank, Wilcoxon, and likelihood ratio tests are all non-significant, suggesting no significant difference between survival curves for the two groups. The Kaplan-Meier estimates of median survival time for radiotherapy with misonidazole group is 258.5 days and for the radiotherapy without misonidazole group is 488 days. The overall median survival time for both groups combined is 361 days. Using the Kaplan-Meier estimates of survival function, a plot of log-cumulative hazard function against the logarithm of the survival time for individuals in two groups indicates that the data is coming from a Weibul distribution. Knowing this information led us to evaluate the performance of the hypertabastic model. First, we fit a hypertabastic accelerated failure time model to analyze the brain cancer data. Then the hypertabastic accelerated failure time model is compared with Weibul, log-logistic, log-normal accelerated failure time models and the Cox proportional hazards model. This model incorporates a binary covariate coded as treatment = 1 for the type of radiotherapy with misonidazole, and as treatment = 0 for radiotherapy without misonidazole. The second covariate is the age of the patient. Thus, this model contains two covariates- treatment and age. We use the method of maximum likelihood to maximize hypertabastic accelerated failure time log-likelihood function for right censored data discussed in section 5. Table 3 gives a statistical summary for the glioma data. For instance, the hypertabastic estimated value for the coefficient of the variable radiosensitizer is 0.4387 with a standard error of 0.3437. The Wald and the likelihood ratio statistics associated with this variable are 1.6294 (p = 0.2018) and 1.6254 (p = 0.2023) respectively. Both tests indicate that the effect of individual variable radiosensitizer is non-significant. The estimated accelerator factor is 1.5507 (exponentiated value of parameter 0.4387). This means that after controlling for the age of the patient, the probability of a patient treated with "therapy with radiosensitizer misonidazole" surviving t days equals to the probability of a patient treated with "therapy without radiosensitizer misonidazole" surviving 1.5507 t days. For instance, the hypertabastic accelerated failure time model suggests that for 49 year old patients (median age for all patients under study), the probability of a patient treated with " therapy with radiosensitizer misonidazole " surviving 293 days equals to the probability of a patient treated with" therapy without radiosensitizer misonidazole " surviving 454 days. The Wald statistic for the age covariate is 22.18 (p < 0.0001).

Bottom Line: We then demonstrate the application of the hypertabastic survival model by applying it to data from two motivating studies.The first one demonstrates the proportional hazards version of the model by applying it to a data set from multiple myeloma study.Based on the results from the simulation study and two applications, the proposed model shows to be a flexible and promising alternative to practitioners in this field.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biostatistics, University of Arkansas for Medical Sciences, Little Rock, AR, USA. mtabatabai@cameron.edu

ABSTRACT
A new two-parameter probability distribution called hypertabastic is introduced to model the survival or time-to-event data. A simulation study was carried out to evaluate the performance of the hypertabastic distribution in comparison with popular distributions. We then demonstrate the application of the hypertabastic survival model by applying it to data from two motivating studies. The first one demonstrates the proportional hazards version of the model by applying it to a data set from multiple myeloma study. The second one demonstrates an accelerated failure time version of the model by applying it to data from a randomized study of glioma patients who underwent radiotherapy treatment with and without radiosensitizer misonidazole. Based on the results from the simulation study and two applications, the proposed model shows to be a flexible and promising alternative to practitioners in this field.

Show MeSH
Related in: MedlinePlus