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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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a) Hypertabastic 3D survival curve with variables time and Log (BUN) for multiple myeloma data; b) Hypertabastic 3D survival curve with variables time and HGB for multiple myeloma data.
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Figure 4: a) Hypertabastic 3D survival curve with variables time and Log (BUN) for multiple myeloma data; b) Hypertabastic 3D survival curve with variables time and HGB for multiple myeloma data.

Mentions: Multiple myeloma is a cancer formed by abnormal white blood cells, called malignant plasma cells. A malignant monoclonal plasma cell is called plasmacytoma. If the disease spreads throughout multiple bone marrow sites in the body, it is called multiple myeloma. This disease weakens a patient's immune system and is usually difficult to cure. To investigate the performance of the hypertabastic proportional hazards model and to compare it with Cox, Weibull, log-logistic and log-normal models, we analyze a cancer data set obtained from a study conducted by Krall et al. [27]. The data contains information on 65 patients with multiple myeloma in which the patients were treated with alkylating agents. This drug is designed to interfere with the cell's DNA and inhibits cancer cell growth. Of these 65 patients, only 17 survived the duration of the study. The data is right-censored and the survival time from the date of diagnosis is measured in months. The covariates have been measured at diagnosis and the covariate list consists of a logarithm of white blood cell count, serum calcium, presence or absence of Bence Jones protein, proteinuria, gender, age, percent myeloid cells in peripheral blood, percent lymphocytes in peripheral blood, logarithm of percent plasma cells in bone marrow, total serum protein, presence or absence of infection, serum globin, logarithm of blood urea nitrogen, fractures, platelets, and hemoglobin. Our first task is to select risk factors that are statistically significant. To accomplish this task we use the hypertabastic log-likelihood function for proportional hazards model and follow the general variable selection strategy outlined by Collet [4]. We also examine the possibility of interactions. The two most significant risk factors that we found are the logarithm of blood urea nitrogen and hemoglobin. Using the stepwise regression, we fit the Cox proportional hazards model. The Kaplan-Meier survival curve for multiple myeloma data is shown in figure 2. The Cox regression did identify the same variables as the most significant prognostic factors. Table 2 gives results for the hypertabastic and the four comparison models. It shows that the -2log-likelihood and AIC statistics are lowest for the hypertabastic model when fitted to the multiple myeloma data. This indicates that the hypertabastic proportional hazards model fits the multiple myeloma data best. The most significant single variable identified by the hypertabastic model is the logarithm of blood urea nitrogen with an estimated chi-square value of 11.11 (p = 0.0014). The second significant variable is hemoglobin. All other models have identified these two variables as the most significant ones. The mean levels of patients' hemoglobin and the logarithm of blood urea nitrogen are 10.20 and 1.39 respectively. At this level, the median survival time for the hypertabastic, log-normal, log-logistic, Weibull and Cox are 20.04, 19.29, 21.01, 21.92 and 19 months respectively. Figures 3a and 3b show the graph of hypertabastic hazard and survival functions for multiple myeloma data. Figure 3a clearly shows that the hypertabastic hazard function is an increasing function of time. By examining figure 3b, we realize that for patients with a Log (BUN) reading of 1.39 and a hemoglobin level of 10.20 there is about a10% chance of survival beyond 65 months. At the above mentioned mean levels for the hemoglobin and logarithm of blood urea nitrogen, the hypertabastic hazard function shows that the failure rate (hazard) reaches its maximum velocity in about 5.15 months. At this point the disease progression has its highest speed (Figure 3c). Figures 4a and 4b show the 3-dimensional graphs for survival of multiple myeloma patients as functions of time and Log(BUN), as well as time and HGB. Other models under consideration had monotone increasing hazard functions (graphs not shown).


Hypertabastic survival model.

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

a) Hypertabastic 3D survival curve with variables time and Log (BUN) for multiple myeloma data; b) Hypertabastic 3D survival curve with variables time and HGB for multiple myeloma data.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: a) Hypertabastic 3D survival curve with variables time and Log (BUN) for multiple myeloma data; b) Hypertabastic 3D survival curve with variables time and HGB for multiple myeloma data.
Mentions: Multiple myeloma is a cancer formed by abnormal white blood cells, called malignant plasma cells. A malignant monoclonal plasma cell is called plasmacytoma. If the disease spreads throughout multiple bone marrow sites in the body, it is called multiple myeloma. This disease weakens a patient's immune system and is usually difficult to cure. To investigate the performance of the hypertabastic proportional hazards model and to compare it with Cox, Weibull, log-logistic and log-normal models, we analyze a cancer data set obtained from a study conducted by Krall et al. [27]. The data contains information on 65 patients with multiple myeloma in which the patients were treated with alkylating agents. This drug is designed to interfere with the cell's DNA and inhibits cancer cell growth. Of these 65 patients, only 17 survived the duration of the study. The data is right-censored and the survival time from the date of diagnosis is measured in months. The covariates have been measured at diagnosis and the covariate list consists of a logarithm of white blood cell count, serum calcium, presence or absence of Bence Jones protein, proteinuria, gender, age, percent myeloid cells in peripheral blood, percent lymphocytes in peripheral blood, logarithm of percent plasma cells in bone marrow, total serum protein, presence or absence of infection, serum globin, logarithm of blood urea nitrogen, fractures, platelets, and hemoglobin. Our first task is to select risk factors that are statistically significant. To accomplish this task we use the hypertabastic log-likelihood function for proportional hazards model and follow the general variable selection strategy outlined by Collet [4]. We also examine the possibility of interactions. The two most significant risk factors that we found are the logarithm of blood urea nitrogen and hemoglobin. Using the stepwise regression, we fit the Cox proportional hazards model. The Kaplan-Meier survival curve for multiple myeloma data is shown in figure 2. The Cox regression did identify the same variables as the most significant prognostic factors. Table 2 gives results for the hypertabastic and the four comparison models. It shows that the -2log-likelihood and AIC statistics are lowest for the hypertabastic model when fitted to the multiple myeloma data. This indicates that the hypertabastic proportional hazards model fits the multiple myeloma data best. The most significant single variable identified by the hypertabastic model is the logarithm of blood urea nitrogen with an estimated chi-square value of 11.11 (p = 0.0014). The second significant variable is hemoglobin. All other models have identified these two variables as the most significant ones. The mean levels of patients' hemoglobin and the logarithm of blood urea nitrogen are 10.20 and 1.39 respectively. At this level, the median survival time for the hypertabastic, log-normal, log-logistic, Weibull and Cox are 20.04, 19.29, 21.01, 21.92 and 19 months respectively. Figures 3a and 3b show the graph of hypertabastic hazard and survival functions for multiple myeloma data. Figure 3a clearly shows that the hypertabastic hazard function is an increasing function of time. By examining figure 3b, we realize that for patients with a Log (BUN) reading of 1.39 and a hemoglobin level of 10.20 there is about a10% chance of survival beyond 65 months. At the above mentioned mean levels for the hemoglobin and logarithm of blood urea nitrogen, the hypertabastic hazard function shows that the failure rate (hazard) reaches its maximum velocity in about 5.15 months. At this point the disease progression has its highest speed (Figure 3c). Figures 4a and 4b show the 3-dimensional graphs for survival of multiple myeloma patients as functions of time and Log(BUN), as well as time and HGB. Other models under consideration had monotone increasing hazard functions (graphs not shown).

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