The transformed family of distributions are sometimes very useful to explore additional properties of the phenomenons which non-transformed (baseline) family of distributions cannot. In this paper, we introduce a new transformed model, called the unit-Gompertz (UG) distribution which exhibit right-skewed (unimodal) and reversed-J shaped density while the hazard rate has constant, increasing, upside-down bathtub and then bathtub shaped hazard rate. Some statistical properties of this new distribution are presented and discussed. Maximum likelihood estimation for the parameters that index UG distribution are derived along with their corresponding asymptotic standard errors. Monte Carlo simulations are conducted to investigate the bias, root mean squared error of the maximum likelihood estimators as well as the coverage probability. Finally, the potentiality of the model is presented and compared with three others distributions using two real data sets.

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Unit-Gompertz Distribution with Applications

Standard parametric survival models are commonly used to estimate long-term survival in oncology health technology assessments; however, they can inadequately represent the complex pattern of hazard functions or underlying mechanism of action (MoA) of immuno-oncology (IO) treatments. The aim of this study was to explore methods for extrapolating overall survival (OS) and provide insights on model selection in the context of the underlying MoA of IO treatments. Standard parametric, flexible parametric, cure, parametric mixture and landmark models were applied to data from ATLANTIC (NCT02087423; data cut-off [DCO] 3 June 2016). The goodness of fit of each model was compared using the observed survival and hazard functions, together with the plausibility of corresponding model extrapolation beyond the trial period. Extrapolations were compared with updated data from ATLANTIC (DCO 7 November 2017) for validation. A close fit to the observed OS was seen with all models; however, projections beyond the trial period differed. Estimated mean OS differed substantially across models. The cure models provided the best fit for the new DCO. Standard parametric models fitted to the initial ATLANTIC DCO generally underestimated longer-term OS, compared with the later DCO. Cure, parametric mixture and response-based landmark models predicted that larger proportions of patients with metastatic non-small cell lung cancer receiving IO treatments may experience long-term survival, which was more in keeping with the observed data. Further research using more mature OS data for IO treatments is needed.

/pdf/estimating-lifetime-benefits-associated-with-immuno-oncology-4ecbyu5jlh.pdf

Estimating Lifetime Benefits Associated with Immuno-Oncology Therapies: Challenges and Approaches for Overall Survival Extrapolations.

This paper uses a power transformation approach to introduce a three-parameter probability distribution which gives another extension of the Gompertz distribution known as “Power Gompertz distribution”. The statistical features of the power Gompertz distribution are systematically derived and studied appropriately. The three parameters of the new model are being estimated using the method of maximum likelihood estimation. The proposed distribution has also been compared to the Gompertz distribution using a real life dataset and the result shows that the Power Gompertz distribution has better performance than the Gompertz distribution and hence will be more useful and effective if applied in some real life situations especially survival analysis and cure fraction modeling just like the conventional Gompertz distribution.

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A Power Gompertz Distribution: Model, Properties and Application to Bladder Cancer Data

We propose a distribution called Odds Exponential Log Logistic Distribution (OELLD), which is an odds family of distribution. Its hazard rate is an increasing and decreasing function based on the value of the parameter. Explicit expressions for the ordinary moments, L-moments, quantile, generating functions, Bonferroni Curve, Lorenz Curve, Gini's index and order statistics are derived. The parameters of the proposed distribution are estimated by using maximum likelihood method and also illustrated by a lifetime data set.

Odds Exponential Log Logistic Distribution: Properties and Estimation

In this paper, we introduce a new continuous probability distribution with five parameters called the modified beta Gompertz distribution. It is derived from the modified beta-G generator proposed by Nadarajah, Teimouri and Shih (2014) and the Gompertz distribution. By investigating its mathematical and practical aspects, we prove that it is quite flexible and can be used effectively in modeling a wide variety of real phenomenon. Among others, we provide useful expansions of crucial functions, quantile function, moments, incomplete moments, moment generating function, en-tropies and order statistics. We discuss the estimation of the model parameters by the obtained maximum likelihood method. We also present a simulation study in order to test validity of maximum likelihood estimators. Finally, we illustrate the flexibility of the distribution by means of two applications to real data.

The Modified Beta Gompertz Distribution: Theory and Applications

In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution. We obtained some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.

/pdf/the-odd-generalized-exponential-gompertz-distribution-11qlf01fs2.pdf

The Odd Generalized Exponential Gompertz Distribution

In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution, We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood method is used for estimating the model parameters and the observed Fisher's information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.

/pdf/the-odd-generalized-exponential-gompertz-1yuyu1hwio.pdf

The Odd Generalized Exponential Gompertz

In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode are investigated. The method of maximum likelihood is used for estimating the model parameters. An applications to real data is carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.

M. E. Mustafa

Papers

The Odd Generalized Exponential Gompertz Distribution

The Odd Generalized Exponential Gompertz

The Odd Generalized Exponential Linear Failure Rate Distribution