Validation of the Smooth Test of Goodness-of-Fit for Proportional Hazards in Cancer Survival Studies

In this study, we validate the smooth test of goodness-of-fit for the proportionality of the hazard function in the two-sample problem in cancer survival studies. The smooth test considered here is an extension of Neyman's smooth test for proportional hazard functions. Simulations are conducted to compare the performance of the smooth test, the data-driven smooth test, the Kolmogorov-Smirnov proportional hazards test and the global test, in terms of power. Eight real cancer datasets from different settings are assessed for the proportional hazard assumption in the Cox proportional hazard models, for validation. The smooth test performed best and is independent of the number of covariates in the Cox proportional hazard models

Scaling land and water technologies in Tanzania: Opportunities, challenges and policy implications

The scaling of land and water technologies has widely increased across different parts of the world; and is recognized as important for ecological systems. These technologies contribute to sustainable management of watersheds on which agriculture, food production and rural livelihoods for most developing communities depend upon. There are ongoing efforts designed to halt land degradation in the Western Usambara which have arisen from pressure on land resources mainly caused by demographic growth, deforestation and the abandoning of the traditional regenerative land use and farming systems. Socio-cultural and economic factors such as education level, age, gender, and land tenure, marital status and income earnings of smallholder farmers are factors considered important in the adoption of land and water management practices. Environmental factors were also identified as limiting factors to smallholder farmers in soil-water management practices. Such factors involved physical distance, slope, type of crops grown and farm sizes. Insecure land tenure especially among women limits their adoption of the technologies. Technological complexity of the technology (farmers prefer technology that are less complex and easier to use), preference for less labor intensive technology, required capital, land ownership (less adoption in new technology on hired/leased land), approach of introducing the technology (preference of participatory bottom up approach), and motivation and the involvement of farmers from conceptualization to implementation are factors that impact adoption of technologies between farmers. Unsustainable cultivation in catchments and destruction of water sources in Tanzania is limiting the flow of water on which some of water use technologies directly depend. In some areas where farmers and pastoralists co-exist, conflicts always arise from grazing on farmland, with destruction to water infrastructure. In recognition of the need for sustainable management of land and water, and the increasing conflicts over use of resources by different sectors, Tanzania has enacted several policies. The irrigation policy calls for the improvement of irrigation water use efficiency and effectiveness by promoting closed conduit systems and high efficiency methods such as drip irrigation and promotion of efficient water utilization technologies such as the System of Rice Intensification. There is need for harmonization and linkage of land and water management and the policies to avoid conflicts. Whereas for example the customary land law recognizes the right to land entailing some resources therewith, the water law does not recognize such customary right by granting the ownership right to water by the owner of land on which the water resource is found. There is need for adequate mechanisms for enforcing policies, regulations and by-laws. Local water governance institutions such as water user associations are important for sustainable scaling of land and water technologies. Horizontal and vertical scaling of the land and water technologies depends on factors such as facilitation of registration of water user associations and empowering them; implementing projects based on actual ground conditions for ease of adoption by communities; and involvement of the local government. Strengthening linkages between relevant institutions and their respective roles and responsibilities also require to be clearly defined. Promotion of land and water technologies should not be gender-blind but rather ensure participation of women and youth in the training and implementation. An integrated systems approach is needed to address the multi-faceted challenges in sustainable land and water management, and a focus on the entire value chain activities; from input supply to output market

A Smooth Test of Goodness-of-Fit for the Baseline Hazard Function for Time-to-First Occurrence in Recurrent Events: An Application to HIV Retention Data

Motivated by HIV retention, we present an application of the smooth test of goodness-of-fit under right-censoring to time to first occurrence of a recurrent event. The smooth test applied here is an extension of Neyman's smooth test to a class of hazard functions for the initial distribution of a recurrent failure-time event. We estimate the baseline hazard function of time-to-first loss to follow-up, using a Block, Borges and Savits (BBS) minimal repair model of the data (n = 2,987,72% censored). Simulations were conducted at various percentages of censoring to assess the performance of the smooth test. Results show that the smooth test performed well under right-censoring

A Smooth Test of Goodness-of-Fit for the Weibull Distribution: An Application to an HIV Retention Data

In this study, we fit the two-parameter Weibull distribution to an HIV retention data and assess the fit using a smooth test of goodness-of-fit. The smooth test described here is a score test and is derived as an extension of the Neyman's smooth test. Simulations are conducted to compare the power of the smooth test with the power of each of three empirical goodness-of-fit tests for the Weibull distribution. Results show that the smooth tests of order three and four are more powerful than the three empirical goodness-of-fit tests. For validation, we used retention data from an HIV care setting in Kenya

A smooth test of goodness-of-fit for the baseline hazard function in recurrent event models

Conference paperIn this paper, we formulate a smooth test of goodness-of-fit for a simple hypothesis about the baseline hazard function in recurrent-event models. The formulation is an extension of Neyman' s goodness-of-fit approach, whose score tests are obtained by embedding the null hypothesis in a larger class of hazard rate functions. Since the application is in recurrent event models , the data is dynamic.A useful feature about this test is the parametric approach that makes inference about the hazard function more efficient. To examine the finite-sample properties of this test, we used simulated data . For validation, we applied the test to a real-life recurrent event data. Results show that the test possesses better power over wide range of alternatives, when compared with similar tests of the chi-square type in the literature.In this paper, we formulate a smooth test of goodness-of-fit for a simple hypothesis about the baseline hazard function in recurrent-event models. The formulation is an extension of Neyman' s goodness-of-fit approach, whose score tests are obtained by embedding the null hypothesis in a larger class of hazard rate functions. Since the application is in recurrent event models , the data is dynamic.A useful feature about this test is the parametric approach that makes inference about the hazard function more efficient. To examine the finite-sample properties of this test, we used simulated data . For validation, we applied the test to a real-life recurrent event data. Results show that the test possesses better power over wide range of alternatives, when compared with similar tests of the chi-square type in the literature

Application of Semi-Markov Process For Model Incremental Change in HIV Staging with Cost Effect

In the recent past, both non-parametric and parametric approaches have consistently been used to model cost effectiveness in a variety of health applications. This study applies the semi-Markov model while presenting the sojourn time with well-defined probability distributions. We employed the Weibull distribution to model the hazard function for each of the defined transition paths. We defined three distinct states of the semi-Markov process using the quantity of HIV virus in the blood of an HIV-infected person i.e., viral load (VL) copies in a milliliter (copies/mL). The three states were defined; VL < 200 copies/mL, 200 copies/mL < VL < 1,000 copies/mL, VL > 1,000 copies/mL and an absorbing state which is naturally death. We also developed a cumulative cost function, purposely to determine the average estimated cost per patient in each of the defined states. Incremental Cost Effectiveness Ratio (ICER) was utilized in the analysis of cost-effectiveness while comparing two program strategies i.e., Patients under the differentiated care model (DCM) and those who are not considered to be in any model of differentiated care during their respective ongoing clinical follow up. Results show the mean cost of the patients for each state 1, 2, and 3 was $765,$ 829, and $1,395 respectively. More so, the computed ICER ratio was$ 484/life-year-saved. In conclusion, the cost of keeping patients in state 1 (on DCM) was relatively cheaper and more efficient compared to the other states

Validation of the smooth test of goodness-of-fit for proportional hazards in Cancer survival studies

Paper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.In this study, we validate the smooth test of goodness-of-fit for the proportionality of the hazard function in the two-sample problem in cancer survival studies. The smooth test considered here is an extension of Neyman’s smooth test for proportional hazard functions. Simulations are conducted to compare the performance of the smooth test, the data-driven smooth test, the Kolmogorov-Smirnov proportional hazards test and the global test, in terms of power. Eight real cancer datasets from different settings are assessed for the proportional hazard assumption in the Cox proportional hazard models, for validation. The smooth test performed best and is independent of the number of covariates in the Cox proportional hazard models.Strathmore University University of South Carolina-Upstat

Smooth tests of goodness of FIT for hazard Functions: an application to HIV retention data

Thesis submitted in total fulfillment of the requirements for the degree of Doctor of Philosophy in Applied Statistics at Strathmore UniversityIn this study, we apply the methodology of smooth tests of goodness-of-fit to hazard functions. The smooth test formulation applied here is an extension of Neyman’s smooth test and is obtained by nesting the null hypothesis in a larger class of probability and hazard rate functions. The study revisits Neyman’s smooth tests and its data-driven versions in the context of classical probability and survival analysis. Though several authors have theoretically looked at the development of Neyman’s smooth tests, the main contribution of this study is modelling loss to follow-up in HIV retention. To the best of our knowledge, this issue has not been given its due share of coverage in the literature. We extend methods proposed by Rayner et al. (2009); Pena (1998a,b) and Kraus (2007a), to an HIV retention setting. The applications dealt with in this thesis also covers performance of other goodness-of-fit (GOF) approaches and compares them with that of smooth tests. Three main methodological approaches are covered under the research methodology. Part I revisits smooth tests for various probability distributions and applies the test when assessing the fit for the two-parameter Weibull distribution to an HIV retention data under the complete and uncensored data scenario. Part II looks at the application of smooth test to Cox proportional hazards models. We assess the proportionality assumption in the two sample problem in cancer survival studies. Part III covers recurrent event situation. We fit Block, Borges and Savits (BBS) minimal repair model to loss to follow-up (LFTU) data and assesses the performance of the smooth test in terms of power.More specifically, Chapter 1 deals with background of GOF in classical probability and survival distributions. The motivation for the study, overview of the smooth test of GOF and comparison with other GOF tests is also covered in this chapter. In Chapter 2, we provide a review of the literature. Chapter 3 details research methodology. We present analysis and results in Chapter 4. Chapter 5 discusses important findings using simulated and real data in the context of HIV retention and overall survival in cancer studies. Chapter 6 covers summary of the thesis, the limitations of the study and possible extensions of the smooth GOF to discrete probability cases. All computations have been implemented in R and the scripts are briefly described in Appendix A. The chapters are self-contained in order to achieve our objective of covering the applications smooth tests of goodness-of-fit approach from distributions with noncensored data to extensions in recurrent events.A major limitation of this study, is that, in clinical studies, particularly involving LTFU data, incomplete data is frequently encountered. Analysis of severity of data incompleteness is a subject of future research

Data driven longitudinal model with application to HIV differentiated care

Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, KenyaDifferentiated care is a new innovative approach for managing HIV/AIDS where ART treatment services are customized by staggering patient’s visits for stable status while reducing unnecessary burdens on the health system. Through provision of differentiated care, the health system can reallocate resources to patients most in need who are failing treatment. The main objective of this study is to develop a data-driven longitudinal model which is applicable to HIV differentiated care. Method: We used routine data of HIV positive patients initiated to ART at the point of care from 4 medical facilities in Nairobi in the year 2018. Since both the GLMM and GEE are extensions of the GLM, we start with a brief overview of GEE then relooked at extensions of GLMM. We specify f (u) and g(p) to be dependent on the type of response Yi . For a binary Yi, we consider f (u) as Bernoulli distribution and g(p) as the logit function, g(u) — log resulting to GLM is the logistic regression. Results show the binary response which was differentiated care category fits well with GLMM. We also found TB-HIV co-infection to be the only significant predictor of differentiated care under both GEE and GLMM.Institute of Mathematical Sciences, Strathmore University, Nairobi, Kenya. School of Mathematics, University of Nairobi, Nairobi, Kenya