A Semi-parametric Two-component “Compound” Mixture Model and Its Application to Estimating Malaria Attributable Fractions

Malaria remains a major epidemiological problem in many developing countries. Malaria is dened as the presence of parasites and symptoms (usually fever) due to the parasites. In endemic areas, an individual may have symptoms attributable either to malaria or to other causes. From a clinical point of view, it is important to correctly diagnose an individual who has developed symptoms so that the appropriate treatments can be given. From an epidemiologic and economic point of view, it is important to determine the proportion of malaria affected cases in individuals who have symptoms so that policies on intervention programmes can be developed. Once symptoms have developed in an individual, the diagnosis of malaria can be based on analysis of the parasite levels in blood samples. However, even a blood test is not conclusive as in endemic areas, many healthy individuals can have parasites in their blood slides. Therefore, data from this type of studies can be viewed as coming from a mixture distribution, with the components corresponding to malaria and nonmalaria cases. A unique feature in this type of data, however, is the fact that a proportion of the non-malaria cases have zero parasite levels. Therefore, one of the component distribu-tions is itself a mixture distribution. In this article, we propose a semi-parametric likelihood approach for estimating the proportion of clinical malaria using parasite level data from a group of individuals with symptoms. Our approach assumes the density ratio for the parasite levels in clinical malaria and non-clinical malaria cases can be modeled using a logistic model. We use empirical likelihood to combine the zero and non-zero data. The maximum semi-parametric likelihood estimate is more ecient than existing non-parametric estimates using only the frequencies of zero and non-zero data. On the other hand, it is more robust than a fully parametric maximum likelihood estimate that assumes a parametric model for the non-zero data. Simulation results show that the performance of the proposed method is satisfactory. The proposed method is used to analyze data from a malaria survey carried out in Tanzania.Attributable fraction; Density ratio model; Empirical likelihood; Malaria; Mixture methods.

Optimal Designs for Evaluating a Series of Treatments

Several articles in this journal have studied optimal designs for testing a series of treatments to identify promising ones for further study. These designs formulate testing as an ongoing process until a promising treatment is identified. This formulation is considered to be more realistic but substantially increases the computational complexity. In this article, we show that these new designs, which control the error rates for a series of treatments, can be reformulated as conventional designs that control the error rates for each individual treatment. This reformulation leads to a more meaningful interpretation of the error rates and hence easier specification of the error rates in practice. The reformulation also allows us to use conventional designs from published tables or standard computer programs to design trials for a series of treatments. We illustrate these using a study in soft tissue sarcoma

A Bayesian Decision Approach for Sample Size Determination in Phase II Trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study

Efficient augmented inverse probability weighted estimation in missing data problems

Singapore Management Universit

Testing intergroup concordance in ranking experiments with two groups of judges

Singapore MOE Academic Research Tier