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PubMed1996

The group sequential triangular test for phase II cancer clinical trials.

In cancer, phase II clinical trials are usually noncomparative. Their purpose is to determine whether a new chemotherapy is effective enough to warrant further evaluation in phase III. Therefore, in order to meet ethical requirements, decision-making methods must allow for early termination when inefficacy (or efficacy) is clear. We previously extended the Triangular Test, a group sequential method initially proposed for phase III trials, to phase II trials and demonstrated its advantages (i.e., type I error rate alpha and power close to the nominal values, reduction of the sample size) over other methods. The aim of this paper is to present the Triangular Test from a practical standpoint that will facilitate its application to phase II clinical trials in oncology. After summarizing the minimal theoretical knowledge required to use the method appropriately, we discuss its use in the design and analysis of a phase II cancer trial.

Algorithms↗
PubMed1998

Residential 222Rn exposure and lung cancer: testing the linear no-threshold theory with ecologic data.

In most rigorous epidemiologic studies, such as case-control and cohort studies, the basic unit of analysis is the individual. Each individual is classified in terms of exposure and disease status. However, in ecologic epidemiologic studies, the unit of analysis is some aggregate group of individuals. Summary measures of exposure and disease frequency are obtained for each aggregate, and the analyses focus on determining whether or not the aggregates with high levels of exposure also display high disease rates. The ecologic study design has major limitations, including ecologic confounding and cross level bias. Cohen has attempted to circumvent these limitations by invoking the linear no-threshold theory of radiation carcinogenesis to derive aggregate "exposures" from individual-level associations. He asserts that, "while an ecologic study cannot determine whether radon causes lung cancer, it can test the validity of a linear-no threshold relationship between them." Cohen compares his testing of the linear no-threshold relationship between radon exposure and lung cancer to the practice of estimating the number of deaths from the person-rem collective dose, dividing the person-rem by the number of individuals in the population to derive the individual average dose, and then determining individual average risk by dividing the number of deaths by the number of individuals in the population. We show that Cohen's erroneous assumptions concerning occupancy rates and smoking effects result in the use of the wrong model to test the linear no-threshold theory. Because of these assumptions, the ecologic confounding and cross level bias associated with Cohen's model invalidate his findings. Furthermore, when more recent Iowa county lung cancer incidence rates are regressed on Cohen's mean radon levels, the reported large negative associations between radon exposure and lung cancer are no longer obtained.

Air Pollutants, Radioactive↗
PubMed1998

Response to Lubin's proposed explanations of our discrepancy.

Lubin's proposal that a correlation between radon and smoking among individuals might explain the very large discrepancy between our data on U.S. counties and the prediction of linear no-threshold theory of radiation induced cancer is tested. It is shown that even correlations far beyond the limits of plausibility cannot explain an appreciable part of our discrepancy. On the other hand, Lubin is commended for proposing a definite potential explanation for our discrepancy that can be quantitatively tested for applicability to our analysis, and further such proposals are strongly invited. All other explanations of our discrepancy and all other reasons for not accepting our conclusions that are proposed in the Lubin paper are shown not to be applicable. The role of plausibility in epidemiological studies is discussed and shown to be all-important.

Air Pollutants, Radioactive↗
PubMed1998

Response to criticisms of Smith et al.

The various criticisms of our test of the linear no-threshold theory of radiation carcinogenesis in the paper by Smith et al. are considered and shown to be invalid. It is shown that there is no significant difference between the BEIR IV formula and the formula we use, that the uncertainties in effective average radon exposures in U.S. counties due to the issues they raise are not very large and that even if they were implausibly large, the results of our study would not be much affected. I review the seven essentially independent methods we used to estimate smoking prevalence, all of which give the same results but most of which, including the most important, were ignored by Smith et al.; explaining our results by uncertainties in smoking data would require correlations between radon and smoking that are grossly implausible. Our use of measurements of radon, smoking, and lung cancer rates from different time periods is justified, and it is shown that if more recent lung cancer rates are used, the results are not changed. Problems in comparing Iowa data with our study are discussed. It is shown that many of their criticisms of our study are more applicable to the case-control and cohort studies that they endorse. Many of their conclusions are presented without valid supporting evidence. A simple procedure is suggested that can easily settle any questions about the validity of our study; with this procedure, I offer to show that any other published ecological study might give invalid results. The point here is that our study is very different from all other published ecological studies.

Air Pollutants, Radioactive↗
PubMed1999

Generalized estimating equations for ordinal categorical data: arbitrary patterns of missing responses and missingness in a key covariate.

We propose methods for regression analysis of repeatedly measured ordinal categorical data when there is nonmonotone missingness in these responses and when a key covariate is missing depending on observables. The methods use ordinal regression models in conjunction with generalized estimating equations (GEEs). We extend the GEE methodology to accommodate arbitrary patterns of missingness in the responses when this missingness is independent of the unobserved responses. We further extend the methodology to provide correction for possible bias when missingness in knowledge of a key covariate may depend on observables. The approach is illustrated with the analysis of data from a study in diagnostic oncology in which multiple correlated receiver operating characteristic curves are estimated and corrected for possible verification bias when the true disease status is missing depending on observables.

Biometry↗