Inference for Constrained Estimation of Tumor Size Distributions

In order to develop better treatment and screening programs for cancer prevention programs, it is important to be able to understand the natural history of the disease and what factors affect its progression. We focus on a particular framework first outlined by Kimmel and Flehinger (1991, Biometrics , 47, 987–1004) and in particular one of their limiting scenarios for analysis. Using an equivalence with a binary regression model, we characterize the nonparametric maximum likelihood estimation procedure for estimation of the tumor size distribution function and give associated asymptotic results. Extensions to semiparametric models and missing data are also described. Application to data from two cancer studies is used to illustrate the finite-sample behavior of the procedure.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65536/1/j.1541-0420.2008.01001.x.pd

Temporal analysis of airborne particulate matter reveals a dose-rate effect on mortality in El Paso: indications of differential toxicity for different particle mixtures

One of two topics explored is the limitations of the daily average in summarizing pollutant hourly profiles. The daily average of hourly measurements of air pollutant constituents provides continuity with previous studies using monitoring technology that only provided the daily average. However, other summary statistics are needed that make better use of all available information in 24-hr profiles. The daily average reflects the total daily dose, obscuring hourly resolution of the dose rate. Air pollutant exposures with comparable total daily doses may have very different effects when occurring at high levels over a few hours as opposed to low levels over a longer time. Alternative data-based choices for summary statistics are provided using principal component analysis to capture the exposure dose rate, while preserving ease of interpretation. This is demonstrated using the earliest hourly particle concentration data available for El Paso from archived records of particulate matter (PM)10. In this way, a significant association between evening PM10 exposures and nonaccidental daily mortality is found in El Paso from 1992 to 1995, otherwise missed using the daily average. Secondly, the nature and, hence, effects of particles in the ambient aerosol during El Paso sandstorms is believed different from that of particles present during stillair conditions resulting from atmospheric temperature inversions. To investigate this, wind speed (ws) is used as a surrogate variable to label PM10 exposures as Low-ws (primarily fine particles), High-ws (primarily coarse particles), or Mid-ws (a mixture of fine and coarse particles). A High-ws evening is significantly associated with a 10% lower risk of mortality on the succeeding third day, as compared with comparable exposures at Low- or Mid-ws. Although this analysis cannot be used to form firm conclusions because it uses a very small data set, it demonstrates the limitations of the daily average and suggests differential toxicity for different particle compositions

Do not weight for heteroscedasticity in nonparametric regression

The potential role of weighting in kernel regression is examined. The concept that weighting has something to do with heteroscedastic errors is shown to be false. However, weighting does affect bias, and ways in which this might be exploited are indicated

Using a continuous time lag to determine the associations between ambient PM2.5 hourly levels and daily mortality

journal articleThe authors are interested in understanding the possible association between exposure to short-term fine particulate matter (PM2.5) peaks that have changing physical characteristics throughout the day and observable health outcomes (daily mortality). To this end, modern statistical methods are used here that allow for a continuous time lag between hourly PM2.5 mass concentration and daily mortality. The functional linear regression model was used to study how hourly PM2.5 mass of past days continuously influences the daily mortality count of the current day. Using a Poisson likelihood with the canonical link, the authors found that a 10- g/m3 increase in the hourly PM2.5 above the hourly average is associated with 1.7% (0.1, 3.4), 2.4% (1.2, 3.7), 1.6% (0.6, 2.7), and 0.8% ( 0.2, 1.8) higher risk of mortality on the same day, next day, 2 days, and 3 days later, respectively. The increase in relative risk is statistically significant for lags of 0-2 days, but not at lag 3. The highest association between PM2.5 mass concentration and daily mortality was found to occur in the morning when both mass and PM number concentrations peak at approximately 8:00 a.m. (lag of 15, 39, and 63 hr). This morning time interval corresponds to automobile traffic rush hour that coincides with a morning atmospheric inversion that traps high concentrations of nanoparticles