Doctor of Science, Harvard University
I much enjoy my research in biostatistics and the constant investigation of the many health questions to which biostatistics can provide an answer. Here follows a summary description of my main interests.
Quantile inference has been a major interest in my methodological and applied research in the recent past and is likely to be foremost in the near future. I first applied quantile regression to study the relationship between longitudinal changes in lung function and body mass index. My methodological research in this field has since branched out in several directions. In collaboration with other researchers I have explored a random-intercept linear model for quantile regression for the analysis of longitudinal and dependent data and later extended it to multi-dimensional random components. Ongoing work tackles some of the computational limitations of these methods and extensions to modeling geometric rates for assessing occurrence of events over time. I have also explored the use of regression methods in the estimation of quantiles of numeric bounded outcomes, ordinal outcomes, and continuous outcomes in the presence of random censoring.
Quantile regression has proved useful to help better understand health problems in a number of studies, such as effect modification of a genetic polymorphisms on cigarette smoking and pulmonary function; longitudinal weight gain and aging, physical activity, and lifestyle; fibrin resistance to lysis in patients with pulmonary hypertension; and reference values for lung function spirometric indexes.
One of my earliest interests in statistical methodology hinged on the study of a non regular scenario in likelihood-based asymptotic inference in which the Fisher information matrix is singular at some critical point in the parameter space. Over the years I have addressed several aspects of the problem and discussed relevant practical applications.
Supported by a grant of the National Institute of Health, I have worked on apply some results from the singular information problem in the estimation of surfaces of relative risk and applying them to clusters detection in small-area cancer studies. These are closely related to semi-parametric regression, in which I first became interested while deriving reference values for lung function in respiratory medicine. I have applied semi-parametric regression in several real problems as, for example, modeling the risk of cancer mortality associated with groundwater uranium over geographical areas.
Rotnitzky A, Cox DR, Bottai M, Robins JM. Likelihood-based asymptotic inference with singular information. Bernoulli 6(2): 243-284, 2000
Bottai M. Use of natural cubic splines for modeling pulmonary function in longitudinal epidemiological studies. Statistica, 61(1): 165-171, 2001
Bottai M. Confidence regions when the Fisher information is zero. Biometrika, 90(1): 73-84, 2003
Bottai M, Orsini N. Confidence intervals for the variance component of random-effects linear models. The Stata Journal, 4(4): 429-435, 2004
Geraci M, Bottai M. Use of auxiliary data in semiparametric regression with nonignorable missing responses. Statistical Modeling, 6(4): 321-336, 2006
Geraci M, Bottai M. Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics 8(1): 140-54, 2007
Bottai M, Geraci M, Lawson A. Testing for Unusual Aggregation of Health Risk in Semiparametric Models. Statistics in Medicine 27(15): 2902-2921, 2008
Liu Y, Bottai M. Mixed-effects models for conditional quantiles with longitudinal data, International Journal of Biostatistics, Vol. 5, Issue 1, Article 28, 2009
Bottai M. Quantile Regression, Encyclopedic Companion to Medical Statistics, 2nd edition, Everitt, B. and Palmer, C.(eds), Wiley & Sons, 2009
Bottai M, Cai B, McKeown ER. Logistic quantile regression for bounded outcomes. Statistics in Medicine, 29: 309-317, 2010
Bottai M, Zhang J. Laplace regression with censored data. Biometrical Journal, 52(4): 487-503, 2010
Bottai M. A regression method for modelling geometric rates. Statistical Methods in Medical Research. 2015, DOI: 10.1177/0962280215606474.
Frumento P, Bottai M. Parametric modeling of quantile regression coefficient functions. Biometrics. 2016, 72(1):74-84.