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Biostatistics develops and applies statistical inference to biological and health questions. Its problems include designing experiments, comparing treatments, measuring biological variation and analyzing survival or repeated observations. The experimental unit must match the independent unit of information: multiple measurements of one organism need not substitute for measurements of multiple organisms.

Suppose a randomized study observes an event in 10 of 100 treated participants and 20 of 100 controls. The estimated risk difference is $0.10-0.20=-0.10$, while the estimated relative risk is $0.10/0.20=0.5$. These express different scales of comparison, and neither alone expresses its uncertainty. Assignment, follow-up and the definition of the event determine what effect can be estimated. For incomplete follow-up, methods from survival analysis distinguish observing no event yet from establishing that an event will never occur.

Germán Rodríguez works on statistical methods for population research. His Princeton teaching and research site connects generalized linear models, survival analysis and demographic questions about event timing. The site's biographical note identifies his training in biostatistics and his work in population research.^[ref]

His Survival Models by Germán Rodríguez explains how survival functions and hazard functions encode the same event-time distribution in different ways. With right censoring, an event observed at $t$ contributes density $f(t)$, whereas an observation ending without an event contributes $S(t)$. Writing the contribution as $S(t)h(t{)}^{\delta }$, with event indicator $\delta \in \{0,1\}$, makes that distinction explicit. These likelihood conventions let incomplete follow-up inform estimation without treating a censored time as an observed failure.^[ref]

John Carlin develops biostatistics for health and medical research, including methods for missing data and causal inference. His institutional profiles describe work on multiple imputation and the need to specify the scientific purpose of an analysis before choosing a regression model.^[ref][ref]

With multiple imputation, several plausible completed datasets represent uncertainty about unobserved values. Their analyses must account both for uncertainty within a completed dataset and for variation between completed datasets. This makes the assumptions about the missing values visible in the analysis. Carlin is a coauthor of Bayesian Data Analysis by Andrew Gelman and others.^[ref]

Robert Tibshirani develops methods for statistical learning and biostatistics, with applications to genomics and medicine. His Stanford research profile connects methodological work with scientific data and computational tools.^[ref]

With Jerome H. Friedman and Trevor Hastie, he developed the Graphical Lasso for estimating a sparse precision matrix. An absolute-value penalty encourages zero entries, which encode conditional independence relationships in a multivariate normal distribution. The method combines a statistical model with an efficient optimization algorithm.^[ref]

Xi Luo develops biostatistics and machine learning methods for biomedical data. His institutional profile identifies applications in neuroscience, genomics and disease research.^[ref]

With Tony Cai and Weidong Liu, he developed CLIME for sparse precision matrix estimation. The method constrains the error of an approximate inverse of the sample covariance matrix and minimizes an entrywise absolute-value objective. Its computation separates into columnwise linear programs.^[ref]