# statistics

## Causal inference with latent variables for unmeasured confounding

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, Statistical analyses of high-throughput sequencing data are often made difficult due to the presence of unmeasured sources of technical and biological variation. Examples of potentially unmeasured technical factors are the time and date when individual samples were prepared for sequencing, as well as which lab personnel performed the experiment.

## Causal mediation analysis for exposure mixtures

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, After the lectures on tmle3shift and tmle3mediate, we’re wondering if a different procedure for mediation analysis could work. Consider a data-generating system for $O = (W, A, Z, Y)$, where $W$ represents three binary covariates, $A$ is a binary exposure of interest, $Z$ are three binary mediators, and $Y$ is a continuous outcome.

## Data-adaptively learning strata-specific causal effects

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, I have a question about applying CV-TMLE to a current research project. I have a cross-sectional dataset from Bangladesh, where the outcome of interest is antenatal care use (binary), the exposure of interest is women’s empowerment (continuous), and the baseline covariates include mother’s age, child’s age, mother and father’s education, number of members in household, number of children under 15, household wealth, and maternal depression.

## Tuning the highly adaptive lasso estimator

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, In chapter 6 of your 2018 book Targeted Learning in Data Science, co-authored with Sherri Rose, you discuss the practical necessity of reducing the number of basis functions incorporated into the highly adaptive lasso (HAL) estimator when the number of covariates grows.

## Applying targeted learning to improve global health equity

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, A pressing issue in the field of global public health is equitable ownership of data and results in terms of both authorship and representation. In some aspects, targeted learning improves equity by bolstering our ability to efficiently draw causal inferences from global health data.

## Machine learning for conditional density estimation

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, I was curious in general about approaching problems that involve machine learning-based estimation of densities rather than scalar quantities (i.e., regression), particularly for continuous variables. As a grounding example, for continuous treatments in the TMLE framework one needs to estimate $P(A \mid W)$, where $A$ is a continuous random variable.

## TMLE of a treatment-specific multivariate survival curve

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, I have a survival analysis question. I am working with a dataset that is left- and right-truncated. I am interested in estimating the treatment-specific multivariate survival function of a time-to-event variable. For example, a study where subjects have been randomized to two different treatment groups with baseline covariates $W$, but we only observe the outcome – time at death – for a left- and right-truncated window.

## Conditions for asymptotic efficiency of TMLE

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, I have a question regarding the requirements for asymptotic efficiency of TMLE. Asymptotic efficiency of TMLE relies on the second-order remainder being negligible. Is this purely a finite-sample concern, or are there potentially parameters of interest where this isn’t true by construction?

## Causal inference with left-censoring and left-truncation

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, As epidemiologists, we wish to study the relationship between time-varying exposure and disease progression over time. A natural choice of study design would be the longitudinal cohort study. In prospective cohorts, participants are not selected from existing data, but enrolled during some enrollment period.

## Stochastic treatment regimes in practice

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, We were discussing practical implementations of stochastic treatment regimes and came up with the following questions we would like to hear your thoughts about. Question 1 (Practical positivity): Is there a recommended procedure for deciding truncation threshold with respect to shifts in the framework of stochastic treatment regimes?

## Feature engineering with large datasets

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, In the article about why we need a statistical revolution at the beginning of the tlverse book, you discuss the “Art” of statistics, and describe a scenario where confounders for a logistic regression are chosen and characterized in such a way to yield a statistically significant result, potentially after multiple iterations that produce an estimate that is not significant.

## Super learning and interaction terms in models

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, I have a question about the step in the Super Learning framework where interaction terms can be added between certain covariates. Is there a principled way to decide what interactions terms should be added from the data alone, or do all interaction specifications have to be based on prior knowledge of the system in question?

## Adaptive designs with continuous treatments

This post is part of our Q&A series. A question from graduate students in our Spring 2021 offering of the new course “Targeted Learning in Practice” at UC Berkeley: Question: Hi Mark, You’ve got me thinking about selecting optimal experiments in the context of shift interventions. For the example we talked about in class, in order to avoid positivity violations, we define shift interventions such that an individual’s value of the intervention node $A$ is shifted by a specified amount $\delta$ unless there is no support for such a shift based on the covariates $W$, in which case $A$ is shifted to the maximum value available for that $W$.

## Estimating effects based upon community-level interventions and optimal interventions

This post is part of our Q&A series. A question from graduate students in our Fall 2020 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, We have been discussing questions regarding community-based interventions and we would like to hear your input on the following three questions: When we estimate the causal effects of community-based interventions, we can use baseline variables to block the effect of the environment on the outcome, so that we can change the problem into individual levels.

## Using a data-adaptive target parameter and CV-TMLE in survival analysis

This post is part of our Q&A series. A question from graduate students in our Fall 2020 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, Within the field of industrial hygiene and occupational epidemiology there is interest in linking possible occupational exposures to deleterious health outcomes, most usually various cancers. Obviously in such a setting, it is nearly impossible without individual chemical biomarkers to have causal identifiability for a specific exposure (for example lead, pesticides, benzene, etc.

## Using time-varying covariates in evaluating the causal effect of a single time point intervention

This post is part of our Q&A series. A question from graduate students in our Fall 2020 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, We have an observational study with fixed baseline intervention, $A$ for statin use vs. no statin use, along with baseline covariates, $L$ such as age, gender, marital status, hypertension, diabetes, hypercholesterolemia, coronary artery disease. Our goal is to predict conversion to the more impaired stage of Alzheimer’s disease.

## TMLE for multi-level treatments and methods for sensitivity analysis

This post is part of our Q&A series. A question from graduate students in our Fall 2020 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, We had two questions for you, 1. How to apply TMLE to treatment with multiple levels and conduct inference? For example, if the potential outcomes are $Y_i(0), Y_i(1), \ldots, Y_i(K)$ for $K$ different possible treatments, i.e., possible values for $A_i$ are from $1$ to $K$, how would TMLE work?

## Estimating causal effects with instrumental variables in survival analysis

This post is part of our Q&A series. A question from graduate students in our Fall 2020 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, In survival analysis, what methods should we use to estimate counterfactuals and causal effect if the conditional independence assumption is violated? For instance, the instrumental variable method in econometrics and Mendelian randomization in biostatistics deal with the unmeasured confounding problem.

## Two-stage sampling and survival analysis

This post is part of our Q&A series. A question from graduate students in our Fall 2019 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, We are wondering under your framework, how to deal with a situation when only right-censored data has a full set of covariates, while the covariates for the non-right-censored data are largely missing. To be specific, we want to find the relation between peoples’ matching property and their marriage durations.

## Estimating the sample average treatment effect under effect modification in a cluster randomized trial

This post is part of our Q&A series. A question from graduate students in our Fall 2019 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, We were wondering about the application of TMLE and superlearner to cluster-randomized study designs, and the adoption of the sample average treatment effect (SATE) as an efficient estimator. From our understanding, although the SATE is not formally identifiable in a finite setting, it is nevertheless an efficient estimate due to its asymptotic behavior (TMLE for the population effect is asymptotically linear and has an asymptotically conservative variance estimator).

## Longitudinal causal model under obscured time-ordering

This post is part of our Q&A series. A question from graduate students in our Fall 2019 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, Suppose we have a longitudinal data structure where information about the intervention and time-varying covariate is collected simultaneously, and their temporal ordering is obscured. For instance, data is collected at monthly health checkups, where $A(t)$ is the subject’s healthy eating habits in the past month, and $L(t)$ is the occurrence of heartburn in the past month.

## Positivity assumption violations and TMLE for longitudinal data with many time-varying covariates

This post is part of our Q&A series. A question from graduate students in our Fall 2019 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, For longitudinal data such as $O=(L_0,A_0,Y_0,L_1,A_1,Y_1,L_2,A_2,Y_2,\ldots )$, we can use G-computation formula with sequential regression method if we treat time $t$ as discrete variable. And you also mentioned that there are more general methods which can deal with the case when $t$ is continuous.

## Simultaneous inference with the Kaplan-Meier estimator of survival

This post is part of our Q&A series. A question from graduate students in our Fall 2019 offering of “Biostatistical Methods: Survival Analysis and Causality” at UC Berkeley: Question: Hi Mark, First of all, I have doubts regarding the simultaneous confidence interval for Kaplan- Meier, since I am not necessarily interested in inference for a parameter. I would like > to know if the 95% confidence band for my KM estimator will hold using the same formula > we did in our R lab without covariates (taken from lectures).

## CV-TMLE and double machine learning

This post is part of our Q&A series. A question from Twitter on choosing between double machine learning and TMLE with cross-validation: https://twitter.com/emaadmanzoor/status/1208924841316880385 Question: @mark_vdlaan Is there an applied researcher’s guide to choosing between double machine learning and TMLE + cross-fitting? PS: Thanks for making these methods and resources so easily accessible! Answer: Thanks for this interesting question. In the past several years, the interest in these machine learning-based estimators has become more widespread, since they allow for the statistical answer to a question to be framed in terms of scientifically meaningful parameters (e.

## Prediction intervals using the TMLE framework

This post is part of our Q&A series. A question from graduate students in our Spring 2019 offering of “Targeted Learning in Biomedical Big Data” at Berkeley: Question: Hi Mark, We are curious about how to use TMLE and influence curves for estimation and inference when the target parameter is a conditional expectation, rather than a scalar. Specifically, suppose I have a data structure $O = (W, Y) \sim P_0$, and sample $n$ times i.

## Applications of TMLE in infectious disease research

This post is part of our Q&A series. A question from graduate students in our Spring 2019 offering of “Targeted Learning in Biomedical Big Data” at Berkeley: Question: Hi Mark, Thanks for teaching this class. It’s been an amazing experience. I have a few questions related to my own research. In infectious disease studies, modeling attempts to create models that estimate protection conferred from vaccination or previous history of infection (natural immunity).

## Adaptive algorithm selection via the Super Learner

This post is part of our Q&A series. A question from graduate students in our Spring 2019 offering of “Targeted Learning in Biomedical Big Data” at Berkeley: Question: Hi Mark, A couple questions I have are about super learning and the strength of the learners as well as potentially adaptively choosing learners. Is there any advantage, theoretical or practical, of having a large library of weaker learners over a small library of stronger learners?

## TMLE versus the one-step estimator

This post is part of our Q&A series. A question from graduate students in our Spring 2019 offering of “Targeted Learning in Biomedical Big Data” at Berkeley: Question: Hi Mark, Is there any theoretical guarantees about relative performances between TMLE and the one-step estimator in finite sample conditions? Thanks, H.R.B. Answer: Hi H.R.B., Finite sample guarantees are very hard to obtain. One can obtain finite-sample confidence intervals by, for example, not relying on a CLT but on finite-sample inequalities for sample means (e.

## Imputation and missing data in the TMLE framework

This post is part of our Q&A series. A question from graduate students in our Spring 2019 offering of “Targeted Learning in Biomedical Big Data” at Berkeley: Question: Hi Mark, For a longitudinal data set if we have missing data, we might want to impute the values with MICE imputation (multiple imputation with chain equations). Can we use TMLE together with multiple imputation? How can we combine the results of all the multiple imputed datasets into a final result and obtain valid inference?

## Adaptive designs and optimal subgroups

This post is part of our Q&A series. A question from graduate students in our Fall 2018 offering of “Special Topics in Biostatistics – Adaptive Designs” at Berkeley: Question: Hi Mark, We were interested in your opinion on few topics that have come up in class a few times. If we isolate an optimal subgroup, we can, perhaps, answer interesting questions about, say, drug efficacy (as in, does this drug work for anybody as opposed to on average?

## Competing risks and non-pathwise differentiable parameters

This post is part of our Q&A series. A question from two graduate students in our Fall 2017 offering of “Survival Analysis and Causality” at Berkeley: Question: Hi Mark, Below are [two] questions [we thought might interest you]. Looking forward to your thoughts on these! Best, S.D. and I.M. Most competing risk analyses assume that the competing risks are independent of one another. What would be your advice on handling the same style of survival data when the occurrence of one of the competing events is informative of the occurrence of the other?

## Leave-p-out Cross-validation

This post is part of our Q&A series. A question from two graduate students in our Fall 2017 offering of “Survival Analysis and Causality” at Berkeley: Question: Hi Mark, [We] were wondering what the implications were for selecting leave one observation out versus leave one cluster out when performing cross-validation on a longitudinal data structure. We understand that computational constraints may render leave-one-out cross-validation to be undesirable, however are we implicitly biasing our model selection by our choice in cross-validation technique?

## Welcome to Mark's Blog

Welcome! This is the research blog of Mark van der Laan. Over the last few years, communication in science has evolved; indeed, many exciting and inspiring research-related ideas are now first communicated informally, with blog posts and the like, before formal publication in academic journals. Blog posts provide an excellent medium through which interesting ideas can be communicated quickly and concisely. We plan to use this blog to share ideas, tips, and examples from our research – and to establish an open dialogue with researchers around the world.