ABSTRACT
Division of Biostatistics, University of California, Berkeley, California, USA
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
8.2 Formulation of Causal Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
8.2.1 Definition of Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
8.2.2 Identifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8.3 Estimation and Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
8.3.1 Overview of Targeted Minimum Loss-Based Estimation 206
8.3.2 Implementation of TMLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.3.2.1 Basic Ingredients . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.3.2.2 Description of Algorithm . . . . . . . . . . . . . . . . . . 211
8.3.3 Asymptotic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
8.4 Extension to the Case of Right-Censored Lifetimes . . . . . . . . . . . . . 215
8.4.1 Causal Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
8.4.2 Estimation and Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
198 Interval-Censored Time-to-Event Data: Methods and Applications
8.5 Alternative Target Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
8.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
8.7 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Appendix: Equivalence of Candidate Interventions on ∆m . . . . . . 227
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
The Adult Antiretroviral Treatment and Resistance Study, often referred to as
the Tshepo Study, was initiated in Botswana in 2002. It was the country’s first
large-scale trial of antiretroviral therapy in individuals infected with the Hu-
man Immunodeficiency Virus (HIV) or having developed the Human Acquired
Immunodeficiency Syndrome (AIDS). Its investigators aimed to evaluate the
potential for drug resistance and toxicity of six antiretroviral combination
therapies, and to determine the effectiveness of two proposed medication ad-
herence strategies. A total of 650 participants meeting inclusion criteria were
assigned to various treatment groups; treatment group allocation was ran-
domized and unblinded to participants. Study participants were followed for
a total of 3 years, with various measurements recorded on distinct sched-
ules. Basic clinical measures, including adherence assessments, were recorded
monthly. Disease progression measures, such as plasma CD4+ cell counts and
HIV RNA levels, were obtained bimonthly. Markers of drug toxicity were as-
sessed monthly for the first 6 months, bimonthly for the next 6 months, and
every 6 months subsequently. Further study details are provided elsewhere;
see, for example, Wester et al. (2010).
