THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Most questions in social and biomedical sciences are causal in nature: what would happen to individuals, or to groups, if part of their environment were changed? In this groundbreaking text, two world-renowned experts present statistical methods for studying such questions. This book starts with the notion of potential outcomes, each corresponding to the outcome that would be realized if a subject were exposed to a particular treatment or regime. In this approach, causal effects are comparisons of such potential outcomes. The fundamental problem of causal inference is that we can only observe one of the potential outcomes for a particular subject. The authors discuss how randomized experiments allow us to assess causal effects and then turn to observational studies. They lay out the assumptions needed for causal inference and describe the leading analysis methods, including, matching, propensity-score methods, and instrumental variables. Many detailed applications are included, with special focus on practical aspects for the empirical researcher.

Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction

https://www.nber.org/system/files/working_papers/w22595/w22595.pdf

Understanding and misunderstanding randomized controlled trials.

Comprehensive Textbook of Psychiatry.

The acute clinical manifestations of COVID-19 have been well characterized1,2, but the post-acute sequelae of this disease have not been comprehensively described. Here we use the national healthcare databases of the US Department of Veterans Affairs to systematically and comprehensively identify 6-month incident sequelae—including diagnoses, medication use and laboratory abnormalities—in patients with COVID-19 who survived for at least 30 days after diagnosis. We show that beyond the first 30 days of illness, people with COVID-19 exhibit a higher risk of death and use of health resources. Our high-dimensional approach identifies incident sequelae in the respiratory system, as well as several other sequelae that include nervous system and neurocognitive disorders, mental health disorders, metabolic disorders, cardiovascular disorders, gastrointestinal disorders, malaise, fatigue, musculoskeletal pain and anaemia. We show increased incident use of several therapeutic agents—including pain medications (opioids and non-opioids) as well as antidepressant, anxiolytic, antihypertensive and oral hypoglycaemic agents—as well as evidence of laboratory abnormalities in several organ systems. Our analysis of an array of prespecified outcomes reveals a risk gradient that increases according to the severity of the acute COVID-19 infection (that is, whether patients were not hospitalized, hospitalized or admitted to intensive care). Our findings show that a substantial burden of health loss that spans pulmonary and several extrapulmonary organ systems is experienced by patients who survive after the acute phase of COVID-19. These results will help to inform health system planning and the development of multidisciplinary care strategies to reduce chronic health loss among individuals with COVID-19. Healthcare data from the US Department of Veterans Affairs are used to characterize the six-month incident sequelae of individuals who survive for at least thirty days after developing COVID-19.

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High-dimensional characterization of post-acute sequelae of COVID-19.

Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights—the balancing weights—that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases. General large-sample results on nonparametric estimation based on these weights are derived. We further propose a new weighting scheme, the overlap weights, in which each unit’s weight is proportional to the probability of that unit being assigned to the opposite group. The overlap weights are bounded, and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing wei...

/pdf/balancing-covariates-via-propensity-score-weighting-59wdv72r5m.pdf

Balancing Covariates via Propensity Score Weighting

Randomized experiments are the "gold standard" for estimating causal effects, yet often in practice, chance imbalances exist in covariate distributions between treatment groups. If covariate data are available before units are exposed to treatments, these chance imbalances can be mitigated by first checking covariate balance before the physical experiment takes place. Provided a precise definition of imbalance has been specified in advance, unbalanced randomizations can be discarded, followed by a rerandomization, and this process can continue until a randomization yielding balance according to the definition is achieved. By improving covariate balance, rerandomization provides more precise and trustworthy estimates of treatment effects.

Rerandomization to improve covariate balance in experiments

Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights---the balancing weights---that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases. General large-sample results on nonparametric estimation based on these weights are derived. We further propose a new weighting scheme, the overlap weights, in which each unit's weight is proportional to the probability of that unit being assigned to the opposite group. The overlap weights are bounded, and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing weights. The overlap weights also possess a desirable small-sample exact balance property, based on which we propose a new method that achieves exact balance for means of any selected set of covariates. Two applications illustrate these methods and compare them with other approaches.

Randomized experiments are the “gold standard” for estimating causal effects, yet often in practice, chance imbalances exist in covariate distributions between treatment groups. If covariate data are available before units are exposed to treatments, these chance imbalances can be mitigated by first checking covariate balance before the physical experiment takes place. Provided a precise definition of imbalance has been specified in advance, unbalanced randomizations can be discarded, followed by a rerandomization, and this process can continue until a randomization yielding balance according to the definition is achieved. By improving covariate balance, rerandomization provides more precise and trustworthy estimates of treatment effects.

/pdf/rerandomization-to-improve-covariate-balance-in-experiments-47u2ld3q4a.pdf

When conducting a randomized experiment, if an allocation yields treatment groups that differ meaningfully with respect to relevant covariates, groups should be rerandomized. The process involves specifying an explicit criterion for whether an allocation is acceptable, based on a measure of covariate balance, and rerandomizing units until an acceptable allocation is obtained. Here, we illustrate how rerandomization could have improved the design of an already conducted randomized experiment on vocabulary and mathematics training programs, then provide a rerandomization procedure for covariates that vary in importance, and finally offer other extensions for rerandomization, including methods addressing computational efficiency. When covariates vary in a priori importance, better balance should be required for more important covariates. Rerandomization based on Mahalanobis distance preserves the joint distribution of covariates, but balances all covariates equally. Here, we propose rerandomizing based on Ma...

Kari Lock Morgan

Papers

Balancing Covariates via Propensity Score Weighting

Rerandomization to improve covariate balance in experiments

Balancing Covariates via Propensity Score Weighting

Rerandomization to improve covariate balance in experiments

Rerandomization to Balance Tiers of Covariates