Rerandomization and optimal matching

On average, randomization achieves balance in covariate distributions between treatment groups; yet practice, chance imbalance exists post randomization, which increases the error estimating effects. This is an important issue, especially cluster randomized trials, where experimental units (the clusters) are highly heterogeneous and relatively few number. To address this, several restricted designs have been proposed to on a covariates of particular interest. More recently, approaches involving rerandomization that aim achieve simultaneous prognostic factors. In this article, we comment some properties rerandomized propose new design for comparing two or more treatments. combines optimal nonbipartite matching subjects together with rerandomization, both aimed at minimizing measure distance elements blocks reductions mean squared estimated Compared existing alternatives, can substantially reduce effect. enhanced efficiency evaluated theoretically empirically, robustness also noted. The generalized three arms. En moyenne, la randomisation parvient à équilibrer les des covariables entre groupes de traitement. Cependant, dans pratique, un déséquilibre aléatoire subsiste après randomisation, ce qui entraîne une augmentation l'erreur l'estimation effets du Ce phénomène revêt grande importance, en particulier le contexte essais randomisés grappes, où unités expérimentales (les grappes) sont très hétérogènes et relativement peu nombreuses. Pour pallier cette problématique, plusieurs modèles restreinte ont été proposés afin d'obtenir équilibre sur quelques d'intérêt spécifiques. Plus récemment, approches impliquant ré-randomisation avancées but d'atteindre simultané facteurs pronostiques majeurs. Les auteurs cet article analysent certaines propriétés présentent nouveau plan visant comparer deux traitements ou plus. schéma combine appariement non-bipartite sujets avec ré-randomisation, tous minimiser mesure éléments blocs réduire quadratique moyenne estimations Comparé aux alternatives existantes, proposé permet manière significative l'effet traitement estimé. L'efficacité améliorée méthode évaluée fois théorique empirique, prenant également compte ses robustesse. De plus, généralisé pour inclure trois bras We consider problems treatments be compared using given set available study. These may quite heterogeneous, even though random assignment balances over heterogeneity any considerable interest, effects then confounded effect (Student, 1938; Rosenbaum & Rubin, 1984; Ming Rosenbaum, 2000; Greevy al., 2004; Hansen, Hansen Bowers, 2008; Bruhn McKenzie, 2009; Krieger, Azriel Kapelner, 2019). One approach through blocking so as examine within-block comparisons control most covariates. Especially when study small there many covariates, effectiveness such reduced (Cochran Cox, 1992; Imai, King Nall, Imbens Athey, 2016). question arises how best carry out experiment minimize potential biases occur obtain precise estimate possible. For purpose, role repeated basic idea being will repeatedly randomize choose gives high degree balance. repeating when, by chance, serious has topic discussion years; example, see Cox (1982). However, building into recent. Rubin (2008) suggested rerandomizing until total samples meets prespecified target, (2009) number times choosing minimizes groups. Morgan (2012, 2015) Xu Kalbfleisch (2010, 2013) considered various aspects problem. Each paper suggests inference should based tests each iteration replicates gave rise data. fact, noted there, analyses t -test, do not take account invalid yield very conservative results. situation all units, along their associated time trial prior randomization. There applications these methods. A primary area application trials (CRTs). commonly used assessing educational public health strategies groups individuals, schools, towns, classrooms, randomly assigned CRT individuals possible naturally group rather than individual. Our interest subject first rose our involvement INSTINCT trial, designed improve ischemic stroke patients emergency departments education. were hospitals widely varying characteristics could affect outcomes Such discussed places; recent reference Hurley (2020). second major pragmatic clinical applied populations. realistic settings typical controlled trials. Again, variable, methods accounting variation important. See Ford Norrie (2016) excellent It noted, however, apply accession time, although it instances extend ideas situation. 2 N randomized, simple case balanced since simplifies notation, general cases developed similar way. i th vector p X , = 1 … . assume independently identically distributed (i.i.d.) covariance matrix ∑ Z represents corresponds 0 control. response Y interested τ E ( | ) − assumed same subjects. focus attention testing null hypothesis no would possible, necessary considered, formulate terms outcomes. ^ ¯ T C where, / average responses those control, respectively. As well known, unbiased estimator that, under standard conditions, approximately normal variance estimated. Given specific substantial among components thus bias. Improvements estimation achieved stratification force Previous work attempted problem ways. (2012) measuring treated satisfied difference means sufficiently small. specifically, they Mahalanobis (MD) D ⊤ obtained multiplier chosen Chi-square distribution degrees freedom if multivariate normal. < refer design/approach MR design. An alternative simply rerandomize fixed times, say M minimum distance. modified referred MMR Either results complicated was 2013), who defined match weighted (BMW) follows: From fit binary logistic regression observed propensity score observation. Blocks (in pairs) bipartite order scores assignments blocks. With matched pairs, ordering them from smallest largest. problems, combinatorial mathematics (Bandelt, Crama Spieksma, 1994; Burkard, Dell'Amico Martello, 2012). BMW design, pairs use score, intended arising weighting arose considering just pursue direction article. analysis too conservative, valid data collected way test. appropriate analyze resulting without rerandomization. particular, parametric nonparametric incorrect potentially detail (2013). Table 4 compares test shows substantial. inference, utilize induced process sampling process. Li, Ding (2018) Li (2020) asymptotic approximate distribution, useful large samples. third approach, (NB) al. (2004). arrange within pairs. known NB algorithms readily available, Beck, Lu (2022). creates size much across full Once formed, pair proceed conceptually works analysis. extended groups, retaining incomplete block (Lu Greevy, 2022). (2013) method nearly non-tripartite higher matchings considerably efficient. suggest approach. pairing obtained, determine respective values select (RNB) retains advantage whole while balancing overall protects against temporal constraints demand introducing experimenter one team involved applying treatment, say. Some theoretical regarding described above normally true model linear error. case, natural measured are, course, strong assumptions and, make non-normal (or sample) matrix. Thus, gains need simulations report Section 5. calculations presented here, give insights available. what follows, following result, does seem explicitly before: Lemma 1.If ∼ Q Cov q Proof.Figure graphical view this. ellipsoid If follows Further, easy Note result holds elliptical finite matrix, replaced 1, unnecessarily outcome. Suppose, 10 total, only 6 nonzero parameters. penalty opposed additional rerandomizations precision. 5000 included about value 50 coefficients. mentioned earlier, MD smaller preassigned (2018), authors satisfy P 001 attain bound 1000. required randomizations 3000 probability 0.05. other hand, choice 1000 depending shown 1. percentiles realizations seen similar. Fixing larger one-quarter considered. Unfortunately, allow (2004), numerical made CR matching, 7% improvement distribution. paired greater. evaluate representative next section. comparisons, miss which, before, allows adjust differ Nall discuss advantages context studies argue forcefully its central role. RNB difficult assess analytically assessed 4. section henceforth, longer require normality term. power requires generating sample determining whether rejected α 05 say) previous paragraph. power. different hypotheses typically calculated time. Also, power, purpose save computation. Nonetheless, extensive computing facility needed. ideal parallel. carried simulation compare (Xu Kalbfleisch, 2010), (Greevy 2004), aims square (MSE) variables specify MD, and/or present. μ =0 ϵ