Two-Treatment Crossover Designs for Estimating a Variety of Effects

Kershner, Ronald P.; Fédérer, Walter T.

doi:10.1080/01621459.1981.10477693

Cited by 92 publications

(19 citation statements)

References 6 publications

(9 reference statements)

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“…David and Kempton (1996) offered interesting and sensible advice about a local form of interference in which the treatment given to one plot in an agricultural experiment can also affect adjacent plots. Although the terms "interference" and "SUTVA" are not typically used, interference that is local in time is widely discussed in crossover studies and is addressed by models for "residual effects," say the lingering effect of the treatment given in the immediately preceding time interval (see, e.g., Grizzle 1965;Kershner and Federer 1981). Methods designed to model local interference are quite useful in some settings, but interference produced by social interaction, the spread of disease, or permanent change due to learning is not typically limited to adjacent or nearby units.…”

Section: Existing Methods For Interference In Experimentsmentioning

confidence: 99%

Interference Between Units in Randomized Experiments

Rosenbaum

2007

Journal of the American Statistical Association

306

269

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In a randomized experiment comparing two treatments, there is interference between units if applying the treatment to one unit may affect other units. Interference implies that treatment effects are not comparisons of two potential responses that a unit may exhibit, one under treatment and the other under control, but instead are inherently more complex. Interference is common in social settings where people communicate, compete, or spread disease; in studies that treat one part of an organism using a symmetrical part as control; in studies that apply different treatments to the same organism at different times; and in many other situations. Available statistical tools are limited. For instance, Fisher's sharp null hypothesis of no treatment effect implicitly entails no interference, and so his randomization test may be used to test no effect, but conventional ways of inverting the test to obtain confidence intervals, say for an additive effect, are not applicable with interference. Another commonly used approach assumes that interference is of a simple parametric form confined to units that are near one another in time or space; this is useful when applicable but is of little use when interference may be widespread and of uncertain form. Exact, nonparametric methods are developed for inverting randomization tests to obtain confidence intervals for magnitudes of effect assuming nothing at all about the structure of the interference between units. The limitations of these methods are discussed. To illustrate the general approach, two simple methods and two simple empirical examples are discussed. Extension to randomization based covariance adjustment is briefly described.

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Section: Existing Methods For Interference In Experimentsmentioning

confidence: 99%

Interference Between Units in Randomized Experiments

Rosenbaum

2007

Journal of the American Statistical Association

306

269

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“…These designs have been devised by several research workers: Williams (1949Williams ( , 1950, Patterson (1950), Patterson and Lucas (1962), Barenblut (1964), Saha (1970), Lawless (1971), Sharma (1975), Kershner and Federer (1981), Pigeon and Raghavarao (1987), Chowdhury (1987) and Varghese et al (2000) etc. are few of them.…”

Section: Introductionmentioning

confidence: 99%

An Incomplete Block Change-Over Design Balanced for First and Second-Order Residual Effect

Chowdhury

Rois

2013

JAS

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“…(2002), Laska and Meisner (1985), Kushner (1997aKushner ( , 1997bKushner ( , 1998, studied universally optimal designs. Mathews (1987Mathews ( , 1990, Kershner, and Federer, (1981) and Kushner (1997a) examined optimal designs of two treatments and gave optimal designs for 3 and 4 years in the case where the model errors are correlated. Finally, Azzalini and Giovagnoli (1987) and Williams and John (2007) are some of the researchers who dealt with the case of correlated errors.…”

Section: Introductionmentioning

confidence: 99%

Two Treatment Repeated Measurement Designs With Uncorrelated Observations: A Compact Review

Chalikias¹

2017

JAS

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Abstract. Afsarinejad (1975,1978) introduced the model for repeated measurement designs without interactions which was the basis for the next researchers. We present the optimal designs for the direct and carry over effect of the model for 2,3, and 4 periods. Moreover, universally optimal designs, Φ optimal and balanced designs are also presented based on the conditions of Cheng and Wu (1980) and Chalikias and Kounias (2012).Keywords: Repeated Measurements designs, direct effects, carry-over effects, universally optimality IntroductionRepeated Measurements designs (or Cross-over designs or Change-over designs) are experimental designs where one of the t treatments is applied to one experimental unit for each of the 2 m ≥ different periods.If n is the number of experimental units, the design is denoted by RMD (t, n, m), where t is the number of treatments and m the number of periods. Balaan (1965) is the first who considered the case of two periods in the model with treatment-period interaction. Some early papers in the field of design optimality from Kiefer and Wolfowitz (1960), Silvey and Titterington (1973) and Wynn (1977), Afsarinejad (1975, 1978) studied the case of universally optimal designs and balanced designs. Cheng and Wu (1980) examined universally optimal and strongly balanced designs. Carriere, K. C. & Huang, R. (2000) considered two period designs for clinical trials Kunert (1983Kunert ( , 1984aKunert ( , 1984bKunert ( , 1991, Kunert, I. and Stufken. J. (2002), Laska and Meisner (1985), Kushner (1997aKushner ( , 1997bKushner ( , 1998, studied universally optimal designs. Mathews (1987, 1990), Kershner, and Federer, (1981) and Kushner (1997a) examined optimal designs of two treatments and gave optimal designs for 3 and 4 years in the case where the model errors are correlated. Finally, Azzalini and Giovagnoli (1987) and Williams and John (2007) are some of the researchers who dealt with the case of correlated errors.The review papers of Stufken (1996) and Jones and Kenward (2014) as and the book of Diggle and Kenword 1994 give useful information and a plethora of reports on the subject. Definitions-Utility-ModelIn this design we are interested in the estimation of the direct effects, i.e. the effect of every treatment in the period which is applied, and the estimation of the carry over effects (or residual effect), i.e. the effect of every treatment in the period following the implementation period. Certainly a treatment may have an effect two periods later, but we will examine only the case of first order residual effects. The Repeated Measurements Designs (RMDs) have several advantages:  It takes only experimental n (experimental units) for nxm observations  If the variability within each experimental unit is less than the variability between experimental units, then RMDs give accurate estimates of some variables.  RMDs are used in clinical trials or in the pharmaceutical industry, where the purpose is the improvement of chronic diseases and not the cure. The disadvantages are:  The durati...

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Two-Treatment Crossover Designs for Estimating a Variety of Effects

Cited by 92 publications

References 6 publications

Interference Between Units in Randomized Experiments

Interference Between Units in Randomized Experiments

An Incomplete Block Change-Over Design Balanced for First and Second-Order Residual Effect

Two Treatment Repeated Measurement Designs With Uncorrelated Observations: A Compact Review

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