<p>Balanced allocation design is considered as paramount interest in the field of biomedical research and clinical trials. It has been analytically established that, ‘balanced allocation’ with regard to equality of covariate means over two treatment groups (referred to as ‘covariate mean balance’) is necessary and sufficient condition of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41096_2024_228_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">$D-$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>D</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41096_2024_228_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$A-$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41096_2024_228_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">$D_{s}-$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>D</mi> <mi>s</mi> </msub> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41096_2024_228_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">$A_{s}-$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>A</mi> <mi>s</mi> </msub> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>optimality. Practically, when several important covariates with different multi-level factors are arbitrarily distributed among the experimental units, an exhaustive search is required to attain balancing for each level of covariates, especially if number of units corresponds to any level of covariates are lesser than the number of treatment groups. Very few studies are discussed on such allocation problem considering optimality.A new search algorithm has been proposed in this context and compared to the existing Wu’s (1981) algorithm through real life examples and simulation studies and found efficient than that.</p>

An Efficient Search Algorithm to Achieve Balanced Allocation Design for Known Categorical Covariates into Multiple Treatment Groups

期刊论文
发表日期：

2025年1月31日

查看全文

Parantap Nag,
Pratibha Karki,
Samrat Hore

摘要

Balanced allocation design is considered as paramount interest in the field of biomedical research and clinical trials. It has been analytically established that, ‘balanced allocation’ with regard to equality of covariate means over two treatment groups (referred to as ‘covariate mean balance’) is necessary and sufficient condition of $D-$ $D -$ , $A-$ $A -$ , $D_{s}-$ $D_{s} -$ and $A_{s}-$ $A_{s} -$ optimality. Practically, when several important covariates with different multi-level factors are arbitrarily distributed among the experimental units, an exhaustive search is required to attain balancing for each level of covariates, especially if number of units corresponds to any level of covariates are lesser than the number of treatment groups. Very few studies are discussed on such allocation problem considering optimality.A new search algorithm has been proposed in this context and compared to the existing Wu’s (1981) algorithm through real life examples and simulation studies and found efficient than that.