Method and apparatus for positionally correcting data in a three dimensional array
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Abstract
An assay is performed such that a compendium of raw assay data is developed and is then positionally corrected. The assay comprises a plurality of longitudinally oriented plates p, each having a wells organized into rows i and columns j. Each well (i, j, p) has a raw value xijp associated therewith that is deconstructed into: a plate effect value representing extraneous effects attributable to the plate p of the well (i, j, p); a row effect value representing extraneous effects attributable to the row i on the plate p of the well (i, j, p); a column effect value representing extraneous effects attributable to the column j on the plate p of the well (i, j, p); a non-additive, interaction effect representing extraneous positional effects attributable to consistent positional effects beyond the plate, row, and column effects previously determined for the (i, j, p) well on plate p; and a residual data value that is left over once all the above extraneous effects are taken into account. Thereafter, the residual data value associated with each well (i, j, p) is employed to represent the well (i, j, p) as compared with all other wells (i, j, p) on the plate p.
4 Citations
58 Claims
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1-9. -9. (canceled)
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10. A method of positionally correcting raw assay data from an assay comprising a plurality of longitudinally oriented plates p, each plate p having a plurality of wells organized into rows i and columns j, each well (i, j, p) having a raw value xijp associated therewith, the raw values xijp comprising the raw assay data, the method comprising deconstructing each raw value xijp of an associated well (i, j, p) into:
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a plate effect value representing extraneous effects attributable to the plate p of the well (i, j, p);
a row effect value representing extraneous effects attributable to the row i on the plate p of the well (i, j, p);
a column effect value representing extraneous effects attributable to the column j on the plate p of the well (i, j, p);
a non-additive, interaction effect value representing extraneous positional effects attributable to consistent positional effects beyond the plate, row, and column effects previously determined for the (i, j, p) well on plate p; and
a residual data value that is left over once all the above extraneous effects are taken into account, the method further comprising employing the residual data value associated with each well (i, j, p) to represent the well (i, j, p) as compared with all other wells (i, j, p) on the plate p. - View Dependent Claims (11, 12, 13, 14, 15, 16)
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17. A method of positionally correcting raw assay data from an assay comprising a plurality of longitudinally oriented plates p, each plate p having a plurality of wells organized into rows i and columns j, each well (i, j, p) having a raw value xijp associated therewith, the raw values xijp comprising the raw assay data, the method comprising:
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resistantly fitting the raw value xijp for each well (i, j) for each plate p to a row-column additive model;
yijp=μ
p+R′
ip+C′
jp+eijp.
where;
yijp=the raw value for the well at row i and column j on plate p;
μ
p=an overall “
average”
for plate p;
R′
ip=a possible systematic measurement row offset for row i on plate p;
C′
jp=a possible systematic measurement column offset for column j on plate p; and
eijp=residual data without taking into account any non-additive interaction offset;
longitudinally (plate-wise) non-linearly smoothing each R′
ip and each C′
jp;
substituting each un-smoothed R′
ip and C′
jp value with a corresponding smoothed Rip and Cjp value and adjusting each residual value eijp to an adjusted e′
ijp;
yijp=μ
p+Rip+Cip+e′
ijp;
longitudinally (plate-wise) non-linearly smoothing each e′
ijp to result in;
yijp=μ
p+Rip+Cjp+smoothp(e′
ijp)+rijpwhere each e′
ijp is deconstructed into smoothp(e′
ijp), a possible systematic non-additive interaction offset for the (i, j) well on plate p, and rijp, residual data left over after taking into account any interaction offset;
wherein each rijp represents a true relative value of the corresponding well (i, j, p) as compared to all other wells (i, j, p) on the plate p. - View Dependent Claims (18, 19, 20, 21, 22, 23, 24)
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25. A computer having computer modules executing thereon for positionally correcting raw assay data from an assay comprising a plurality of longitudinally oriented plates p, each plate p having a plurality of wells organized into rows i and columns j, each well (i, j, p) having a raw value xijp associated therewith, the raw values xijp comprising the raw assay data, the modules comprising a first module deconstructing each raw value xijp of an associated well (i, j, p) into:
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a plate effect value representing extraneous effects attributable to the plate p of the well (i, j, p);
a row effect value representing extraneous effects attributable to the row i on the plate p of the well (i, j, p);
a column effect value representing extraneous effects attributable to the column j on the plate p of the well (i, j, p);
a non-additive, interaction effect representing extraneous positional effects attributable to consistent positional effects beyond the plate, row, and column effects determined for the (i, j, p) well on plate p; and
a residual data value that is left over once all the above extraneous effects are taken into account, the computer further comprising a second module employing the residual data value associated with each well (i, j, p) to represent the well (i, j, p) as compared with all other wells (i, j, p) on the plate p. - View Dependent Claims (26, 27, 28, 29, 30, 31, 32)
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33. A computer having computer modules executing thereon for positionally correcting raw assay data from an assay comprising a plurality of longitudinally oriented plates p, each plate p having a plurality of wells organized into rows i and columns j, each well (i, j, p) having a raw value xijp associated therewith, the raw values xijp comprising the raw assay data, the modules comprising:
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a first module resistantly fitting the raw value xijp for each well (i, j) for each plate p to a row-column additive model;
yijp=μ
p+R′
ip+C′
jp+eijp.
where;
yijp=the raw value for the well at row i and column j on plate p;
μ
p=an overall “
average”
for plate p;
R′
ip=a possible systematic measurement row offset for row i on plate p;
C′
jp=a possible systematic measurement column offset for column j on plate p; and
eijp=residual data without taking into account any non-additive interaction offset;
a second module longitudinally (plate-wise) non-linearly smoothing each R′
ip and each C′
jp;
a third module substituting each un-smoothed R′
ip and C′
jp value with a corresponding smoothed Rip and Cjp value and adjusting each residual value eijp to an adjusted e′
ijp;
yijp=μ
p+Rip+Cip+e′
ijp; and
a fourth module longitudinally (plate-wise) non-linearly smoothing each e′
ijp to result in;
yijp=μ
p+Rip+Cjp+smoothp(e′
ijp)+rijpwhere each e′
ijp is deconstructed into smoothp(e′
ijp), a possible systematic non-additive interaction offset for the (i, j) well on plate p and rijp residual data value left over after taking into account any non-additive interaction offset;
wherein each rijp represents a true relative value of the corresponding well (i, j, p) as compared to all other wells (i, j, p) on the plate p. - View Dependent Claims (34, 35, 36, 37, 38, 39, 40, 41)
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42. A computer-readable medium having computer-executable modules thereon for positionally correcting raw assay data from an assay comprising a plurality of longitudinally oriented plates p, each plate p having a plurality of wells organized into rows i and columns j, each well (i, j, p) having a raw value xijp associated therewith, the raw values xijp comprising the raw assay data, the modules comprising a first module for deconstructing each raw value xijp of an associated well (i, j, p) into:
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a plate effect value representing extraneous effects attributable to the plate p of the well (i, j, p);
a row effect value representing extraneous effects attributable to the row i on the plate p of the well (i, j, p);
a column effect value representing extraneous effects attributable to the column j on the plate p of the well (i, j, p);
a non-additive, interaction effect representing extraneous positional effects attributable to systematic positional effects beyond the plate, row, and column effects previously determined for the (i, j, p) well on plate p; and
a residual data value that is left over once all the above extraneous effects are taken into account, the computer further comprising a second module for employing the residual data value associated with each well (i, j, p) to represent the well (i, j, p) as compared with all other wells (i, j, p) on the plate p. - View Dependent Claims (43, 44, 45, 46, 47, 48, 49)
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50. A computer-readable medium having computer-executable modules thereon for positionally correcting raw assay data from an assay comprising a plurality of longitudinally oriented plates p, each plate p having a plurality of wells organized into rows i and columns j, each well (i, j, p) having a raw value xijp associated therewith, the raw values xijp comprising the raw assay data, the modules comprising:
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a first module for resistantly fitting the raw value xijp for each well (i, j) for each plate p to a row-column additive model;
yijp=μ
p+R′
ip+C′
jp+eijp.
where;
yijp=the raw value for the well at row i and column j on plate p;
μ
p=an overall “
average”
for plate p;
R′
ip=a possible systematic measurement row offset for row i on plate p;
C′
jp=a possible systematic measurement column offset for column j on plate p; and
eijp=residual data without taking into account any non-additive interaction offset;
a second module for longitudinally (plate-wise) non-linearly smoothing each R′
ip and each C′
jp;
a third module for substituting each un-smoothed R′
ip and C′
jp value with a corresponding smoothed Rip and Cjp value and adjusting each residual value eijp to an adjusted e′
ijp;
yijp=μ
p+Rip+Cip+e′
ijp; and
a fourth module for longitudinally (plate-wise) non-linearly smoothing each e′
ijp to result in;
yijp=μ
p+Rip+Cjp+smoothp(e′
ijp)+rijpwhere each e′
ijp is deconstructed into smoothp(e′
ijp), a possible systematic non-additive interaction measurement offset for the (i, j) well on plate p, and rijp, residual data left over after taking into account any interaction offset;
wherein each rijp represents a true relative value of the corresponding well (i, j, p) as compared to all other wells (i, j, p) on the plate p. - View Dependent Claims (51, 52, 53, 54, 55, 56, 57, 58)
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Specification