Technical Appendix
Analysis of positive biopsy rate, NRL vs. UPL
Student’s unpaired t test with unequal variances
P value
0.9736
P value summary
ns
Significantly different? (P < 0.05)
No
One- or two-tailed P value?
Two-tailed
t=0.03396
Welch-corrected t, df
df=10.17
How big is the difference?
Mean ± SEM of column UPL
Mean ± SEM of column NRL
Difference between means
95% confidence interval
R square
0.4027 ± 0.005083 N=7
0.4030 ± 0.007990 N=7
0.0003216 ± 0.009470
-0.02073 to
0.02137
0.000113
F test to compare variances
F,DFn, Dfd
P value
P value summary
Significantly different? (P < 0.05)
2.471, 6, 6
0.2954
ns
No
Model comparison
Null H. Population means identical
Alternative H: Distinct population
means
Ratio of probabilities
Difference in AICc
SS
0.003767
DF
13
0.003767
12
Probability it is
correct
83.94%
16.06%
5.227
-3.308
Specimen Vials/Biopsy, NRL vs. UPL, 2005-11
Student’s unpaired t test with unequal variances
0.0432
P value
P value summary
*
Significantly different? (P < 0.05)
Yes
One- or two-tailed P value?
Two-tailed
Welch-corrected t, df
t=2.305 df=10.28
How big is the difference?
Mean ± SEM of column A
Mean ± SEM of column B
Difference between means
95% confidence interval
R square
F test to compare variances
F,DFn, Dfd
P value
P value summary
Significantly different? (P < 0.05)
Model comparison
Null H. Population means identical
Alternative H: Distinct population
means
Ratio of probabilities
Difference in AICc
9.030 ± 0.4115 N=7
10.16 ± 0.2666 N=7
1.130 ± 0.4903
0.04192 to 2.219
0.3408
2.383, 6, 6
0.3146
ns
No
SS
14.57
DF
13
10.1
12
Probability it is correct
28.66%
71.34%
2.489
1.824
Trends in Specimen Vials/Biopsy, Total
Best-fit values
Slope
Y-intercept when X=0.0
X-intercept when Y=0.0
1/slope
95% Confidence Intervals
Slope
Y-intercept when X=0.0
X-intercept when Y=0.0
Goodness of Fit
R square
Sy.x
Is slope significantly non-zero?
F
DFn, DFd
P value
Deviation from zero?
Data
Number of X values
Maximum number of Y replicates
Total number of values
Number of missing values
Equation
0.6492 ± 0.04726
-1294 ± 94.83
1993
1.540
0.3712 ± 0.01052
-735.8 ± 21.14
1982
2.694
0.4458 to 0.8526
-1702 to -885.7
1987 to 1996
0.2375 to 0.5049
-1004 to -467.2
1967 to 1990
0.9895
0.1057
0.9992
0.01488
188.7
1.000, 2.000
0.0053
Significant
1245
1.000, 1.000
0.0180
Significant
4
1
4
3
Y = 0.6492*X - 1294
3
1
3
4
Y = 0.3712*X - 735.8
Are the slopes equal?
F = 14.6822. DFn=1 DFd=3
P=0.03132
If the overall slopes were identical, there is a 3.1% chance of randomly choosing data points with slopes
this different. You can conclude that the differences between the slopes are significant.
Because the slopes differ so much, it is not possible to test whether the intercepts differ significantly.
Difference in Specimen Vials/Biopsy, Total, 2005-08 and 2009-11
Unpaired t test with Welch's correction
P value
P value summary
Significantly different? (P < 0.05)
One- or two-tailed P value?
Welch-corrected t, df
How big is the difference?
Mean ± SEM of column A
Mean ± SEM of column B
Difference between means
95% confidence interval
R square
F test to compare variances
F,DFn, Dfd
P value
P value summary
Significantly different? (P < 0.05)
Model comparison
Null H. Population means identical
Alternative H: Distinct population means
Ratio of probabilities
Difference in AICc
0.0336
*
Yes
Two-tailed
t=3.07 df=4.32
8.82 ± 0.421 N=4
10.3 ± 0.214 N=3
1.45 ± 0.473
0.177 to 2.73
0.686
5.15, 3, 2
0.3339
ns
No
SS
6.02
2.41
DF
6
5
Probability it is correct
57.20%
42.80%
1.34
-0.580
Trends in Specimen Vials/Biopsy, NRL
Best-fit values
Slope
Y-intercept when X=0.0
X-intercept when Y=0.0
1/slope
95% Confidence Intervals
Slope
Y-intercept when X=0.0
X-intercept when Y=0.0
Goodness of Fit
R square
Sy.x
Is slope significantly non-zero?
F
DFn, DFd
P value
Deviation from zero?
Data
Number of X values
Maximum number of Y
replicates
Total number of values
Number of missing values
Equation
NRL, 2005-8
NRL, 2009-11
0.2454 ± 0.008718
-483.3 ± 17.52
1969
4.075
0.7109 ± 0.02751
-1418 ± 55.21
1995
1.407
0.1346 to 0.3562
-706.0 to -260.7
1936 to 1982
0.5925 to 0.8293
-1656 to -1180
1992 to 1996
0.9987
0.01233
0.997
0.06152
792.3
1.000, 1.000
0.0226
Significant
667.5
1.000, 2.000
0.0015
Significant
3
4
1
3
4
1
4
3
Y = 0.2454*X - 483.3
Y = 0.7109*X - 1418
Are the slopes equal?
F = 120.238. DFn=1 DFd=3
P=0.001624
If the overall slopes were identical, there is a 0.16% chance of randomly choosing data points with slopes this
different. You can conclude that the differences between the slopes are very significant.
Trends in Specimen Vials/Biopsy, UPL
UPL 2005-8
Best-fit values
0.3740 ± 0.01627
Slope
-741.2 ± 32.70
Y-intercept when X=0.0
1982
X-intercept when Y=0.0
2.674
1/slope
95% Confidence Intervals
0.1673 to 0.5808
Slope
-1157 to -325.7
Y-intercept when X=0.0
1947 to 1992
X-intercept when Y=0.0
Goodness of Fit
0.9981
R square
0.02301
Sy.x
Is slope significantly non-zero?
528.5
F
1.000, 1.000
DFn, DFd
0.0277
P value
Significant
Deviation from zero?
Data
3
Number of X values
Maximum number of Y
1
replicates
3
Total number of values
4
Number of missing values
Equation
Y = 0.3740*X - 741.2
UPL 2009-11
0.5346 ± 0.1862
-1063 ± 373.6
1988
1.871
-0.2667 to 1.336
-2671 to 545.0
-infinity to 1999
0.8047
0.4164
8.241
1.000, 2.000
0.1029
Not Significant
4
1
4
3
Y = 0.5346*X - 1063
Are the slopes equal?
F = 0.318103. DFn=1 DFd=3
P=0.6122
If the overall slopes were identical, there is a 61% chance of randomly choosing data points with slopes this
tifferent. You can conclude that the differences between the slopes are not significant.
Since the slopes are not significantly different, it is possible to calculate one slope for all the data.
The pooled slope equals 0.488713
Difference in Specimen Vials/Biopsy, NRL vs. UPL, 2009-11
Student’s unpaired t test with unequal variances
0.0817
P value
ns
P value summary
No
Significantly different? (P < 0.05)
Two-tailed
One- or two-tailed P value?
t=2.435 df=3.453
Welch-corrected t, df
How big is the difference?
Mean ± SEM of column A
Mean ± SEM of column B
Difference between means
95% confidence interval
R square
F test to compare variances
F,DFn, Dfd
P value
P value summary
Significantly different? (P < 0.05)
Model comparison
Null H. Population means identical
Alternative H: Distinct population
means
Ratio of probabilities
Difference in AICc
10.58 ± 0.2162 N=3
9.951 ± 0.1418 N=3
-0.6295 ± 0.2585
-1.394 to 0.1354
0.632
2.323, 2, 2
0.602
ns
No
SS
DF
0.9955
5
Probability it is
correct
90.66%
0.401
4
9.34%
9.702
-4.545
Correlation Between Positive Biopsy Rate and Specimen Vials/Biopsy
Positive Biopsy Rate vs. Specimen Vials/Biopsy
Pearson r
r
95% confidence interval
R square
P value
P (two-tailed)
P value summary
Significant? (alpha =
0.05)
Number of XY Pairs
0.9665
0.7844 to 0.9952
0.9342
0.0004
***
Yes
7
Segmented Regression Analysis
Scenario 1: No transition point
12.0
Specimen Vials/Biopsy
10.0
8.0
6.0
y = 0.4535x + 7.632
R² = 0.957
4.0
2.0
0.0
2005
2006
2007
2008
2009
2010
2011
Year
Scenario 2: Transition point 2006
12.0
Specimen Vials/Biopsy
10.0
y = 0.3527x + 8.1927
R² = 0.9251
8.0
6.0
y = 0.4838x + 7.4447
R² = 1
4.0
2.0
0.0
2005
2006
2007
2008
Year
2009
2010
2011
Scenario 3: Transition point 2007
12.0
Specimen Vials/Biopsy
10.0
y = 0.2709x + 8.6836
R² = 0.9158
8.0
6.0
y = 0.5794x + 7.3173
R² = 0.991
4.0
2.0
0.0
2005
2006
2007
2008
2009
2010
2011
Year
Scenario 4: Transition point 2008
12.0
Specimen Vials/Biopsy
10.0
y = 0.3712x + 8.0485
R² = 0.9992
8.0
6.0
y = 0.6492x + 7.2009
R² = 0.9895
4.0
2.0
0.0
2005
2006
2007
2008
Year
2009
2010
2011
Scenario 5: Transition point 2009
12.0
Specimen Vials/Biopsy
10.0
y = 0.3894x + 7.927
R² = 1
8.0
6.0
y = 0.5419x + 7.4155
R² = 0.9553
4.0
2.0
0.0
2005
2006
2007
2008
2009
2010
Year
Analysis:
Scenario
1
2
3
4
5
Pre-Transition
0.957
1
0.991
0.9895
0.9553
Post-Transition
0.957
0.9251
0.9158
0.9992
1
Sum of R^2
1.914
1.9251
1.9068
1.9887
1.9553
Best fit of segmented lines to data point: scenario 4, transition point 2008.
Mean of R^2
0.957
0.96255
0.9534
0.99435
0.97765
2011