Post on 14-Mar-2020
APPENDIX 2 Segmented regression analysis of interrupted time series
data
Figure 3: Segmented regression analysis of interrupted time series data; redrawn from MacDougall
(2005)
REFERENCE: MacDougall, C. and R. E. Polk (2005). "Antimicrobial Stewardship Programs in Health Care Systems."
Clinical Microbiology Reviews 18(4): 638-656.
APPENDIX 3 Observed versus predicted counts (lagged vacation
period shown by black rectangle)
APPENDIX 4: Graph of Pearson residuals versus predicted values from
the models
APPENDIX 5: Results of sensitivity analysis (no lag)
The GENMOD Procedure
State=ACT
Friday, September 27, 2019 11:33:50 AM 1
Model Information
Data Set WORK.WEEK19
Distribution Negative Binomial
Link Function Log
Dependent Variable Count Count
Number of Observations Read 17
Number of Observations Used 17
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 11 18.6532 1.6957
Scaled Deviance 11 18.6532 1.6957
Pearson Chi-Square 11 18.6078 1.6916
Scaled Pearson X2 11 18.6078 1.6916
Log Likelihood 12958.6076
Full Log Likelihood -82.5194
AIC (smaller is better) 179.0389
AICC (smaller is better) 191.4833
BIC (smaller is better) 184.8714
Algorithm converged.
Analysis Of Maximum Likelihood Parameter Estimates
Parameter DF Estimate
Standard
Error
Wald 95%
Confidence
Limits
Wald
Chi-Square Pr > ChiSq
Intercept 1 4.0531 0.1278 3.8026 4.3035 1006.15 <.0001
wk 1 0.2025 0.0261 0.1513 0.2537 60.08 <.0001
Vacation 1 -0.3423 0.2226 -0.7786 0.0940 2.36 0.1241
postvac 1 -0.9092 0.2287 -1.3574 -0.4611 15.81 <.0001
vacwk 1 -0.3377 0.2493 -0.8264 0.1509 1.84 0.1755
postwk 1 -0.2126 0.0516 -0.3138 -0.1115 16.97 <.0001
Dispersion 1 0.0265 0.0123 0.0107 0.0657
The GENMOD Procedure
State=ACT
Friday, September 27, 2019 11:33:50 AM 2
Note: The negative binomial dispersion parameter was estimated by maximum likelihood.
The GENMOD Procedure
State=NSW
Friday, September 27, 2019 11:33:50 AM 3
Model Information
Data Set WORK.WEEK19
Distribution Negative Binomial
Link Function Log
Dependent Variable Count Count
Number of Observations Read 17
Number of Observations Used 17
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 11 17.2499 1.5682
Scaled Deviance 11 17.2499 1.5682
Pearson Chi-Square 11 17.5667 1.5970
Scaled Pearson X2 11 17.5667 1.5970
Log Likelihood 687324.4417
Full Log Likelihood -123.4419
AIC (smaller is better) 260.8838
AICC (smaller is better) 273.3282
BIC (smaller is better) 266.7163
Algorithm converged.
Analysis Of Maximum Likelihood Parameter Estimates
Parameter DF Estimate
Standard
Error
Wald 95%
Confidence
Limits
Wald
Chi-Square Pr > ChiSq
Intercept 1 7.1594 0.0477 7.0658 7.2529 22483.8 <.0001
wk 1 0.2513 0.0100 0.2317 0.2708 633.27 <.0001
Vacation 1 -0.3949 0.0911 -0.5735 -0.2163 18.78 <.0001
postvac 1 -1.1929 0.0903 -1.3698 -1.0160 174.71 <.0001
vacwk 1 -0.4404 0.1035 -0.6432 -0.2376 18.12 <.0001
postwk 1 -0.2610 0.0200 -0.3003 -0.2218 169.75 <.0001
Dispersion 1 0.0052 0.0019 0.0025 0.0106
The GENMOD Procedure
State=NSW
Friday, September 27, 2019 11:33:50 AM 4
Note: The negative binomial dispersion parameter was estimated by maximum likelihood.
The GENMOD Procedure
State=QLD
Friday, September 27, 2019 11:33:50 AM 5
Model Information
Data Set WORK.WEEK19
Distribution Negative Binomial
Link Function Log
Dependent Variable Count Count
Number of Observations Read 17
Number of Observations Used 17
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 11 16.8421 1.5311
Scaled Deviance 11 16.8421 1.5311
Pearson Chi-Square 11 16.0505 1.4591
Scaled Pearson X2 11 16.0505 1.4591
Log Likelihood 312799.6948
Full Log Likelihood -117.5330
AIC (smaller is better) 249.0659
AICC (smaller is better) 261.5104
BIC (smaller is better) 254.8984
Algorithm converged.
Analysis Of Maximum Likelihood Parameter Estimates
Parameter DF Estimate
Standard
Error
Wald 95%
Confidence
Limits
Wald
Chi-Square Pr > ChiSq
Intercept 1 6.3271 0.0752 6.1797 6.4745 7079.13 <.0001
wk 1 0.2307 0.0178 0.1958 0.2655 168.36 <.0001
Vacation 1 -0.2432 0.1418 -0.5211 0.0348 2.94 0.0864
postvac 1 -0.4808 0.1442 -0.7635 -0.1981 11.11 0.0009
vacwk 1 -0.3933 0.1582 -0.7034 -0.0833 6.18 0.0129
postwk 1 -0.1853 0.0284 -0.2409 -0.1296 42.59 <.0001
Dispersion 1 0.0120 0.0042 0.0060 0.0240
The GENMOD Procedure
State=QLD
Friday, September 27, 2019 11:33:50 AM 6
Note: The negative binomial dispersion parameter was estimated by maximum likelihood.
The GENMOD Procedure
State=SA
Friday, September 27, 2019 11:33:50 AM 7
Model Information
Data Set WORK.WEEK19
Distribution Negative Binomial
Link Function Log
Dependent Variable Count Count
Number of Observations Read 17
Number of Observations Used 17
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 11 16.7721 1.5247
Scaled Deviance 11 16.7721 1.5247
Pearson Chi-Square 11 17.1145 1.5559
Scaled Pearson X2 11 17.1145 1.5559
Log Likelihood 64654.2133
Full Log Likelihood -99.0507
AIC (smaller is better) 212.1014
AICC (smaller is better) 224.5458
BIC (smaller is better) 217.9339
Algorithm converged.
Analysis Of Maximum Likelihood Parameter Estimates
Parameter DF Estimate
Standard
Error
Wald 95%
Confidence
Limits
Wald
Chi-Square Pr > ChiSq
Intercept 1 7.5506 0.0921 7.3701 7.7311 6722.28 <.0001
wk 1 -0.2042 0.0195 -0.2424 -0.1660 109.98 <.0001
Vacation 1 0.3417 0.1931 -0.0368 0.7202 3.13 0.0768
postvac 1 0.2312 0.1875 -0.1362 0.5986 1.52 0.2174
vacwk 1 0.0497 0.2247 -0.3907 0.4901 0.05 0.8251
postwk 1 0.2627 0.0426 0.1792 0.3463 37.96 <.0001
Dispersion 1 0.0225 0.0083 0.0109 0.0464
The GENMOD Procedure
State=SA
Friday, September 27, 2019 11:33:50 AM 8
Note: The negative binomial dispersion parameter was estimated by maximum likelihood.
The GENMOD Procedure
State=VIC
Friday, September 27, 2019 11:33:50 AM 9
Model Information
Data Set WORK.WEEK19
Distribution Negative Binomial
Link Function Log
Dependent Variable Count Count
Number of Observations Read 17
Number of Observations Used 17
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 11 17.1907 1.5628
Scaled Deviance 11 17.1907 1.5628
Pearson Chi-Square 11 16.7645 1.5240
Scaled Pearson X2 11 16.7645 1.5240
Log Likelihood 301681.8712
Full Log Likelihood -116.6948
AIC (smaller is better) 247.3896
AICC (smaller is better) 259.8340
BIC (smaller is better) 253.2221
Algorithm converged.
Analysis Of Maximum Likelihood Parameter Estimates
Parameter DF Estimate
Standard
Error
Wald 95%
Confidence
Limits
Wald
Chi-Square Pr > ChiSq
Intercept 1 7.2885 0.0618 7.1674 7.4095 13925.1 <.0001
wk 1 0.1199 0.0148 0.0908 0.1490 65.38 <.0001
Vacation 1 0.0094 0.1177 -0.2212 0.2400 0.01 0.9364
postvac 1 -0.6088 0.1189 -0.8418 -0.3758 26.22 <.0001
vacwk 1 -0.1639 0.1303 -0.4194 0.0915 1.58 0.2085
postwk 1 -0.1321 0.0227 -0.1765 -0.0876 33.95 <.0001
Dispersion 1 0.0081 0.0030 0.0040 0.0166
The GENMOD Procedure
State=VIC
Friday, September 27, 2019 11:33:50 AM 10
Note: The negative binomial dispersion parameter was estimated by maximum likelihood.
The GENMOD Procedure
State=WA
Friday, September 27, 2019 11:33:50 AM 11
Model Information
Data Set WORK.WEEK19
Distribution Negative Binomial
Link Function Log
Dependent Variable Count Count
Number of Observations Read 17
Number of Observations Used 17
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 11 16.9313 1.5392
Scaled Deviance 11 16.9313 1.5392
Pearson Chi-Square 11 17.0235 1.5476
Scaled Pearson X2 11 17.0235 1.5476
Log Likelihood 16331.9710
Full Log Likelihood -89.0651
AIC (smaller is better) 192.1302
AICC (smaller is better) 204.5746
BIC (smaller is better) 197.9627
Algorithm converged.
Analysis Of Maximum Likelihood Parameter Estimates
Parameter DF Estimate
Standard
Error
Wald 95%
Confidence
Limits
Wald
Chi-Square Pr > ChiSq
Intercept 1 5.1100 0.2033 4.7115 5.5085 631.72 <.0001
wk 1 0.1450 0.0442 0.0584 0.2316 10.78 0.0010
Vacation 1 -0.9990 0.3819 -1.7475 -0.2505 6.84 0.0089
postvac 1 -2.2228 0.3927 -2.9924 -1.4531 32.04 <.0001
vacwk 1 -0.4136 0.4234 -1.2434 0.4162 0.95 0.3286
postwk 1 -0.3356 0.0874 -0.5068 -0.1644 14.76 0.0001
Dispersion 1 0.0835 0.0307 0.0406 0.1718
The GENMOD Procedure
State=WA
Friday, September 27, 2019 11:33:50 AM 12
Note: The negative binomial dispersion parameter was estimated by maximum likelihood.
State=ACT
Friday, September 27, 2019 11:33:50 AM 13
Plot of predicted*week. Symbol used is 'e'. Plot of Count*week. Symbol used is 'o'. | | 300 + | e | | | | | 250 + e | o | e o o | o | e | o e e e P | o e e e r 200 + e | e d | i | c | o o t | e | e d 150 + | V | o a | e l | o u | o e | e 100 + | | e | | e | | e o 50 + | | o | | | | 0 + | ---+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-- 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 week NOTE: 4 obs hidden.
State=NSW
Friday, September 27, 2019 11:33:50 AM 14
Plot of predicted*week. Symbol used is 'e'. Plot of Count*week. Symbol used is 'o'. 10000 + | | e | | 9000 + | | o | e | 8000 + | | | e | P 7000 + o r | e e | d | o i | e e o c 6000 + e e e t | e e e | o o d | | o V 5000 + a | l | e u | e | 4000 + o | | e | | 3000 + | e | | | e 2000 + | | e | | e 1000 + ---+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-- 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 week NOTE: 9 obs hidden.
State=QLD
Friday, September 27, 2019 11:33:50 AM 15
Plot of predicted*week. Symbol used is 'e'. Plot of Count*week. Symbol used is 'o'. 5000 + | | | | e 4500 + o o | o e | o | e | 4000 + e | o | e | o | e P 3500 + e r | e | d | i | c 3000 + t | e | e e d | | o o V 2500 + a | e l | u | e e | o o 2000 + | | e | | 1500 + | e | | | e 1000 + o | e | o | e | e 500 + o ---+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-- 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 week NOTE: 4 obs hidden.
State=SA
Friday, September 27, 2019 11:33:50 AM 16
Plot of predicted*week. Symbol used is 'e'. Plot of Count*week. Symbol used is 'o'. 2000 + | | e | o | 1800 + | | | | 1600 + o o | e | | | P 1400 + r | e | d | e i | c 1200 + t | e | d | | e V 1000 + a | o l | u | e | e 800 + | o | | e | 600 + | e | o | o | o e e 400 + | e e o | e e e | o e e | e o o 200 + ---+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-- 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 week NOTE: 5 obs hidden.
State=VIC
Friday, September 27, 2019 11:33:50 AM 17
Plot of predicted*week. Symbol used is 'e'. Plot of Count*week. Symbol used is 'o'. | | 4000 + | | e | | e | | 3500 + | | e | o | | P | r 3000 + e e | o d | i | o c | t | o e o e e e | e e d 2500 + o e e | e V | e o a | o l | o u | e | o e 2000 + | | e | | o | e | 1500 + | e | | | o | | 1000 + | ---+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-- 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 week NOTE: 5 obs hidden.
State=WA
Friday, September 27, 2019 11:33:50 AM 18
Plot of predicted*week. Symbol used is 'e'. Plot of Count*week. Symbol used is 'o'. | | 600 + | | | | | e | 500 + | o | | e | | P | o r 400 + e e | d | o i | c | o e t | o e | d 300 + o e | V | a | e l | u | e e | e 200 + | e | e e | | | o | 100 + o | o e | e | o e o | e e | e | 0 + | ---+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-- 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 week NOTE: 6 obs hidden.
Friday, September 27, 2019 11:33:50 AM 19
Plot of pearson*predicted. Legend: A = 1 obs, B = 2 obs, etc. | | 2.5 + | | A A | A 2.0 + A A | A | A | A 1.5 + A A | A A | A A | B A P 1.0 + A A A e | A a | A A A A A r | B AA s 0.5 + A o | A n | A A A A B | A A R 0.0 + BCAA A A A A A A A e | A AA A A A s | A A A i | A A A A A A d -0.5 + A A A u | AA A A A A a | A A A l | A A -1.0 + A A | A A A | AA AA A | -1.5 + A A A | A A | A | A -2.0 + A | A | | -2.5 + | --+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-- 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Predicted Value