Table 2.
Count regression model selection for the association between deprivation and incidence of infectious diseases in the North East of England, 2007–2011
| Group | Dataset | Mean count (variance) | Zero counts (%) | Poisson model | ZIP model | Negative binomial model | ZINB model | Final model | Residuals‡ | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| GOF | AIC | Vuong | AIC | ΔAIC* | LRT | AIC | Ref.† | Δ AIC* | Vuong | AIC | Ref.† | ΔAIC* | ||||||
| BBV | HBV infection | 0·5 (1·20) | 73·13 | 0·5974 | 2688·15 | 0·0129 | 2646·69 | 41·46 | <0·0001 | 2640·09 | ZIP | 6·5950 | 0·2645 | 2609·86 | NB | 30·2310 | NB | Bimodal |
| HCV infection | 0·6 (1·78) | 65·70 | <0·0001 | 3297·41 | 0·0001 | 3208·84 | 88·57 | <0·0001 | 3163·59 | ZIP | 45·2500 | Did not converge | NB | Bimodal | ||||
| HIV infection | 0·1 (0·17) | 89·79 | 1·0000 | 1221·36 | 0·0359 | 1209·11 | 12·25 | 0·0090 | 1215·70 | ZIP | −6·5900 | <0·0001 | 1209·11 | ZIP | 0·0000 | ZIP | Normal | |
| IBD | Invasive GAS infection | 0·2 (0·16) | 85·08 | 1·0000 | 1547·07 | 0·2220 | 1546·04 | 1·03 | 0·5000 | 1547·07 | Poisson | 0·0000 | n.a. | 1546·04 | Poisson | 1·0290 | Poisson | Bimodal |
| Invasive meningococcal infection | 0·2 (0·2) | 80·92 | 1·0000 | 1833·24 | 0·4435 | 1833·14 | 0·10 | 0·2410 | 1897·69 | Poisson | −64·4500 | Did not converge | Poisson | Bimodal | ||||
| Invasive pneumococcal infection | 0·8 (0·88) | 47·77 | 0·0004 | 3824·18 | 0·2869 | 3820·83 | 3·35 | 0·1130 | 3820·71 | Poisson | 3·4660 | 0·5002 | 3822·71 | NB | −2·0000 | NB | Bimodal | |
| IID | Campylobacteriosis | 9·1 (16·90) | 0·06 | <0·0001 | 8968·73 | 0·5015 | 8970·73 | −2·00 | <0·0001 | 8851·94 | Poisson | 116·7970 | 0·6873 | 8853·94 | NB | −2·0000 | NB | Normal |
| Cryptosporidiosis | 0·6 (0·93) | 57·67 | <0·0001 | 3701·46 | 0·0004 | 3643·18 | 58·27 | <0·0001 | 3635·16 | ZIP | 8·0190 | Did not converge | NB | Bimodal | ||||
| E. coli O157 infection | 0·2 (0·31) | 84·72 | 1·0000 | 1849·14 | 0·0002 | 1769·68 | 79·45 | <0·0001 | 1772·10 | ZIP | −2·4170 | 0·1860 | 1767·69 | ZIP | 1·9950 | ZIP | Normal | |
| Giardiasis | 0·1 (0·13) | 89·79 | 1·0000 | 1181·32 | 0·2797 | 1179·32 | 2·01 | 0·0750 | 1179·25 | Poisson | 2·0710 | Did not converge | Poisson | Bimodal | ||||
| Salmonellosis | 1·3 (1·68) | 30·56 | <0·0001 | 4954·11 | 0·0639 | 4944·17 | 9·94 | <0·0001 | 4932·55 | Poisson | 21·5590 | 0·3544 | 4931·58 | NB | 0·9740 | NB | Bimodal | |
| Shigellosis | 0·1 (0·17) | 89·19 | 1·0000 | 1322·53 | 0·0375 | 1303·02 | 19·51 | <0·0001 | 1304·63 | ZIP | −1·6160 | <0·0001 | 1303·02 | ZIP | 0·0000 | ZIP | Normal | |
| STI | Chlamydia infection | 16·3 (114·75) | 0·12 | <0·0001 | 12286·15 | 0·2136 | 12402·45 | −116·30 | <0·0001 | 10794·84 | Poisson | 1491·3100 | 0·5013 | 10796·84 | NB | −2·0000 | NB | Normal |
| Genital herpes | 2·5 (5·53) | 14·67 | <0·0001 | 6519·80 | 0·0004 | 6463·26 | 56·54 | <0·0001 | 6380·17 | ZIP | 83·0880 | 0·1768 | 6378·25 | NB | 1·9220 | NB | Bimodal | |
| Genital warts | 9·5 (37·40) | 0·12 | <0·0001 | 9719·94 | 0·1753 | 9712·69 | 7·25 | <0·0001 | 9208·55 | Poisson | 511·3900 | 0·5019 | 9210·55 | NB | −2·0000 | NB | Normal | |
| Gonorrhoea | 1·8 (3·88) | 28·44 | <0·0001 | 5515·32 | 0·0006 | 5463·17 | 52·15 | <0·0001 | 5436·05 | ZIP | 27·1220 | 0·1525 | 5432·93 | NB | 3·1230 | NB | Bimodal | |
| Syphilis | 0·2 (0·31) | 83·64 | 1·0000 | 1820·41 | 0·0033 | 1782·72 | 37·69 | <0·0001 | 1790·35 | ZIP | −7·6330 | Did not converge | ZIP | Normal | ||||
| TB | Tuberculosis | 0·3 (0·68) | 80·13 | 1·0000 | 1925·97 | 0·0974 | 1918·59 | 7·38 | 0·0030 | 1918·35 | Poisson | 7·6240 | 0·2148 | 1975·60 | NB | −57·2530 | NB | Bimodal |
| VPD | Measles | 0·2 (0·35) | 93·78 | 1·0000 | 1272·75 | Did not converge | <0·0001 | 997·65 | Poisson | 275·0984 | 0·2136 | 994·67 | NB | 2·9823 | NB | Normal | ||
| Mumps | 0·6 (1·36) | 59·78 | 0·0006 | 3351·60 | 0·0146 | 3327·67 | 23·93 | <0·0001 | 3323·82 | ZIP | 3·8510 | 0·1771 | 3319·82 | NB | 4·0010 | NB | Bimodal | |
| Pertussis | 0·1 (0·20) | 87·98 | 1·0000 | 1508·98 | 0·0042 | 1464·64 | 44·34 | <0·0001 | 1462·52 | ZIP | 2·1230 | 0·4800 | 1462·50 | ZIP | 2·1360 | ZIP | Normal | |
AIC, Akaike's Information Criterion; BBV, bloodborne viruses; GAS, group A streptococcal; GOF, goodness of fit; HBV, hepatitis B virus; HCV, hepatitis C virus; IBD, invasive bacterial diseases; IID, infectious intestinal infections; n.a., not available; LRT, likelihood ratio test; NB, negative binomial; STI, sexually-transmitted infections; TB, tuberculosis; VPD, vaccine-preventable diseases; ZINB, zero-inflated negative binomial; ZIP, zero-inflated Poisson.
Difference in AIC between the model of interest and the reference model.
Reference model for testing.
Distribution of residuals for the final model assessed by eye.