APPENDIX: CUSUM METHOD OF MONITORING

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1 APPENDIX: CUSUM METHOD OF MONITORING This appendix describes the application of the cusum technique for monitoring cases of disease. The emphasis is on the practical application of the technique rather than its theoretical basis. SURVEILLANCE TIME PERIOD AND BASELINE RATES Two interrelated parameters of the cusum monitoring system need to be determined in advance. First, the monitoring frequency must be decided- this can be monthly, quarterly, annually or over any other convenient period. Obviously, the more frequent the monitoring the quicker a rise may be detected in principle. However, frequent monitoring reduces the number of expected cases in each monitoring period, and if this number becomes very low, the efficiency of the system is reduced. Although the method can work for expected mean incidences of as low as 0.2 cases, it is suggested that, unless the requirement for early warning is overriding, the monitoring period be chosen so as to provide around 1 expected case or more in each monitoring period. The monitoring period having been decided, the baseline expected incidence of cases in that period should be calculated. This should be based on previous experience, preferably over a number of years. Chapter 7 discusses baseline rates and their amendment.

2 10 IDENTIFICATION OF MAN-MADE ENVIRONMENTAL HAZARDS BASICS OF CUSUM ANALYSIS The surveillance system described here is designed to provide a warning after three time periods* on average of a significant rise in incidence and to produce only one false alarm every 500 months on average. A parameter k is subtracted from the observed number of cases in each month (or from a function of the observed number of cases - depending on the expected monthly number of cases). The result is then added to the cusum each month, and when the cusum reaches the value of the other parameter h, a significant rise in incidence is judged to have occurred. The values of h and k also depend on the expected monthly incidence, as described below. CALCULATING THE CUSUM Expected Baseline of Less than 9 Cases per Month (or Monitoring Period) Values of h and k are determined from Table A. by selecting the value of expected mean in the table nearest to the calculated value and reading off h and k. k is then subtracted monthly from the observed number of cases and the result added to the cusum, but the cusum must not be allowed to fall below zero (negative values being replaced by zero). If the cusum reaches the value h, an increase has occurred. Expected Baseline of 9 or More Cases per Month k and h are always set at 1 and 2, respectively. Where X is the observed number of cases in the current month (or monitoring period) and X is the expected baseline incidence, calculate Y as follows: X-X Y=-- yx The parameter k (i.e. 1) is then subtracted from Y and the result added to the cusum. An increase has occurred if the cusum reaches h (i.e. 2). *For the rest of this appendix it will be assumed for ease that monthly monitoring has been chosen and month is used wherever the monitoring time period is considered.

3 APPENDIX: CUSUM METHOD OF MONITORING 11 RESETTING THE CUSUM When the cusum reaches the warning level h, it can be left at that level or reset to zero. If the cusum is reset to zero and the increase is not due to chance, then the system should produce repeat warnings (by the cusum passing h) on average every months. Resetting the cusum to zero will test the persistence of the increase in mean incidence, which may be useful if regular but temporary fluctuations, perhaps seasonal, occur in the incidence of cases. EXAMPLES Example 1 Condition Z has a mean expected monthly incidence of 2 cases a month. From Table A. we select values of k as and h as 7 (2 being nearest to 2.0 in Table A.). Table A.1 shows the calculation over 7 months- the Table A.l Month Number of cases Cases- k Cusum underlying mean for the first months is, in fact, 2, but this rises to 6 for the fifth month onwards, producing a warning in the third month after this increase. The cusum in the seventh month is therefore 9, which is greater than the value of h (i.e. 7), so an increase is recorded by the system. Note that the cusum was not allowed to fall below zero in the early months. Example 2 Condition X has a mean expected monthly incidence of 15. cases per month. This is greater than 9, so k is set at 1 and h at 2. The cusum cal-

4 12 IDENTIFICATION OF MAN-MADE ENVIRONMENTAL HAZARDS culation is as shown in Table A.2. The cusum has now passed h (2) and an increase is deemed to have occurred. Table A.2 x-x Month Number of cases Y=-- Y-k Cusum.Jx Table A. Values of k and h corresponding to specific baseline incidence levels (derived from Reference 1, Chapter 7) Baseline mean incidence < k (reference value) h (cusum warning level)

5 APPENDIX: CUSUM METHOD OF MONITORING 1 Table A. cont'd. Baseline mean incidence k h (cusum (reference value) warning level).2i I I IO IO IO II II II IO

6 Index Acid rain, 2 7 Age, as confounding variable, 8, 11 Age standardisation, Air pollution, 2-26, 0, 69, 72, 111 Alcohol, 1 -Aminobiphenyl, Aminopterin, 9 Anaemia, 5 Analytical epidemiology, 6-66, 70-72, 7, 7 measures in, types of, 6-65 Anencephalus, 1 Animal experiments, evidence from, value of, 2-5, 118 Anophthalmos, 20 Asbestos, 6 blue, Asbestosis, Asthma, 5, 26,0 Behavioural factors, as confounding variables, 5 Behavioural influences on health, 2, Benzene, 17 Benzidine, 1 7, Bhopal chemical plant accid~nt, India, 5 Bias in epidemiological studies, Biological/organic environment, 5 Bladder cancer,, 18, 19, 101, 115 Blood pressure, 27, 70 Blue asbestos, Brain damage, 9 Bronchitis, Burkitt's lymphoma, 6 Cadmium contamination of soil residence time, 26 at Shipham, Somerset, UK, 16-17,72,8 Cancer,, 5, 16, 2, 5, 58, 67, 68, 71, 108, 126 (see also Carcinogens) bladder,, 18, 19, 101, 115 Burkitt's lymphoma, 6 of cervix, 7 in Clinton County, Pa., USA, colon, 19 and electromagnetic radiation, and fluoridation, 22-2, 69, 111 gastro-intestinal, 19 initiators of, 5 kidney, 7 larynx,

7 INDEX 15 and lead, 27 leukaemia, 20-21,29,6,51, 101, 110 lung,, 7, 25, 29, 6, 51, 101, 109, mortality statistics, UK, ~ 1, 52, 101 mouth, in New Jersey, USA, 19 and nitrate levels in drinkingwater, 2 and nuclear power plants, oesophagus,, 19 pancreas, promoters of, 5 rectum, 19 skin, stomach, 19, 2, 2 thyroid, 1 in Torfaen area, Wales, 19 viruses as a cause of, 6 vagina, 7 and Windscale reactor fire, UK, 12,67 Cancer registries, 75, 77 Carcinogens, 17, 2, 27,5-7, 0,2 bladder, 18, - laboratory tests for, 2- Cardiovascular disease, 0, 5, 70, 11 Car exhaust fumes, 1, 6, 10, 27, 69 Case-control studies, 6-6, 65-66,70,71, 72, 7, 77-78, 81, 97, 100 significance testing and confidence intervals in, 9-95 Causality, criteria for, biological plausibility, coherence of evidence, 111 consistency, dose-response gradient, establishment of, experiment, 111 proof of, 1 OS reasoning by analogy, relationships in time, 108 specificity, strength of association, 106 Central nervous system malformations, 5 Cerebrovascular disease, 75, 101 Cervical cancer, 7 Chance in epidemiological studies, Chemical plant accidents, I 0, 11, 68 Bhopal, India, 5 Seveso, Italy, 15-16,0, 71, 107, 108 Chemical workers, children of, malformations in, 0, 1 Chernobyl nuclear plant accident, USSR, 1, 20 Chloracne, see Seveso industrial accident, Italy Cholera, 5 Chorioretinitis, 9 Chromosomal abnormality, 7, 8 Cigarette smoking, see Smoking Circulatory system anomalies, 52 Clean Air legislation, UK, 6-7 Climate, Clinton County, Pa., USA, cancer mortalityratesfor, 17-19, 68, 115 Colon, cancer of, 19 Confidence intervals, 85, 86 calculation of, 87 in case-control studies, 9-95 for rates data, for ratios, 91-9 Confounding variables, 25,8-5, 6, age, 8, 11 behavioural factors, 5 ethnic and racial origin, 51-52, 115 occupation, 115 region, 51, 11 sex, 50, 11

8 16 INDEX smoking, 5, 6, socio-economic factors, 52-5, 11 Congenital malformation incidence at birth rate, formula for, 56 Congenital malformation ratios, 58 Congenital malformation registries, 75,77 Congenital malformations, 2, 5, 19,7-0, 52, 5, 120 monitoring of, 77 Cosmetics, 27 Cracow air pollution study, Poland, 25, 72 Craniofacial defects, 9 Cross-section studies, Cusum technique for monitoring environmental hazards, , Cytomegalovirus, 9 Data, 7-78 availability of, 7-75 baseline, 77 exposure, 78 hospital, 76 mortality, of population at risk, 66 quality of, 7 routine, 7 registry, DDT, 26 Deafness, 9 Death rate, formula for, 56 Descriptive epidemiology, 7, 8-6,67-70,7-7,81 measures in, 5-6 Diet, 5, 5 Diethylstilboestrol, 7 Diffused long-term hazards, 2I-29, 69, 70,7,97 air pollution, 2-26, 0, 69, 72 electromagnetic radiation, fluoridation of water, 22-2, 69, Ill lead in environment, 26-28, 0,69 nitrate levels in drinking-water, 2-2 Digestive ailments,, 5, 11 Dioxins, 15-16, I9 Direct standardisation, 57 Disease levels, 8I Disease markers, 69 Disease registers, 75 Down's syndrome, I-1, 8, I Drake Superfund study, Clinton County, Pa., USA, 17-19, 68, 1I5 Dundalk area, Ireland, incidence of Down's syndrome in, 1-I Ear reduction defects, 9 Edwards's syndrome, 8 Electromagnetic radiation, 28-29, 72,8,108 Environment, definition of, Environmental control, 6 Environmental epidemiology, I 0 I Environmental studies, combining results of, 116 Epidemiological methods and studies, 7 Epstein-Barr virus, 6 Ethnic and racial origin, as confounding variable, 51-52, 115 Exomphalos, 99 Expected levels, 81-8 Experimental epidemiology, 111 Experiments, laboratory animal, 2 other, advantages of, 2 Exposure, assessment of, 8 Extrapolation biological, numerical, Eye defects, 9 Eye malformations, 19 Fertilisers, 6, 21, 2 Fertility disorders, 8, 0

9 INDEX 17 Fish, 21 Fluoridation of water, 22-2, 69, 111 Gas process workers, children of, malformations in, 1 Gastro-intestinal cancer, 19, 2 Gastro-intestinal illness, 0 Health, group influences on, 2- Heart defects, 9 Heart disease, 2, Hereditary influences on health, 2- High-voltage substations, 7 Historical prospective studies, 6 5 Hospital data, Hydrocarbons, 7 Hypertension, 16 Hypospadias, 1 Incidence, definition of, 5 Indirect standardisation, 57, 58, 60 Infant mortality rate, formula for, 56 Infectious disease, 5 Influenza, 5 Iodine-11, 1 Ionising radiation, 7, 6 exposure to, 126 Ischaemic heart disease, 51 Itai-itai disease, 16 Kidney cancer, 7 Kidney disorders, 16 Laboratory experiments, evidence from, value of, 2-5, 118 Larynx, cancer of, Lead in blood, 26 in environment, 6, 10, 26-28, 0,69 Leukaemia, 20-21,29,6,51, 101, 110 Life expectation, 1 Limb reduction defects, 9 London 'smog', December 1952, 7, Ill Long-term hazards, see Diffused long-term hazards; Spot long-term hazards Lung cancer,,, 7, 25, 29, 5, 6, 51,101,109, Malaria, 5 Malformations, see Central nervous system malformations; Circulatory system anomalies; Congenital malformations; Eye malformations Maryport, Cumbria, UK, incidence of Down's syndrome in, 1 Measles, 5 Mesothelioma, Methyl isocyanate, 5 Methyl mercury, 21 Microcephaly, 9 Microphthalmos, 20 Minimata disease, 21 Mining accidents, Miscarriages, 15, 8 Monitoring environmental hazards, cusum technique for, , sets technique for, 122, 12 Monitoring diseases, by case mapping and mortality, Monitoring systems, interpreting warnings from, Mortality data, Mortality, social class differences in, 8 Motor neurone disease, 5 Motor traffic accidents, Motor vehicles, see Car exhaust fumes; Motor traffic accidents Mouth cancer, Mutagenicity,, 5,7-8,9, 0,2

10 18 INDEX /-Naphthylamine, 17 2-Naphthylamine, Natural physical environment, Neurological disorders, 0 New Jersey, USA, toxic waste dumps in, study of, 19, Nitrates, 6, 2-2, 26 N-Nitroso compounds, 2, 2 Nuclear power plant accidents, 11 Chernobyl, USSR, 1, 20 Three Mile Island, Pa., USA, 1-15, 71, 11 Windscale, UK, 12-1, 20,67 Nuclear power plants, 1, 20-21, 68, 8, 110 Nuclear production waste, 6 Null hypothesis, 86-87, 96 Occupation, as confounding variable, 115 Occupational environment, 5 Odds ratio, 66 Oesophageal cancer,, 19 Osteomalacia, 16 Paint, 27 Pancreas, cancer of, Patau's syndrome, 8 PCBs, see Polychlorinated biphenyls Period prevalence, 5 Pesticides, 1 Petroleum, 7 Petroleum workers, children of, malformations in, 1 PMR, see Proportional mortality ratio Pneumoconiosis, Polonium-210, 1 Polychlorinated biphenyls, 15, 19 Power of study, see Significance, power and sample size Precancerous states, 7 Pregnancy, complications of, Preservatives, food, 2 Prevalence, definition of, 5 Probability assessment, 126 Probability measures, 126 Prospective studies, 6 5, 66, 71, 72,7,81 Proportional measures, 56 Proportional mortality ratio ' ' Proportions, see Rates, ratios and proportions Prospective studies, in hazard investigations, 71 Radiation,, 7, 12-1, 110 (see also Electromagnetic radiation; Ionising radiation) Radiotherapy, 9 Rates, ratios and proportions, Ratios, see Proportional mortality ratio; Rates, ratios and proportions; Sex ratio; Standardised morality ratio Recall bias, 78 Re-Chem plant, Torfaen, Gwent, 19, 77 Rectum, cancer of, 19 Reference population, choice of, 65,82-8,92 Reference rates, 82 Region, as confounding variable, 51, 11 Registry data, Relative risk, Reproductive health, effects of radiation on, 1 Respiratory ailments,, 25, 5, 11 Retinoblastoma, 6 Risk, public assessment of 1 Royal Commission on En~ironmental Pollution, 26 Rubella virus, 9 Sample size, see Significance, power and sample size Sellafield nuclear plant, Cumbria, UK, 20, 21, 8, 110 see also Windscale reactor fire

11 Sets technique for monitoring environmental hazards, 122, 12 Seveso industrial accident, Italy, 15-16,0,71, 107, 108 Sex, as confounding variable, 50, 11 Sex ratio, 19, 25, 8, 56 Shellfish, 21 Shipham, Somerset, UK, cadmium contamination of soil at, 16-17, 72, 8 Significance testing, calculation of, 87 in case-control studies, 9-95 for rates data, for ratios, 91-9 Significance, power and sample size, Single-event hazards, see Spot single-event hazards Skin cancer, 'Smog', London, December 1952, 7' 111 Smoke emissions, 6, 7 Smoking, 1,, 5, 18, 9, 5, 57, interaction of, with air pollution, 25 and lung cancer,, 7, 5, 6, 6' 109' as confounding variable, 5, 6, SMR, see Standardised mortality ratio Social environment, 5-6 Socio-economic factors, as confounding variables, 52-5, 11 Spina bifida, 1, 52 INDEX 19 nuclear power plants, 20-21, 68, 8, 110 toxic waste disposal, 17-20, 68, 77 Spot single-event hazards, 10, 11-16,67-68,70,71,7,97 Seveso industrial accident, Italy, 15-16,0, 71, 107, 108 Three Mile Island nuclear power plant accident, Pa., USA, 1-1 5' 71 ' 11 Windsca1e reactor fire, UK, 12-1,20,67 Yusho poisoning episode, Japan, 15, 0,67 Standardisation and summary measures, 57-6 proportional mortality ratio, 58, standardised mortality ratio, 58-60, 62-6 Standardised mortality ratio, 58-60,62-6,82,8,86,9, 97 Statistical inference, 85 Statistical methods, errors in, 8-85 Statistical significance, limits to, Statistical techniques, 81 Statistical and non-statistical errors, Stillbirths, 5, 1, 27, 52, 7 Stomach cancer, 19, 2, 2 Summary measures, see Standardisation and summary measures Surveillance, local and national, 121 Spontaneous abortions, 15, 19, 27, 2,,5-T, 26 8, 71, 11 Teratogenicity, 5, 9-0,2, Spot long-term hazards, 10, 16-21, 2,, 7,8-Tetrachlorodibenzo-p , 70, 71-72, 7, 97 dioxin, 15-16,0 cadmium contamination of soil, Thalidomide, 9, 120 Shipham, Somerset, UK, Three Mile Island nuclear power 16-17, 72, 8 plant accident, Pa., USA, Minimata disease, , 71, 11

12 10 INDEX Thyroid cancer, 1 Tobacco, see Smoking Torfaen area, Wales, incidence of eye malformations in ' ' Toxic waste, 110 Toxicity, 0-2, Toxicological research, Toxic waste disposal, 1, 10, 17-20,68-69, 77, 115 Toxoplasma gonadii, 9 Tracheo-oesophageal fistula, atresia and stenosis, 1, 99 Tuberculosis, 5 Type I statistical error, 96 Type II statistical error, 96 Typhoid, 5 Vaginal cancer, 7 Vegetables, 2, 2 Viral infections, 6 Vitamin C, 2 Waste, toxic, see Toxic waste disposal Water fluoridation of, 22-2, 69, 111 hardness of, nitrate levels in, 2-2 Whooping-cough, 5 Windscale reactor fire, UK, 12-1,20,67 Worksop, UK, cancer mortality in, 2 Yusho poisoning episode, Japan, 15,0,67

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