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Describing the risk of an event and identifying risk factors

Describing the risk of an event and identifying risk factors. Caroline Sabin Professor of Medical Statistics and Epidemiology, Research Department of Infection and Population Health, Division of Population Health, Royal Free and UC Medical School. Studying the risk of an event.

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Describing the risk of an event and identifying risk factors

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  1. Describing the risk of an event and identifying risk factors Caroline Sabin Professor of Medical Statistics and Epidemiology, Research Department of Infection and Population Health, Division of Population Health, Royal Free and UC Medical School

  2. Studying the risk of an event • We may be interested in the probability that some event occurs (eg. a new AIDS event, virological response, virological failure) • Can describe this using different words (eg. the risk, incidence, prevalence) depending on the context (cross-sectional or longitudinal study) • The variable of interest is often a proportion, but we may also be interested in the rate at which an event occurs, or the time taken to develop the event

  3. Measures of risk • Incidence • The proportion of patients without the event of interest who develop the event over the study period • Can only estimate incidence from a longitudinal study • We must exclude those who have the event at start of study from the calculation

  4. Measures of risk • Prevalence • The proportion of all patients in study who have the event at a particular point in time • We can estimate prevalence from longitudinal or cross-sectional studies • We generally include all patients in calculation

  5. Measures of risk • Prevalence • The proportion of all patients in study who have the event at a particular point in time • We can estimate prevalence from longitudinal or cross-sectional studies • We generally include all patients in calculation Both incidence and prevalence can be seen as a measure of the ‘risk’ of an event depending on the study design (cross-sectional or longitudinal)

  6. Example – study of AIDS events in 15 patients AIDS defining diagnosis Patient Time New AIDS-defining event

  7. Example – study of AIDS events in 15 patients Patient Time Start of study End of study New AIDS-defining event

  8. Example – study of AIDS events in 15 patients At start of study, 6 out of 15 patients have AIDS Patient Start of study End of study Time New AIDS-defining event

  9. Example – study of AIDS events in 15 patients At start of study, 6 out of 15 patients have AIDS Prevalence of AIDS = 6/15 (40%) Patient Start of study End of study Time New AIDS-defining event

  10. Example – study of AIDS events in 15 patients At start of study, 6 out of 15 patients have AIDS Prevalence of AIDS = 6/15 (40%) 15-6=9 patients do not have AIDS at start of study Patient Start of study End of study Time New AIDS-defining event

  11. Example – study of AIDS events in 15 patients Patient Over follow-up, 4 of the 9 patients without AIDS develop new AIDS event Start of study End of study Time New AIDS-defining event

  12. Example – study of AIDS events in 15 patients Patient Over follow-up, 4 of the 9 patients without AIDS develop new AIDS event Incidence of AIDS = 4/9 (44%) Start of study End of study Time New AIDS-defining event

  13. Alternative measures of the risk – the Odds Odds of an event = No. patients with the event over study period No. patients without the event over study period

  14. Example – study of AIDS events in 15 patients Patient Over follow-up, 4 of the 9 patients without AIDS develop new AIDS event, and 5 do not Start of study End of study Time New AIDS-defining event

  15. What happens if the amount of follow-up differs on the patients - the ideal situation Patient Time Start of study End of study Virological failure (2 consecutive VL>500 copies/ml)

  16. What happens if the amount of follow-up differs on the patients - what really happens Patient Time Start of study End of study Virological failure (2 consecutive VL>500 copies/ml)

  17. What happens if amount of follow-up differs on the patients • Six of the patients experienced virological failure during the study • However, some patients were followed for longer periods than others • Follow-up on patients who did not experience virological failure before dropping out of the study is censored – all we know is that these patients had not experienced failure by the time they were lost to follow-up

  18. Why is it important to take account of the different follow-up times • Patients who were followed for the whole study period had a greater chance of experiencing virological failure, simply because they were followed for longer • Estimates of the incidence of virological failure (6/15) will be underestimated, as patients who were censored may have experienced virological failure at a subsequent time point • If censoring differs between groups, there is the potential for comparisons to be seriously biased • Must use appropriate methods to analyse these data

  19. Suitable approaches for analysis – the event rate Event rate = Number of patients developing event of interest Total years of follow-up in the group

  20. Calculating the rate Person-years of follow-up on study Event Patient y n y n n n n y n n n y n y y 4 5 5 2.6 4.9 4.1 2.4 5 2.7 1.6 5 5 4.3 5 3.7 Time Start of study End of study Total : 60.3 6 5 years

  21. Calculating the event rate Rate = Number of patients experiencing virological failure Total years of follow-up in the group = 6 60.3 = 0.1 event per year of follow-up (equivalently, 1 event per 10.05 years)

  22. The rate (cont.) • Rate may be expressed relative to any period of time (eg. per 100 patient-years, 1,000 patient-years, per patient-month etc.) depending on frequency of event • Can compare rates in two groups by calculating the relative rate (rate in group 1 divided by rate in group 2) which is interpreted in a similar manner to RR • Can calculate confidence intervals and p-values for the relative rate

  23. Example : The D:A:D study – relationship between exposure to protease inhibitors and MI Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356: 1723-35

  24. Comparing the rates in different groups – the relative rate

  25. Comparing the rate of an event in two or more groups • We are often interested in whether the rate at which an event occurs is different in one group compared to another • For example, is there a real difference in the rate of MI in those exposed to PIs for different lengths of time? • In order to study this, we can calculate the relative rate • This is calculated as the ratio of the rates in the two groups

  26. Comparing the rate of an event in two or more groups Relative rate (RR) of an event = Rate of event in group with factor of interest Rate of event in group without factor of interest

  27. Comparing the rate of an event in two or more groups • The RR is a positive number • Takes values between 0 (when the rate in the group with the factor is zero) and infinity (when the rate in the group without the factor is zero)

  28. Interpreting the RR RR

  29. Interpreting the RR > 1 RR

  30. Interpreting the RR Factor is associated with an increased rate of the event. Factor is a possible RISK FACTOR > 1 RR

  31. Interpreting the RR Factor is associated with an increased rate of the event. Factor is a possible RISK FACTOR > 1 RR = 1

  32. Interpreting the RR Factor is associated with an increased rate of the event. Factor is a possible RISK FACTOR > 1 The rate of the event is the same in both groups. Factor is not associated with either an increased or decreased rate of the event. RR = 1

  33. Interpreting the RR Factor is associated with an increased rate of the event. Factor is a possible RISK FACTOR > 1 The rate of the event is the same in both groups.Factor is not associated with either an increased or decreased rate of the event. RR = 1 < 1

  34. Interpreting the RR Factor is associated with an increased rate of the event. Factor is a possible RISK FACTOR > 1 The rate of the event is the same in both groups.Factor is not associated with either an increased or decreased rate of the event. RR = 1 Factor is associated with a decreased rate of the event. Factor is a possible PROTECTIVE FACTOR < 1

  35. Calculating and interpreting the relative rate Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356: 1723-35

  36. Calculating and interpreting the relative rate Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356: 1723-35

  37. Calculating and interpreting the relative rate MI rate is 1.7 times as high in those exposed to PIs for <1 year compared to those never exposed to PIs Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356: 1723-35

  38. Calculating and interpreting the relative rate Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356: 1723-35

  39. Calculating and interpreting the relative rate Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356: 1723-35

  40. Limitations of this approach • These unadjusted relative rates do not take account of the fact that the characteristics of patients exposed to PIs for <1 year may be different to those who have never been exposed to PIs • We have to take account of these differences in our analyses • We usually use Poisson regression to obtain estimates of the RR that are ADJUSTED for any differences in patient characteristics

  41. Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) * Model also adjusted for body mass index, family history of CHD, previous CV event, cohort, transmission group, ethnicity, and calendar year Adapted from: DAD Study Group. N Engl J Med 2007; 356: 1723-1735

  42. Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) * Model also adjusted for body mass index, family history of CHD, previous CV event, cohort, transmission group, ethnicity, and calendar year Adapted from: DAD Study Group. N Engl J Med 2007; 356: 1723-1735

  43. Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) * Model also adjusted for body mass index, family history of CHD, previous CV event, cohort, transmission group, ethnicity, and calendar year Adapted from: DAD Study Group. N Engl J Med 2007; 356: 1723-1735

  44. Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) * Model also adjusted for body mass index, family history of CHD, previous CV event, cohort, transmission group, ethnicity, and calendar year Adapted from: DAD Study Group. N Engl J Med 2007; 356: 1723-1735

  45. Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) * Model also adjusted for body mass index, family history of CHD, previous CV event, cohort, transmission group, ethnicity, and calendar year Adapted from: DAD Study Group. N Engl J Med 2007; 356: 1723-1735

  46. Summary • Many statistics aim to describe the ‘risk’ of an event; the choice of statistic depends on the type of study and whether patient follow-up is censored • Relative rates indicate whether a factor is associated with an increased (RR>1) or decreased (RR<1) risk of the event occurring • Unadjusted RRs do not take account of differences in patient characteristics (e.g. age, sex, previous treatment history) between those with and without the factor; hence, we use a regression model (e.g. Poisson regression) to obtain adjusted RRs

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