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 We may be interested in the probability that some event occurs (eg. a new AIDS event, virological response, virological failure) 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) 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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

What happens if amount of follow-up differs on the patients Six of the patients experienced virological failure during the study Six of the patients experienced virological failure during the study However, some patients were followed for longer periods than others 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 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

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 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 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 If censoring differs between groups, there is the potential for comparisons to be seriously biased Must use appropriate methods to analyse these data Must use appropriate methods to analyse these data

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

Calculating the rate Person-years of follow-up on study Total : years Patient Start of study Time End of study Event ynynnnnynnnynyyynynnnnynnnynyy

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

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 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 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 Can calculate confidence intervals and p-values for the relative rate

Example : The D:A:D study – relationship between exposure to protease inhibitors and MI PI exposure (years) No. events Person years Rate (/1000 years) None < > Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356:

Comparing the rates in different groups – the relative rate

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 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? 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 In order to study this, we can calculate the relative rate This is calculated as the ratio of the rates in the two groups This is calculated as the ratio of the rates in the two groups

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

Comparing the rate of an event in two or more groups The RR is a positive number 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) 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)

Interpreting the RR RR

Interpreting the RR RR > 1

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

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

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

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

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

Calculating and interpreting the relative rate PI exposure (years) No. events Person years Rate (/1000 years) Relative rate None Ref. < > Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356:

Calculating and interpreting the relative rate PI exposure (years) No. events Person years Rate (/1000 years) Relative rate None Ref. < / 1.5 = > Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356:

Calculating and interpreting the relative rate PI exposure (years) No. events Person years Rate (/1000 years) Relative rate None Ref. < / 1.5 = > Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356: MI rate is 1.7 times as high in those exposed to PIs for <1 year compared to those never exposed to PIs

Calculating and interpreting the relative rate PI exposure (years) No. events Person years Rate (/1000 years) Relative rate None Ref. < /1.5 = > Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356:

Calculating and interpreting the relative rate PI exposure (years) No. events Person years Rate (/1000 years) Relative rate None Ref. < > Data taken from The DAD Study Group. Class of Antiretroviral drugs and the risk of myocardial infarction. NEJM 2007; 356:

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 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 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 We usually use Poisson regression to obtain estimates of the RR that are ADJUSTED for any differences in patient characteristics

Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) VariableRelative rate95% CI Exposure to PIs (/year) Exposure to NNRTIs (/year) Age (/5 years) Male sex Smoking status Current Former Never1- Not known Adapted from: DAD Study Group. N Engl J Med 2007; 356: * Model also adjusted for body mass index, family history of CHD, previous CV event, cohort, transmission group, ethnicity, and calendar year

Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) VariableRelative rate95% CI Exposure to PIs (/year) Exposure to NNRTIs (/year) Age (/5 years) Male sex Smoking status Current Former Never1- Not known * 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:

Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) VariableRelative rate95% CI Exposure to PIs (/year) Exposure to NNRTIs (/year) Age (/5 years) Male sex Smoking status Current Former Never1- Not known * 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:

Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) VariableRelative rate95% CI Exposure to PIs (/year) Exposure to NNRTIs (/year) Age (/5 years) Male sex Smoking status Current Former Never1- Not known * 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:

Relationship between exposure to PIs, NNRTIs and rate of myocardial infarction (D:A:D) VariableRelative rate95% CI Exposure to PIs (/year) Exposure to NNRTIs (/year) Age (/5 years) Male sex Smoking status Current Former Never1- Not known * 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:

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 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) 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 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