Lecture 5:The Natural History of Disease: Ways to Express Prognosis

Reading:Gordis - Chapter 5 Lilienfeld and Stolley - Chapter 10, pp. 218-220

Introduction

• How can we characterize the natural history of disease in quantitative terms– That is: what is the prognosis?

• Problems in defining disease– Determine when the disease begins– Histological confirmation– Determine stage of disease

Introduction

• Screening tests and diagnostic tests characterize people as sick or well– Once diagnosed as sick – the question is:

How sick and what duration cure or death

Introduction

• Quantification is important because:– Knowing severity is useful in setting

priorities for clinical services and public health programs

– Patients want to know the prognosis– Baseline prognosis is useful when

evaluating new therapies

Prognosis

• Prognosis can be expressed in terms of deaths from the disease or survivors with the disease.

• Ways to express prognosis:– Case-fatality rate– Five-year survival– Observed survival rate

Life table analysis Kaplan-Meier method Median survival time

Case-fatality rate• Case-fatality rate =

Number of people who die from the diseaseNumber of people with the disease

• Given that a person has the disease – what is their risk of dying from that disease

• Different than mortality rate (how?)• Case-fatality often used for acute diseases of

short duration• In chronic disease, death may occur many

years after diagnosis and the possibility of death from other causes becomes more likely.

Case-fatality rate: example

• 1000 new recruits get infected with disease X over a 15 day period

• 10 die within 5 days of diagnosis• Case-fatality rate: 10/1000 = 1%

Person-years of follow-up

• Incidence rate – using person-time for denominator

• Because with chronic diseases– the diagnosis are not clustered around a

single event (like an industrial exposure)• Follow-up may differ and these differences

can be “adjusted” by using person-time in the denominator

Person-years of follow-up

• Assumptions with incidence rate:– Prognosis is the same over the entire

follow-up period– That is:

• Following 5 people for 2 years

will give the same information as

following 2 people for 5 years

Person-years: example

YearPeople entering

People Dying

PY Follow-up

People entering

People Dying

PY Follow-up

People entering

People Dying

PY Follow-up

1 100 10 95 100 41 79.5 100 0 1002 90 9 85.5 59 0 59 100 0 1003 81 8 77 59 0 59 100 0 1004 73 7 69.5 59 0 59 100 0 1005 66 7 62.5 59 0 59 100 41 79.5

41 389.5 41 315.5 41 479.5

Events per 100 PY 10.53

Events per 100 PY 13.00

Events per 100 PY 8.55

CI 41/100 0.41 CI 41/100 0.41 CI 41/100 0.41

Five-year survival

• Percent of patients who are alive 5 years after diagnosis. – Nothing magical about 5 years– Most deaths from cancer occur during this

period (historically)• Convenient

– However, changes in screening may affect the time of diagnosis

Five-year survival

• Comparing 5-year survival among groups is only informative if the individuals began at a similar stage of disease– The interval between diagnosis and death

may be increased not because of better treatment but because of earlier diagnosis

– Lead time bias

Five-year survival

• What if we want to examine the effects of a therapy that was introduced 2 years ago.

• Do we wait for 5 years so we can use the 5-year survival rate?

• We use life table analysis

From person-years example

• In the previous example:– 10.53 cases /100 PY / over 5 years

or 2.1 cases / 100 PY / per year?– 13 cases / 100 PY / over 5 years

or 2.6 cases / 100 PY / per year?– 8.55 cases / 1000 PY / over 5 years

or 1.7 cases / 100 PY / per year?

Life table analysis

• Previous to now – when we used follow-up time we were describing the RATE at which disease occurred.

• How do we assess the RISK of disease development using follow-up time?– Without making the assumption that risk is

the same across all strata of time

Life table analysis

• Calculate the probabilities (risks) of surviving different lengths of time

• Using all of the data available• If follow-up is complete:

– the easiest way is using the cumulative incidence

• Follow-up is usually NOT complete– Therefore: LIFE TABLES and Kaplan

Meier

Life table analysis without withdrew

YearAlive at

beginning

Died during

interval

Effective Number at

riskProportion

who diedProportion

Surviving

Cumulative proportion

surviving

Cumulative risk of death

1 100 10 100 0.100 0.900 0.900 0.1002 90 9 90 0.100 0.900 0.810 0.1903 81 8 81 0.099 0.901 0.730 0.270

4 73 7 73 0.096 0.904 0.660 0.3405 66 7 66 0.106 0.894 0.590 0.410

Cumulative proportion surviving = Pr(survival time t) =Pr(survival time t | survival time t-1) x Pr(survival time t-1) So:0.81 = 0.9 x 0.90.73 =0.901 x 0.810.66 = 0.904 x 0.73

Life table analysis with withdrew

• Withdrew or loss to follow-up• Effective number at risk = alive at beginning – ½ x withdrew

So

375 = 375 – 0

175.5 = 197 – ½ x 43

…

YearAlive at

beginning

Died during

interval Withdrew

Effective Number at

riskProportion

who diedProportion

Surviving

Cumulative proportion

survivingCumulative

risk of death1 375 178 0 375.0 0.475 0.525 0.525 0.4752 197 83 43 175.5 0.473 0.527 0.277 0.7233 71 19 16 63.0 0.302 0.698 0.193 0.8074 36 7 13 29.5 0.237 0.763 0.147 0.8535 16 2 6 13.0 0.154 0.846 0.125 0.875

Kaplan-Meier method

• In the life table analysis, we predetermine the intervals (e.g., 1 year).

• Kaplan-Meier method identifies the exact point in time when each death occurred– Each death determines the interval

Kaplan-Meier method: example

4 10 14 24

Patient 1Patient 2Patient 3Patient 4Patient 5Patient 6

died

dieddied

died

loss to follow-up

loss to follow-up

4 10 14 24

10080604020

Percent surviving

Life table analysis

• Assumptions in using Life Tables– No secular (temporal) change in the

effectiveness of treatment or in survivorship over calendar time

– Survival experience of those lost to follow-up is the same as the experience of those who are followed

Median survival time

• The length of time that half of the study population survives

• Two advantages over mean survival– Less affected by extremes (outliers)– Can be calculated before the end

To observe the mean survival – we need to observe all of the events

Generalizability of survival data

• The cohort must be at a similar stage of disease

• Patient data from clinics or hospitals may not be generalizable to all patients in the general population

• Referral patients may not represent all sick individuals