Calculations and definitions Flashcards
Prevalence
the proportion (or %) with the disease at a particular point in time
Prevalence = (number with the disease at a particular time)/(total number in population at that time)
Risk/Cumulative incidence
the proportion (or %) of new cases of disease occurring in a specified time period
Risk = (number of new cases of disease in period)/(total number disease-free at outset)
Incidence rate (incidence)
rate at which new cases are occurring
Incidence (rate) = (number of new cases of disease)/(total number disease free at outset x time interval)
‘per’ whatever 1 unit of time input e.g. 1 year if time interval is 5 years
Reference range
e.g. 95% reference range: 95% of data lies within the 95% reference range
Only for a normally distributed population
95% Reference Range = (X ̅-1.96xSD) to (X ̅+1.96xSD)
X ̅ = mean
SD = SD of X ̅
i.e. 95% reference range = mean ± 1.96xSD
95% CI
the range of values within which we can be 95% confident the true value lies
What do reference range and SD measure?
how much variation there is between the individual observations in the sample
What do confidence intervals and SE measure?
how precise an estimate the sample mean is of the true population mean, given the sample size
Risk ratio (relative risk) (RR)
the risk of disease in exposed individuals compared to unexposed
RR>1: increased risk
RR<1: reduced risk
Risk ratio = (risk in exposed individuals)/(risk in unexposed individuals) = (d1/n1)/(d0/n0)
D = number with disease
H = healthy
So d + h = n (total number of individuals)
Where are risk ratios used?
- RCTs
- cohort studies
Risk difference (RD)
this is simply the difference in risk between exposed and non-exposed groups
Risk difference = risk in exposed – risk in unexposed = d1/n1 - d0/n0
NNTB or NNTH
- Number needed to treat to benefit (NNTB) – how many patients need to be treated to prevent 1 event or whatever
- Number needed to treat to harm (NNTH) – how many patients need to be treated for 1 complication to occur
the inverse of the RD (1/RD) but using the POSITIVE value of the RD (so if it is a negative just use the positive)
NNTB is rounded up to nearest integer, NNTH is rounded down
Odds of disease
probability of an event/disease sort of versus probability of it not occurring (whereas risk is just probability of it occurring)
Odds of disease = (number with disease)/(number without disease)= (number of cases)/(number of controls)= d/h
so compares number with to number WITHOUT rather than to total
What are odds ratios used?
case control studies
When are the odds of disease approximately the same as the risk of disease?
when a disease is so rare that the number of individuals without disease is approx. equal to the total number of individuals (i.e. h approx same as n)
Odds ratio (cross-product ratio)
Odds ratio = (odds of disease in exposed individuals)/(odds of disease in unexposed individuals)= (d1/h1)/(d0/h0 )
Sensitivity
probability of a positive test in people with the disease i.e. the proportion of people with disease (true positives) correctly identified
sensitivity = true positives/total positives (with disease)
Specificity
probability of a negative test result in people without the disease i.e. the proportion of people without the disease (true negatives) identified as not having it
specificity = true negatives/total negatives (without disease)
Positive likelihood ratio
how much more often does a positive test occur in people with disease compared to those without disease
+ve LR = sensitivity/1-specificity
Negative likelihood ratio
how much less likely is a negative test result in people with the disease compared to those without the disease
-ve LR = 1 - sensitivity/specificity
What does a likelihood ratio close to 1 indicate?
no better than random
Incremental cost-effectiveness ratio (ICER)
gives a valuation PER incremental effect of new treatment e.g. £ per QUALY
Incremental cost-effectiveness ratio (ICER) = (difference in cost)/(difference in effect)
Positive predictive value
the probability of having disease if you test positive
PPV=(true positive)/(true positive+false positive)
Negative predictive value
the probability of being disease free if the test result is negative
NPV=(true negative)/(true negative +false negative)
What is a type I error?
false positive - reject the null hypothesis when there is not a genuine effect
What is a type II error?
false negative - fail to reject the null hypothesis when there is a genuine effect
