Paper 2b things Flashcards
What is standardisation
standardisation gives us a single figure to compare the death rates in two populations whilst accounting for different population distributions - adjusts crude rates for age
Pros: allows you to compare populations with different age structures
adjusts for confounding
Cons:
it is a weighted average - harder to interpret and doesnt show true rate
requires data on age specific rates (for direct)
result depends on choice of standard population
Direct standardisation?
The ratio of the directly standardized rates can then be calculated to provide a single summary measure of the difference in mortality between the two populations. The ratio of the standardized rates is called the Comparative Mortality Ratio (CMR) and is calculated by dividing the overall age adjusted rate in country B by the rate in country A. For example:
Comparative Mortality Ratio = 9.6/7.1 = 1.35
This CMR is interpreted as: after controlling for the confounding affects of age, the mortality in Country B is 35% higher than in country A.
Pros
Preserves differences between populations. So two directly standardised populations can be compared.
Standardised rates can be compared over time
Cons
Requires lots of data
Not good for unstable rates or small numbers
indirect standardisation?
The indirect method is used to calculate the SMR and is used when the age-specific rates for the study population are unknown or not available or unstable/small numbers.
SMR = number of observed deaths / number of expected deaths
SMR can be expressed in 100s in multiplied by 100 (SMR=100=base/reference)
A standardised mortality ratio (SMR) describes whether a specific population are more, less or equally as likely to die than a standard/ reference population
if 95% CI for SMR includes 1.0 (or 100) then it is not significant
Interpretation:
SMR < 1.0 (or 100) fewer than expected deaths in the study population
SMR = 1.0 number of observed deaths = number of expected deaths in the study population
SMR >1.0 indicates there were more than expected deaths in the study population (excess deaths)
pros: It is more stable as it minimises the variance, giving a smaller standard error and narrower confidence interval than direct method. Useful when dealing with small populations.
Cons
Indirectly standardised ratios for areas A and B may be compared with the standard but should only be directly compared to each other if the age structures of areas A and B are similar to the standard, or if the ratio of their age-specific mortality rates to that of the standard is consistent across the age groups
Critical value for Chi Square
3.84.
z score critical value
1.96
interpreting results with 95% CI
95% probability / confidence that the true value lies within this range (or, if the study was repeated 100 times, expect 95 results within this range). 95% confidence interval does not include 1, so p<0.05 (in fact, lower 95% CL considerably greater that 1, so p can be deduced to be much less than 0.05).
5 reasons for a result
Chance
Confounding
Bias
Reverse causality
True effect
variance vs SD vs SE
- Variance vs. Standard Deviation: Variance is the average of the squared differences from the mean, while standard deviation is the square root of the variance. Standard deviation is more interpretable because it is in the same units as the data.
Standard Deviation vs. Standard Error: Standard deviation measures the spread of data points in a sample, while standard error measures the precision of the sample mean as an estimate of the population mean.
Type 1 and 2 errors?
Type I error = rejecting the null hypothesis when its actually true (false positive – i.e. you find an effect when none actually exists) - α
Type II error = accepting the null hypothesis when its actually false (false negative – i.e. there is an effect but you fail to find it) - β (beta is the probability of a type II error occurring, usually set at 20% or 0.2)
Bonferroni correction =
used to adjust the acceptable p value for the number of hypothesis tests performed. It works by adjusting the significance level (α\alphaα) to reduce the likelihood of false positives.
Z test
Chi square test
Compares proportions / frequencies across 2 or more groups
expected = row total x column total / sample total
used when each category is over 5 otherwise use Fisher’s exact
McNemars test
non parametric test for comparing 2 paired samples to test for a difference (Chi square is equivalent for independent samples) e.g. matched pairs with control or before and after measures for one person
Cells in table tell you how many pairs where individuals experienced that outcome e.g. for death or survive there would be 4 possible combinations for pairs: both died, both survived, treated person died other one survived, untreated person died treated person survived
discordant pair = where individuals experienced different outcomes (e.g. one died, one survived)
n12 is the same as cell b
n21 is the same as cell c
critical value at p=0.05 is 3.84
Proportional mortality ratio
This measures the proportion of deaths occurring from a given cause for a particular occupation relative to the proportion of deaths from that cause in the whole population. useful when you don’t know the denominator of the occupation group
when asked what you would recommend on the basis of results
consider -
generalisability -Location and population type
lNeed to look at more than one study
Potential problems with the study quality - bias and confounding
Perhaps didn’t consider harms related to the treatment
Proportional risk reduction
reduction in risk relative to the original risk
e.g. risk reduction between two years = 27%-15% = 12%
proportional risk reduction = 12/27
number needed to treat
attributable risk and fraction
AR = absolute difference in incidence between exposed and unexposed in a study - tells you how much of the disease among the exposed is due to the exposure - measure of the strength of association
ARF = % of cases in the exposed group which is attributed to the exposure
assumes:
causality
population attributable risk and fraction
PAR = excess risk of disease in a population that can be attributed to the exposure
PARF = * This is the % of excess risk in the population that is attributable to the exposure
* And, assuming a fully causal relationship & counterfactual model
* This is the % of the risk of the disease in the population that would be avoided if the exposure were eliminated.
e.g. among the population 51% of lung cancer cases is attributable to smoking
assumes:
causality
What is I^2
The I² statistic describes the percentage of variation across studies that is due to heterogeneity rather than chance
common guidelines for interpretation include:
0% to 25%: Low heterogeneity.
25% to 50%: Moderate heterogeneity.
50% to 75%: Substantial heterogeneity.
75% to 100%: Considerable heterogeneity.
how do you interpret the odds ratio from logistic regression / apply it to different values of a independent variable e.g. OR for every 10 mins additional travel =0.97, what is the OR for 20mins additional travel?
OR is multiplicative - so you do the OR to the power of how many times more units you have i.e. would be 0.97^2
or if you have an odds ratio of 1.03 is given per cigarette smoked per day - if you smoke 20 a day, the OR is 1.03^20
also applies to the confidence interval
