so you've just run a multiple Cox

regression model maybe you're not sure

what it means or you've been nagging

feeling that you could have run it a

different way and got different answers

or both so let me go through the example

which in this course concerns predictors

of mortality following an emergency

hospital admission for heart failure in

this example there are five predictors

in the model age gender COPD ethnic

group and the number of prior miss

outpatients appointments I'll start with

the easy ones gender and COPD so here's

the output for gender patients with

gender equals two

the females have a hazard ratio of

naught point seven eight to two decimal

places

compared with patients with the other

gender value males the 95% confidence

interval goes from naught point six five

to null point nine three with a p-value

of naught point naught naught seven so

that's clear evidence on an association

between females and a lower hazard of

mortality the women in this sample lived

longer after their admission their

hazard is 22% lower than that of the

males where do I get the 22% from well

that's just a hundred minus seventy

eight you can get that if you realize

that the hazard for females is not point

seven eight times or 78% of the hazard

for males

similarly patients with COPD have a

hazard ratio of 1.15 relative to those

without COPD their hazard is 15% higher

than that of patients without COPD

however in this case the confidence

interval goes from something below one

to something above one and a p-value is

naught point one eight eight so not

statistically significant we don't have

enough evidence for a relation between

COPD and death in this sample next let's

look at F net group or has given you

hazard ratios for ethnic groups two

three eight

9 the relatives equip one which is white

people the only statistically

significant difference is that ethnic

group three-engine subcontinent has

lower hazard with P equals naught point

naught 4/7 so just sneaks under the

conventional work point naught 5

threshold patients from the engine

subcontinent lived longer than white

people in the sample after their

admission so you've already seen how to

interpret the hazard ratio for age when

it's fitted as a single term for 1 year

increase in age the hazard increases by

a multiple of 1.06 so a 6% rise for

every year you age the p-values

miniscule so this relation is not due to

chance lastly you have the hazard ratio

for the number of previous missed

appointments which is 1.18 for each

appointment missed for hazards increases

by 18% that's quite a lot as with age

the assumption here is that there is a

linear relation between the predictor

and the hazard for death later I'll show

you how to test that assumption but how

else could you have included this

variable in the model well you can group

it instead but how the simplest is to

dichotomize turn it into a yes/no

variable had the patient missed at least

one appointment yes or no that seems

like a lot of information thrown away as

11% missed more than one appointment so

what about three groups

none missed one missed or two or more

missed looking at the numbers of

patients that seems feasible but could

you manage four groups of five the

descriptive statistics showed that three

percent missed five or more but we're

talking tiny numbers of patients in this

sample who missed that many so where do

you draw the line so

times if the relation is not linear or

because it's easier to explain results

using categories to your particular

audience then you can use categories a

simple look at the width of the

confidence intervals for each category

will tell you whether you've stretched

your sample too thin and have too few

patients in some of the categories it's

another example of the art of statistics

so it's important to remember that each

of these associations is adjusted for

the other predictors in the model just

as with any multiple regression model

for instance females have a lower hazard

after accounting for the effect of age

ethnic group COPD and prior missed

appointments so this Cox model showed

statistically significant relations for

age gender ethnic group - any just and

missed appointments but not for COPD in

this sample each of these relations is

adjusted for the other predictors same

with the data preparation and a

descriptives done I hope you'll agree

that fitting this model was

straightforward however stay alert it's

not every model goes according to plan

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