Protein measurements in mg/ml were performed in 20 patients at 1, 5, 8 and 12 days after admission. Twelve patients lived and 8 died. You plotted the protein level for the living and the dead patients as shown in the attached figure. How could you show that the protein level is different between the living and the dead patients, what statistical test could you use to show that the curves are significantly different? Attached is an excel table with the data obtained. Thank you very much in advance.
You can use an ANCOVA model with Y = log(Conc), X = Days and A = Survived:
Y ~ 1 + A + X + A:X
Using simple coding of A (0 = "survived", 1="died"), the coefficients are:
1 (intercept) = mean logConc at day 0 in survivors
A = mean differences in logConc between dead and survivors at day 0
X = mean change per day in logConc in survivors
A:X = "group:time interaction" = difference in X between dead and survivors.
I think that both, A and A:X are both interesting (it might possibly be that there is no clear difference at day 0, but there is a recorgnizeable stronger increase in patients that do not survive). If day 0 is some arbitrary time point (like time of admission or time of starting the treatment), A itself is not very interesting, and you should focus on interpreting X:A.
Jos Feys made an important addition: it should be repeated measures (apart from what the model is the same). A very modern way to adress this is by using random effects. Here, I think, it would be advantagous to use a random effect for the intercept (A) AND another for the slope (X).
Jos Feys the suggested analysis is a two-way ANOVA with repeated measures, right? My doubt is if it is correct to consider alive and dead as a factor in the ANOVA, since it would not be an independent variable. Thank you very much for the R script
Friends wrote accurate and correct instructions in this regard. However, test the following model as well
Logit[P(Y=living)] = Ln[(P(Y=living)/P(Y=Dead)] = β0 + β1*Day 1 + β2*Day 5 + β3*Day 8 + β4*Day 12
Here Kaplan Meier survival curves between two groups can be plotted. The probability of survival can be known at each of the time intervals as the understanding is deaths would have occurred at various time points. You can also do a log-rank test for comparison.
- Badges
- Science topic
- Similar topics
- Correction