I'm trying to figure out what is the most appropriate statistic test for use with my data and was hoping for some advice.
The primary data consists of a binary independent variable (patient test - positive or negative; there are some missing values which are being excluded for now) for which we want to determine if it is predictive for a given clinical outcome.
The outcome is ordinal (negative or grade 1 - 4), however we are interested in any positive outcome so this could be simplified to a binary outcome (negative or positive), although if the test is only predictive for some grades this would be good to know.
In the simplified case, I could use a chi-square test. I'm less certain how to deal with the ordinal outcome.
Additionally, each patient has multiple tests and outcomes measured at different times, but the number of repeats and the times are not the same for all patients.
There are also a number of other data pertaining to each patient, some of which are binary (eg. sex, one of 2 research centers, certain other test results), ordinal (different test results) and continuous (age, yet some more test results which - in some cases complicated by a continuous result or N/A).
If the outcome were continuous I think I'd be looking at using a mixed effects linear model so I could determine if there were any effects or interactions with the various secondary independent variables. Is there something equivalent I can do for ordinal and/or binary outcome?
Thanks for your advice! Ric
Edit1 (in response to answer below by Macro): I did read your linked answer for more discussion re: random effects vs GEE. However, I'm honestly still unclear on when you would want an individual vs a population based coefficient.
To address my data specifically, we want to determine how well, if at all, the hypothesized predictor can predict the outcome. If we find it is a good predictor then we would want to be able to say when testing new patients in the future that given they are positive for test X, they are Z times more likely to become positive for outcome Y -- this will affect the course of treatment.
So would I want a random effects or a GEE model to answer this question? What would be a similar scenario where I would want the other model?
As a preliminary experiment I did a Fisher's Exact test on X vs Y (ignoring the fact that many observations are repeated measures) and found evidence for a possible trend but not a statistically significant effect (p ~ 0.1).
I repeated this after splitting the data into 2 sets based on research centre. Centre 1: p=1, odds ratio ~ 1. Centre 2: p=0.02, odds ratio ~ 3. Other independent factors may influence whether X predicts Y or may correlate with Centre.
Is logistic regression still an appropriate method to explorer these effects on the predictive effect of X? If it just tells me that X is not predictive but some other factor is, while interesting, it would not answer our primary question. If it tells us that X is predictive, but only for Centre 2, and especially for older patients at early times since treatment, that is the sort of thing we are looking for.
Edit2 (interpreting results?): So I've been playing with this the last few days but still having trouble making sense of it. I've found some helpful texts on logistic regression using glm() but nothing on lme4 that I was able to fully grok. Perhaps if you know of a good tutorial on the subject...
In any case, to fill in some details on the data set here's a table summarizing the variable structures:
variable type levels missing values id factor 76 0 inst factor 2 0 d1 Date NA 0 d2 integer NA 0 d3 Date NA 0 d4 integer NA 0 a integer NA 2 b integer NA 6 c factor 2 2 d factor 2 6 e factor 2 7 f factor 2 2 g logical NA 6 h integer NA 12 i numeric NA 43 j factor 2 0 x factor 2 0 y factor 2 0
The primary hypothesis is that x can predict y. y is the response variable. I initially removed any observations in which x or y were missing. 192 observations remained for 76 patients. There are missing values, however, for several of the variables: especially h and i, which based on some preliminary tests look like they might be important. There are 50 records in which some variable has a missing value, leaving 142 records with no missing values in any variable.
As far as I understand, glmer() has no way of dealing with missing values and by default will omit the entire record if it has any missing values in the variables being used. I think this may be problematic due to the relatively small sample and effect sizes so I'm not sure what the best way of dealing with this would be.
"id" is the patient id is what I am trying to use as the random effect with all other variables being fixed effects. I've found putting too many variables in the formula will cause glmer to fail to converge. Below are the commands I used for a few simpler models and results:
lr1 <- glmer(formula = y ~ x + 1|id, data = s.dat, family = binomial);
Generalized linear mixed model fit by the Laplace approximation Formula: y ~ x + 1 | id Data: s.dat AIC BIC logLik deviance 238.9 252 -115.4 230.9 Random effects: Groups Name Variance Std.Dev. Corr id (Intercept) 0.97379 0.98681 xpositive 0.01454 0.12058 1.000 Number of obs: 197, groups: id, 76 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) -1.1343 0.2121 -5.349 8.85e-08 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
lr2 <- glmer(formula = y ~ x * inst + 1|id, data = s.dat, family = binomial);
Generalized linear mixed model fit by the Laplace approximation Formula: y ~ x * inst + 1 | id Data: s.dat AIC BIC logLik deviance 252.7 288.8 -115.4 230.7 Random effects: Groups Name Variance Std.Dev. Corr id (Intercept) 1.016604 1.00827 xpositive 0.072397 0.26907 1.000 instI2 1.626269 1.27525 -0.683 -0.683 xpositive:instI2 0.135144 0.36762 -0.817 -0.817 0.137 Number of obs: 197, groups: id, 76 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) -1.1224 0.2099 -5.347 8.96e-08 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
lr3 <- glmer(formula = y ~ x * inst + h + i + 1|id, data = s.dat, family = binomial);
Warning message: In mer_finalize(ans) : iteration limit reached without convergence (9)
lr4 <- glmer(formula = y ~ x + h + i + 1|id, data = s.dat, family = binomial);
Generalized linear mixed model fit by the Laplace approximation Formula: y ~ x + h + i + 1 | id Data: s.dat AIC BIC logLik deviance 184.6 217.1 -81.31 162.6 Random effects: Groups Name Variance Std.Dev. Corr id (Intercept) 1.1663e+01 3.41508554 xpositive 1.2627e+00 1.12369065 -0.284 h 7.9415e-02 0.28180626 -0.998 0.229 i 2.1064e-07 0.00045896 0.107 0.923 -0.164 Number of obs: 142, groups: id, 57 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) -1.3359 0.2792 -4.785 1.71e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
I don't really understand what this is telling me, or why all my variables are showing up as random effects instead of fixed effects.
Any enlightenment will be greatly appreciated!