I am trying to find out, whether I have enough power to conduct a Cox proportional hazards model using R.
My predictor is intelligence and my outcome is cancer. My sample size is 22,000 and I predict 600 cancer cases over 25 years.
Furthermore, I would like to know, whether I have enough power to test gender interactions, if half of my sample if female and 200 of the 600 cancer cases are.
I predict a hazard ratios of at least 1.3.
The functions that I have found in R all require a binary predictor, but intelligence is metric, and I could not find any functions for that.
Related
I am using GLMMs in R to examine the influence of continuous predictor variables (x) on biological counts variable (y). My response variables (n=5) each have a high number of zeros (data distribution), so I have tested the fit of various distributions (genpois, poisson, nbinom1, nbinom2, zip, zinb1, zinb2) and selected the best fit one according to the lowest AIC/LogLik value.
According to this selection criteria, three of my response variables with the highest number of zeros are best fit to the zero inflated negative binomial (zinb2) distribution. Compared to the regular NB distribution (non-zero inflated), the delta AIC is between 30-150.
My question is: must I use the ZI models for these variables considering the dAIC? I have received advice from a statistician that if dAIC is small enough between the ZI and non-ZI model, use the non-ZI model even if it is marginally worse fit since ZI models involve much more complicated modelling & interpretation. The distribution matters in this case because ZINB / NB models select a different combination of top candidate models when testing my predictors.
Thank you for any clarification!
I am analysing a household budget survey dataset with the aim of analysing whether households who spend more on alcohol also spend more on other discretionary items such as restaurants and entertainment (large sample size over 200,000).
Given the large number of households reporting zero expenditure for each of these items, I had non-normally distributed errors in my linear regression model and therefore used a logistic regression.
When I ran my logistic regression I came across quasi-complete separation. Based on an analysis of the literature, it seems a Firth’s penalised logistic regression was the most appropriate:
Regression <- logistf(restaurant_spender ~ alc_spender + income_quintiles + eduation_hh, data = alcohol, weights = weight, firth=FALSE)
Where:
restaurant_spender is binary (=1 if they spend anything on restaurants and 0 otherwise)
alc_spender same as above but for alcohol
income_quintiles is a categorical variable separating households into one of five income quintiles
education_hh is a categorical variable indicating the highest level of education for the household head.
And to get the odds ratios:
exp(coef(Regression))
This produces odds ratio I would expect and my confidence intervals make sense. However, my Chi-squared values are all infinite.
I have tabbed all of my independent variables against my dependent variable and there are no categories with 0 (in fact, they are evenly distributed).
My questions are:
1) Am I doing anything obviously wrong in running a Firth’s penalised logistic regression in R?
2) Are infinite chi-squared values implausible?
3) Is there some other way in R to test why I am getting quasi-separation apart from tabbing independent and dependent variables?
Any help would be greatly appreciated.
(I am using R and the lqmm package)
I was wondering how to consider autocorrelation in a Linear Quantile mixed models (LQMM).
I have a data frame that looks like this:
df1<-data.frame( Time=seq(as.POSIXct("2017-11-13 00:00:00",tz="UTC"),
as.POSIXct("2017-11-13 00:1:59",tz="UTC"),"sec"),
HeartRate=rnorm(120, mean=60, sd=10),
Treatment=rep("TreatmentA",120),
AnimalID=rep("ID01",120),
Experiment=rep("Exp01",120))
df2<-data.frame( Time=seq(as.POSIXct("2017-08-11 00:00:00",tz="UTC"),
as.POSIXct("2017-08-11 00:1:59",tz="UTC"),"sec"),
HeartRate=rnorm(120, mean=62, sd=14),
Treatment=rep("TreatmentB",120),
AnimalID=rep("ID02",120),
Experiment=rep("Exp02",120))
df<-rbind(df1,df2)
head(df)
With:
The heart rates (HeartRate) that are measured every second on some animals (AnimalID). These measures are carried during an experiment (Experiment) with different treatment possible (Treatment). Each animal (AnimalID) was observed for multiple experiments with different treatments. I wish to look at the effect of the variable Treatment on the 90th percentile of the Heart Rates but including Experiment as a random effect and consider the autocorrelation (as heart rates are taken every second). (If there is a way to include AnimalID as random effect as well it would be even better)
Model for now:
library(lqmm)
model<-lqmm(fixed= HeartRate ~ Treatment, random= ~1| Exp01, data=df, tau=0.9)
Thank you very much in advance for your help.
Let me know if you need more information.
For resources on thinking about this type of problem you might look at chapters 17 and 19 of Koenker et al. 2018 Handbook of Quantile Regression from CRC Press. Neither chapter has nice R code to go from, but they discuss different approaches to the kind of data you're working with. lqmm does use nlme machinery, so there may be a way to customize the covariance matrices for the random effects, but I suspect it would be easiest to either ask for help from the package author or to do a deep dive into the package code to figure out how to do that.
Another resource is the quantile regression model for mixed effects models accounting for autocorrelation in 'Quantile regression for mixed models with an application to examine blood pressure trends in China' by Smith et al. (2015). They model a bivariate response with a copula, but you could do the simplified version with univariate response. I think their model only at this points incorporates lag-1 correlation structure within subjects/clusters. The code for that model does not seem to be available online either though.
Apologies in advance for no data samples:
I built out a random forest of 128 trees with no tuning having 1 binary outcome and 4 explanatory continuous variables. I then compared the AUC of this forest against a forest already built and predicting on cases. What I want to figure out is how to determine what exactly is lending predictive power to this new forest. Univariate analysis with the outcome variable led to no significant findings. Any technique recommendations would be greatly appreciated.
EDIT: To summarize, I want to perform multivariate analysis on these 4 explanatory variables to identify what interactions are taking place that may explain the forest's predictive power.
Random Forest is what's known as a "black box" learning algorithm, because there is no good way to interpret the relationship between input and outcome variables. You can however use something like the variable importance plot or partial dependence plot to give you a sense of what variables are contributing the most in making predictions.
Here are some discussions on variable importance plots, also here and here. It is implemented in the randomForest package as varImpPlot() and in the caret package as varImp(). The interpretation of this plot depends on the metric you are using to assess variable importance. For example if you use MeanDecreaseAccuracy, a high value for a variable would mean that on average, a model that includes this variable reduces classification error by a good amount.
Here are some other discussions on partial dependence plots for predictive models, also here. It is implemented in the randomForest package as partialPlot().
In practice, 4 explanatory variables is not many, so you can just easily run a binary logistic regression (possibly with a L2 regularization) for a more interpretative model. And compare it's performance against a random forest. See this discussion about variable selection. It is implemented in the glmnet package. Basically a L2 regularization, also known as ridge, is a penalty term added to your loss function that shrinks your coefficients for reduced variance, at the expense of increased bias. This effectively reduces prediction error if the amount of reduced variance more than compensates for the bias (this is often the case). Since you only have 4 inputs variables, I suggested L2 instead of L1 (also known as lasso, which also does automatic feature selection). See this answer for ridge and lasso shrinkage parameter tuning using cv.glmnet: How to estimate shrinkage parameter in Lasso or ridge regression with >50K variables?
I am attempting to run mixed effects logistic regression models, yet am concerned about the variable samples sizes in each cluster/group, and also the very low number of "successes" in some models.
I have ~ 700 trees distributed across 163 field plots (i.e., the cluster/group), visited annually from 2004-11. I am fitting separate mixed effects logistic regression models (hereafter GLMMs) for each year of the study to compare this output to inference from a shared frailty model (i.e., survival analysis with random effect).
The number of trees per plot varies from 1-22. Also, some years have a very low number of "successes" (i.e., diseased trees). For example, in 2011 there were only 4 successes out of 694 "failures" (i.e., healthy trees).
My questions are: (1) is there a general rule for the ideal number of samples|group when the inference focus is only on estimating the fixed effects in the GLMM, and (2) are GLMMs stable when there is such an extreme difference in the ratio of successes:failures.
Thank you for any advice or suggestions of sources.
-Sarah
(Hi, Sarah, sorry I didn't answer previously via e-mail ...)
It's hard to answer these questions in general -- you're stuck
with your data, right? So it's not a question of power analysis.
If you want to make sure that your results will be reasonably
reliable, probably the best thing to do is to run some simulations.
I'm going to show off a fairly recent feature of lme4 (in the
development version 1.1-1, on Github), which is to simulate
data from a GLMM given a formula and a set of parameters.
First I have to simulate the predictor variables (you wouldn't
have to do this, since you already have the data -- although
you might want to try varying the range of number of plots,
trees per plot, etc.).
set.seed(101)
## simulate number of trees per plot
## want mean of 700/163=4.3 trees, range=1-22
## by trial and error this is about right
r1 <- rnbinom(163,mu=3.3,size=2)+1
## generate plots and trees within plots
d <- data.frame(plot=factor(rep(1:163,r1)),
tree=factor(unlist(lapply(r1,seq))))
## expand by year
library(plyr)
d2 <- ddply(d,c("plot","tree"),
transform,year=factor(2004:2011))
Now set up the parameters: I'm going to assume year is a fixed
effect and that overall disease incidence is plogis(-2)=0.12 except
in 2011 when it is plogis(-2-3)=0.0067. The among-plot standard deviation
is 1 (on the logit scale), as is the among-tree-within-plot standard
deviation:
beta <- c(-2,0,0,0,0,0,0,-3)
theta <- c(1,1) ## sd by plot and plot:tree
Now simulate: year as fixed effect, plot and tree-within-plot as
random effects
library(lme4)
s1 <- simulate(~year+(1|plot/tree),family=binomial,
newdata=d2,newparams=list(beta=beta,theta=theta))
d2$diseased <- s1[[1]]
Summarize/check:
d2sum <- ddply(d2,c("year","plot"),
summarise,
n=length(tree),
nDis=sum(diseased),
propDis=nDis/n)
library(ggplot2)
library(Hmisc) ## for mean_cl_boot
theme_set(theme_bw())
ggplot(d2sum,aes(x=year,y=propDis))+geom_point(aes(size=n),alpha=0.3)+
stat_summary(fun.data=mean_cl_boot,colour="red")
Now fit the model:
g1 <- glmer(diseased~year+(1|plot/tree),family=binomial,
data=d2)
fixef(g1)
You can try this many times and see how often the results are reliable ...
As Josh said, this is a better questions for CrossValidated.
There are no hard and fast rules for logistic regression, but one rule of thumb is 10 successes and 10 failures are needed per cell in the design (cluster in this case) times the number continuous variables in the model.
In your case, I would think the model, if it converges, would be unstable. You can examine that by bootstrapping the errors of the estimates of the fixed effects.