qif

Estimation and inference in longitudinal data analysis using marginal models/ Peter X.K. Song

https://github.com/umich-biostatistics/qif

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Estimation and inference in longitudinal data analysis using marginal models/ Peter X.K. Song

README.Rmd

---
output: github_document
---



```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
```
# qif




##  Quadratic Inference Function fit of balanced longitudinal data

Developed to perform the estimation and inference for regression
         coefficient parameters in longitudinal marginal models using the method of
         quadratic inference functions. Like generalized estimating equations, this
         method is also a quasi-likelihood inference method. It has been showed that
         the method gives consistent estimators of the regression coefficients even
         if the correlation structure is misspecified, and it is more efficient than
         GEE when the correlation structure is misspecified. Based on Qu, A.,
         Lindsay, B.G. and Li, B. (2000) DOI: 10.1093/biomet/87.4.823.

## Merits of QIF

Like generalized estimating equations (GEE), QIF is also a quasilikelihood inference method. It has been showed that

1. QIF gives consistent estimators of the regression coefficients even if the correlation structure
is misspecified. GEE has the same property.

2. QIF estimators are of the same efficiency as GEE estimators when the correlation structure
is correctly specified, but more efficient when the correlation structure is misspecified.

3. QIF gives a goodness-of-fit test for the validity of the first moment assumption pertaining to
the unbiasedness of inference function. This assumption is crucial to ensure the consistency
in estimation. GEE cannot provide this test.

4. QIF is robust against a small portion of outliers/contaminated data; refer to Qu, A. and Song,
P. (2004), “Assessing robustness of generalised estimating equations and quadratic inference
functions”, Biometrika, 91, 447-459.

5. QIF is analogous to -2*log-likelihood, so it enables naturally to define some model selection
criteria, such as Akaike Information Criterion (AIC) and Bayes Information Criterion (BIC).

## Installation

You can install the released version of qif from [CRAN](https://CRAN.R-project.org) with:

``` r
install.packages("qif")
```

Or install the development version from [Github](https://github.com/umich-biostatistics/qif) with:

``` r
install.packages("devtools") # you need devtools to install packages from Github
devtools::install_github("umich-biostatistics/qif")
```

## Examples

``` r
## Marginal log-linear model for the epileptic seizures count data
## (Diggle et al., 2002, Analysis of Longitudinal Data, 2nd Ed., Oxford Press).

# Read in the epilepsy data set:
data(epil)

# Fit the QIF model:
fit <- qif(y ~ base + trt + lage + V4, id=subject, data=epil,
                                       family=poisson, corstr="AR-1")
 
# Alternately, use ginv() from package MASS
fit <- qif(y ~ base + trt + lage + V4, id=subject, data=epil,
                      family=poisson, corstr="AR-1", invfun = "ginv")


# Print summary of QIF fit:
summary(fit)


## Second example: MS study
data(exacerb)

qif_BIN_IND<-qif(exacerbation ~ treatment + time + duration + time2, id=id,
                        data=exacerb, family=binomial, corstr="independence")
                        
qif_BIN_AR1<-qif(exacerbation ~ treatment + time + duration + time2, id=id,
                        data=exacerb, family=binomial, corstr="AR-1")
                        
qif_BIN_CS<-qif(exacerbation ~ treatment + time + duration + time2, id=id,
                        data=exacerb, family=binomial, corstr="exchangeable")
                        
qif_BIN_UN<-qif(exacerbation ~ treatment + time + duration + time2, id=id,
                        data=exacerb, family=binomial, corstr="unstructured")

summary(qif_BIN_CS)

qif_BIN_CS$statistics

qif_BIN_CS$covariance
```

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