Description Usage Arguments Details Value Author(s) References See Also Examples

Estimates Intracluster Correlation coefficients (ICC) in 16 different methods and it's confidence intervals (CI) in 5 different methods given the data on cluster labels and outcomes

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`cid` |
Column name indicating cluster id in the dataframe |

`y` |
Column name indicating binary response in the dataframe |

`data` |
A dataframe containing |

`method` |
The method to be used to compute ICC. A single or multiple methods can be used at a time. By default, all 16 methods will be used. See Details for more. |

`ci.type` |
Type of confidence interval to be computed. By default all 5 types will be reported. See Details for more |

`alpha` |
The significance level to be used while computing confidence interval. Default value is 0.05 |

`kappa` |
Value of Kappa to be used in computing Stabilized ICC when the method |

`nAGQ` |
An integer scaler, as in |

`M` |
Number of Monte Carlo replicates used in ICC computation method |

If in the dataframe, the cluster id (`cid`

) is not a factor, it will be changed to a factor and a warning message will be given

If estimate of ICC in any method is outside the interval [0, 1], the estimate and corresponding confidence interval (if appropriate) will not be provided and warning messages will be produced

If the lower limit of any confidence interval is below 0 and upper limit is above 1, they will be replaced by 0 and 1 respectively and a warning message will be produced

Method `aov`

computes the analysis of variance estimate of ICC. This estimator was originally proposed for continuous variables, but various authors (e.g. Elston, 1977) have suggested it's use for binary variables

Method `aovs`

gives estimate of ICC using a modification of analysis of variance technique (see Fleiss, 1981)

Method `keq`

computes moment estimate of ICC suggested by Kleinman (1973), uses equal weight *w_{i} = 1/k*, for each of *k* clusters

Method `kpr`

computes moment estimate of ICC suggested by Kleinman (1973), uses weights proportional to cluster size *w_{i} = n_{i}/N*

Method `keqs`

gives a modified moment estimate of ICC with equal weights (`keq`

) (see Kleinman, 1973)

Method `kprs`

gives a modified moment estimate of ICC with weights proportional to cluster size (`kpr`

) (see Kleinman, 1973)

Method `stab`

provides a stabilizd estimate of ICC proposed by Tamura and Young (1987)

Method `ub`

computes moment estimate of ICC from an unbiased estimating equation (see Yamamoto and Yanagimoto, 1992)

Method `fc`

gives Fleiss-Cuzick estimate of ICC (see Fleiss and Cuzick, 1979)

Method `mak`

computes Mak's estimate of ICC (see Mak, 1988)

Method `peq`

computes weighted correlation estimate of ICC proposed by Karlin, Cameron, and Williams (1981) using equal weight to every pair of observations

Method `pgp`

computes weighted correlation estimate of ICC proposed by Karlin, Cameron, and Williams (1981) using equal weight to each cluster irrespective of size

Method `ppr`

computes weighted correlation estimate of ICC proposed by Karlin, Cameron, and Williams (1981) by weighting each pair according to the total number of pairs in which the individuals appear

Method `rm`

estimates ICC using resampling method proposed by Chakraborty and Sen (2016)

Method `lin`

estimates ICC using model linearization proposed by Goldstein et al. (2002)

Method `sim`

estimates ICC using Monte Carlo simulation proposed by Goldstein et al. (2002)

CI type `aov`

computes confidence interval for ICC using Simith's large sample approximation (see Smith, 1957)

CI type `wal`

computes confidence interval for ICC using modified Wald test (see Zou and Donner, 2004).

CI type `fc`

gives Fleiss-Cuzick confidence interval for ICC (see Fleiss and Cuzick, 1979; and Zou and Donner, 2004)

CI type `peq`

estimates confidence interval for ICC based on direct calculation of correlation between observations within clusters (see Zou and Donner, 2004; and Wu, Crespi, and Wong, 2012)

CI type `rm`

gives confidence interval for ICC using resampling method by Chakraborty and Sen (2016)

`estimates` |
A dataframe containing the name of methods used and corresponding estimates of Intracluster Correlation coefficients |

`ci` |
A dataframe containing names of confidence interval types and corresponding estimated confidence intervals |

Akhtar Hossain mhossain@email.sc.edu

Hirshikesh Chakraborty rishi.c@duke.edu

Chakraborty, H. and Sen, P.K., 2016. Resampling method to estimate intra-cluster correlation for clustered binary data. Communications in Statistics-Theory and Methods, 45(8), pp.2368-2377.

Elston, R.C., Hill, W.G. and Smith, C., 1977. Query: Estimating" Heritability" of a dichotomous trait. Biometrics, 33(1), pp.231-236.

Fleiss, J.L., Levin, B. and Paik, M.C., 2013. Statistical methods for rates and proportions. John Wiley & Sons.

Fleiss, J.L. and Cuzick, J., 1979. The reliability of dichotomous judgments: Unequal numbers of judges per subject. Applied Psychological Measurement, 3(4), pp.537-542.

Goldstein, H., Browne, W., Rasbash, J., 2002. Partitioning variation in multilevel models, Understanding Statistics: Statistical Issues in Psychology, Education, and the Social Sciences, 1 (4), pp.223-231.

Karlin, S., Cameron, E.C. and Williams, P.T., 1981. Sibling and parent–offspring correlation estimation with variable family size. Proceedings of the National Academy of Sciences, 78(5), pp.2664-2668.

Kleinman, J.C., 1973. Proportions with extraneous variance: single and independent samples. Journal of the American Statistical Association, 68(341), pp.46-54.

Mak, T.K., 1988. Analysing intraclass correlation for dichotomous variables. Applied Statistics, pp.344-352.

Smith, C.A.B., 1957. On the estimation of intraclass correlation. Annals of human genetics, 21(4), pp.363-373.

Tamura, R.N. and Young, S.S., 1987. A stabilized moment estimator for the beta-binomial distribution. Biometrics, pp.813-824.

Wu, S., Crespi, C.M. and Wong, W.K., 2012. Comparison of methods for estimating the intraclass correlation coefficient for binary responses in cancer prevention cluster randomized trials. Contemporary clinical trials, 33(5), pp.869-880.

Yamamoto, E. and Yanagimoto, T., 1992. Moment estimators for the beta-binomial distribution. Journal of applied statistics, 19(2), pp.273-283.

Zou, G., Donner, A., 2004 Confidence interval estimation of the intraclass correlation coefficient for binary outcome data, Biometrics, 60(3), pp.807-811.

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