# Hybrid Design MLE and likelihood

### Description

hybdes() computes the MLE for a Hybrid Design. hyblik() computes the likelihood for a Hybrid Design at a specified parameter vector

### Usage

1 2 3 |

### Arguments

`MM` |
MM is a matrix of margin totals. Rows are groups, columns are margin totals |

`NN` |
NN is a matrix of outcome margin totals. Rows are groups, columns are margin totals. NN is always a K x 2 matrix, where K is the number of groups |

`cc` |
cc is a list of case-control data. Each element is a table with exposure (rows) and outcome (columns) |

`ntrue` |
The number of groups that should be calculated using the true hybrid likelihood, rather than an approximation. |

`aprx` |
Type of approximation to use when calculating the hybrid likelihood. Default is the binomial approximation. |

`start.mle` |
Starting value for the Newton-Raphson algorithm used to determine Hybrid Design MLE. |

`group.int` |
A logical indicator of whether or not groups should be treated as having different intercept parameters. |

`betafct` |
A function used to specify the model of interest by reparamterizing the hybrid likelihood. betafct() takes in group-specific parameters associated with each level of the exposure variable. The default function corresponds to a model with an intercept parameter and log-odds-ratio parameters relating levels of X to the baseline level, X = 0 (i.e. column 1 of MM). |

`print.level` |
Argument passed into nlm() |

`iterlim` |
Argument passed into nlm() |

`beta.matrix` |
Parameter values for likelihood calculation; used only in hyblik(). This should be entered in the form of a matrix, with one row per group and one column per parameter. |

### Value

`mle ` |
MLE of the hybrid design |

`start.mle ` |
Result of clogit function (stratified case-control MLE) |

### Author(s)

E. Smoot

### References

Smoot, E., and S. Haneuse. "On the Analysis of Hybrid Designs that Combine Group- and Individual-Level Data." Biometrics (in press, 2014).

### Examples

1 | ```
#hybdes(MM, NN, cc, approx='NA')
``` |