Getting error to display radio button value in General Settings page

Apart from the isset issue, pointed by Rarst, there’s an error in the sanitization function. esc_attr seems not to work with radio buttons, using esc_sql does the job.
You’re also missing the checked state for the buttons:

add_filter( 'admin_init', 'myservice_register_function' );

function myservice_register_function()
{
    register_setting( 'general', 'my_service', 'esc_sql' );
    add_settings_field(
        'my_service', 
        '<label for="service_need">'.__('Do You need My Service' , 'my_service' ).'</label>' , 
        'service_function', 
        'general'
    );
}

function service_function()
{
    $options = get_option( 'my_service', '');
    $yes = $no = '';
    if( isset( $options['service'] ) )
    {
        if( $options['service'] == 'YES') 
        {
            echo 'Yes, Service Need<br />'; 
            $yes=" checked="checked"";
        }
        if( $options['service'] == 'NO') 
        {
            echo 'No Need Service<br />';
            $no = ' checked="checked"';
        }
    }
    ?>
    <input type="radio"  name="my_service[service]" value="YES"<?php echo $yes; ?> />
    <label> NEED </label>

    <input type="radio"  name="my_service[service]" value="NO"<?php echo $no; ?> />
    <label> NO NEED </label> 
    <?php
}