# Temper market share data

Respondents can overstate behavior changes in an anticipated future share distribution when one or more new products offered. In this tutorial we demonstrate how a scale question can be used to adjust overstated market share distributions in an exercise called "tempering".

In this example, we use a data process to calculate a tempered share by reducing the new product shares, and redistributing the reduced shares back into the products that respondents currently use.

## Example questionnaire

A survey asks for current prescribing behavior in Q100. Then in Q200 the survey asks for a new distribution assuming that Product X and Y are available for prescribing. If Product X and Y receive larger market shares than expected, you can use a scale question such as Q210 to temper down the stated shares.

Q100. Approximate what percentage of the following products do you currently prescribe:

Q100_1 Product A ____ %
Q100_2 Product B ____ %
Q100_3 Product C ____ %

Q200. Should Product X and Product Y be available, what will your future prescribing distribution be:

Q200_1 Product A ____ %
Q200_2 Product B ____ %
Q200_3 Product C ____ %
Q200_4 Product X ____ %
Q200_5 Product Y ____ %

Q210. What is your overall likelihood of using Product X and Y

Q210_1 Product X:

1: Not at all likely
2: Somewhat likely
3: Fairly likely
4: Very likely

Q210_2 Product Y:

1: Not at all likely
2: Somewhat likely
3: Fairly likely
4: Very likely

## Choose a factor to weight stated shares by

Determine a likelihood factor (%) for each value in Q210. For example, if Q210_1 (Product X) had an average value of "2: Somewhat likely", then we will temper using a likelihood factor of 25%.  We are essentially weighting stated future shares for Product X and Y by their likelihood to prescribe in Q210.

Assumptions:

1. This is the scale for tempering the shares in Q200_4 and Q200_5 based on Q210_1, and Q210_2:

1 (Not at all likely): 0%
2 (Somewhat likely): 25%
3 (Fairly likely): 50%
4 (Very likely): 75%

2. Tempered shares for Products X and Y are calculated by subtracting tempered future shares (column N) from the stated future shares (column E). The stated current shares (Q100) are used to distribute the tempered shares.

(Note - array used to distribute shares need to be greater than or equal to zero individually, and sum to a positive number if any shares are to be distributed)

Calculated Example:

An example of calculation for one respondent would be: Below is a sample code for the data process:

## Data process code:

```/**
* @method data process
*
* Tempering calculations
*
* Tempering - please find the scale attached below

* Q100 - Current distribution (baseline) - use for distribution
* Q200 - Product X and Y, future distribution
* Q210 - Likelihood of Product 1
*/

// Bring in data
var rows = data['main']

/**
* @method temper
* @param PREFIX - to add in front of the redistribution_array and temper_array
* @param tempering - specifies tempering factor for each possible response in scale_array
* @param distribution_array - array of column names corresponding to percent of patients on each (current) therapy; used as reference for proportionally redistributing tempered shares..
* @param redistribution_array - array of column names corresponding to percent of patients on each (current) therapy in a future scenario; these shares will be increased as a result of tempering
* @param temper_array - array of column names of potential new future therapy; these are the values to be reduce via tempering;
* @param scale_array - array of column names of physicians' estimate of likelihood to prescribe new product at all
*
* Algorithm
* 1. calculate the tempering factor for each item in the temper_array using the scale_array and the tempering factor object.
*    The tempering factor object should have attributes for each valid response in the scale array.  (e.g. scale array answer ranges from 0 to 10, and the tempering object has the tempering values for each of 0 to 10.)
* 2. Take the items in the temper_array, and reduce them by the tempering factor calculated by 1.
* 3. Calculate the redistribution_total by summing up the reductions in the temper_array due to tempering.
* 4. Distribute the 3. into the redistribution_array based on distribution_array.
*
*
* Constraint 1: distribution_array and redistribution_array should be the same length,
* Constraint 2: temper_array and scale_array should be the same length
* Constraint 3: distribution_array should have a non-zero sum
*
* @example
*    var prefix = "t_"
*    var tempering = tempering['initial'] // this is an object to interpret the scale array
*    var tempering = {
*    initial: {
*        "1": 0.00,
*        "2": 0.25,
*        "3": 0.50,
*        "4": 0.75
*         }
*     };
*
*    var d_array =  ["q100_1","q100_2","q100_3"];
*    var r_array =  ["q200_1","q200_2","q202_3"];
*    var t_array =  ["q200_4","q204_5"];
*    var s_array =  ["q210_1","q210_2"];
*
*/
function temper(row, PREFIX,  tempering, distribution_array, redistribution_array, temper_array, scale_array) {

var distribution_length = distribution_array.length
var temper_length = temper_array.length
var redistribution_total = 0;
var distribution_total = 0

// calculate total for the distribution total.  Need to make sure that The amount is non-zero, or else tempering amount should be left as NAs.

for (d=0;d<distribution_length;d++){
distribution_total = distribution_total + (+row[distribution_array[d]] || 0)
}

if (distribution_total >0) {

for (t=0; t<temper_length; t++ ){
var tempering_factor = tempering[row[scale_array[t]]]
if (typeof tempering_factor == 'undefined') console.log("blank tempering factor", t, scale_array[t],temper_array[t], row[scale_array[t]], row[temper_array[t]],row.respid);
row[PREFIX + temper_array[t]] = (+row[temper_array[t]] * tempering_factor) || 0;
if (typeof row[PREFIX + temper_array[t]] == 'undefined') console.log("tempered undefined", PREFIX + temper_array[t], row[temper_array[t]],tempering_factor)
redistribution_total += +row[temper_array[t]] - (+row[PREFIX + temper_array[t]]);
}

for (d=0;d<distribution_length;d++){
row[PREFIX + redistribution_array[d]] = +row[redistribution_array[d]] +  (row[distribution_array[d]]||0)/distribution_total * redistribution_total;
if (typeof row[PREFIX + redistribution_array[d]] == 'undefined') console.log("redistribution undefined", PREFIX + redistribution_array[d], row[redistribution_array[d]],(row[distribution_array[d]]||0)/distribution_total,redistribution_total)
}
}
}
var tempering = {
initial: {
"1": 0.00,
"2": 0.25,
"3": 0.50,
"4": 0.75
}
};

rows.forEach(function(row){
// Setup tempering arrays.  Could create multiple sets:
var Q200_d_array =  ["q100_1","q100_2","q100_3"];
var Q200_r_array =  ["q200_1","q200_2","q200_3"];
var Q200_t_array =  ["q200_4","q200_5"];
var Q200_s_array =  ["q210_1","q210_2"];
// Run temper calculation to create t_Q200
temper(row, 't_',  tempering['initial'], Q200_d_array, Q200_r_array,   Q200_t_array,   Q200_s_array)
})

return rows;
```