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;