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;