Statistics: Blood glucose levels

  Blood glucose levelscan be measured with a standard blood glucose meter (glucometer). The glucometer measures the glucose level in a droplet of blood in mg/dL (milligrams/deciliter). The “normal” (or target) range for fasting glucose readings taken from whole blood is 70-105 mg/dL. Readings from 106-121 are categorized as “pre-diabetic” and values of 122 and above are deemed ‘diabetic’. An example of a glucometer is shown below. A patient’s insurance plan switches him over to a new glucometer (Livongo) when he still has a supply of test strips for the older glucometer (One Touch). Naturally he is interested in the consistency of the two meters, so collects data from the same finger poke each day for several months. All readings were taken as ‘fasting’ readings. In other words, no food was eaten for at least 8 hours prior to the data collection so all readings are from a ‘common state’. On dates when information is available for both meters, the readings were taken from the same drop of blood, usually within a few seconds of each other. The actual times may not match as the One Touch meter requires manual setting of the time which drifts. The Livongo meter is like a cell phone so the time is always accurate. The data for the One Touch meter is in the file one_touch.txt and looks like this (these are space delimited – not tab delimited): Date Time BG ----------------- 02jan21 10:14 122 05jan21 10:36 122 08jan21 11:44 109 The data for the Livongo glucometer looks like this and is stored in Livongo.csv – notice this file has comma separated fields and there are extra ‘tags’ for meal, etc. The only fields you will need to read are Date, Time and Blood Glucose. Date,Time,Blood Glucose (mg/dL),Meal Tag,Carbs,Insulin,Feeling Tag,Note 04/16/2022,11:31,95,Before breakfast,,,I feel fine, 04/14/2022,11:23,96,Before breakfast,,,I feel fine, 04/13/2022,10:49,96,Before breakfast,,,I feel fine, 04/09/2022,12:21,106,Before breakfast,,,I feel fine, 04/10/2022,12:25,93,Before breakfast,,,I feel fine, 04/12/2022,10:25,100,Before breakfast,,,I feel fine, a) The basic question of interest here is whether or not the two meters provide the same results. Consider not only the equality of the readings but also the variation within each meter. Be sure to provide adequate summary statistics, graphics and inferential statistics to answer this question. b) The One Touch manufacturer states that its readings should be within 20% of the ‘true value’ as determined at a clinic laboratory. If we use the Livongo readings as the ‘true value’, does the One Touch data meet the accuracy criteria they specify? Support your answer with summary stats and/or graphics. c) The patient started on a new medication to reduce overall body inflammation (FYI high inflammation = more pain) on December 17, 2021. Use ONLY the One Touch data, compare the glucose readings from before this date to the glucose readings once on the new medication. Does there seem to be any change in the glucose readings with the onset of the new medication? Provide summary statistics and graphics to support your answer. Exercise via long walks is recorded in the file walks.txt and looks like this: Date Step_Count Total_Time Mileage ---------------------------------------- 07mar21 5890 0:57:19 2.92 09mar21 5534 0:51:58 2.78 13mar21 6583 1:05:21 3.29 Step count represents the number of steps taken over the duration of the walk. Total Time is the duration of the walk and is expressed as h:mm:ss (hours, minutes, seconds). So on March 7, the walk took a little less than one hour and covered a distance of 2.92 miles and required 5890 steps. d) We are interested in how the medication mentioned in part c) may be impacting the exercise measured by the walking data. There are two different response variables here that may represent different aspects of exercise quality – the step count and the time required. Longer steps (associated with less pain during walking) will yield lower step counts. Also, faster walks suggest less pain. Since the walks are of different lengths, you must create new variables to allow ‘apples-to-apples’ comparisons. Compare the step counts before and after starting the medication. Does the medication seem to have impacted the step counts? e) Repeat the analysis in part d for the time required for the walks. Does it seem that the medication has impacted the times required? Provide statistics and graphics to support your answer. Does the medication seem to be helping based upon these walking measurements?