The sample size necessary to detect a significant reduction in change
over time (80% power; alpha=0.5) was determined in a sample of 65
participants with PSP. Analyses were completed first within the full
sample. Follow-up analyses were completed in subsamples: 1) FTLD-CDR
global score <= 1; and 2); FTLD-CDR global score ≤ 1 and baseline
PSPRS ≤ 25. All results suggest that the PSPRS provides the strongest
signal, followed by the FTLD-CDR Sum of boxes score. Regarding cognitive
measures, Semantic fluency (specifically Animals) and Trial Making Test
B provide the strongest signal. The UDS3-EF, a composite of executive
functioning, does not provide a better signal as compared to Animals or
Trails B.
The first tab (data set) provides descriptions of the data.
## [1] "Sample is reduced to those with two time points."
## [1] "Simple change score is calculated (Varible at time 2 minus variable at time 1)."
## [1] "If participant has more than two visits, the first two visits are used."
## [1] "Results are displayed for those change scores."## [1] "Power set to 80%, alpha - 0.5"## Variable N Mean Drug_effect Treated_Mean Estimated_Sample
## 1 moca_total 43 7.535 30% reduction 5.274 370
## 2 psprs_totalcln 61 1.631 30% reduction 1.142 559
## 3 ftldcdr_sob 48 -1.604 30% reduction -1.123 1059
## 4 uds3_ef 43 1.15 30% reduction 0.805 1464
## 5 uds.ef.rest 31 2.879 30% reduction 2.015 1697
## 6 flu_animal 47 -1.085 30% reduction -0.76 2180
## 7 flu_veg 49 -1.265 30% reduction -0.886 2416
## 8 flu_fwords 50 -0.76 30% reduction -0.532 2691
## 9 udsvertn 49 -0.653 30% reduction -0.457 2699
## 10 flu_lwords 51 -0.128 30% reduction -0.09 3061
## 11 traila_ratio 53 -0.138 30% reduction -0.096 3767
## 12 trailb_ratio 47 -0.362 30% reduction -0.253 4251
## 13 dig_back_sum 49 -0.551 30% reduction -0.386 4951| Overall | |
|---|---|
| n | 65 |
| days_between_visit (mean (SD)) | 286.34 (82.04) |
| age_at_visit (mean (SD)) | 68.20 (7.42) |
| education (mean (SD)) | 15.69 (2.56) |
| sex_at_birth = M (%) | 37 (56.9) |
| ftldcdr_global (%) | |
| 0 | 1 ( 1.5) |
| 0.5 | 21 (32.3) |
| 1 | 28 (43.1) |
| 2 | 13 (20.0) |
| 3 | 2 ( 3.1) |
| genetic_status (%) | |
| MAPT | 2 ( 3.1) |
| NONE-Research genetic testing completed and no mutation identified | 48 (73.8) |
| OTHER-Variant of unknown significance | 3 ( 4.6) |
| Pending results | 12 (18.5) |
| moca_total (mean (SD)) | 21.32 (4.67) |
| psprs_totalcln (mean (SD)) | 29.64 (12.01) |
| ftldcdr_sob (mean (SD)) | 5.25 (3.88) |
| uds3_ef (mean (SD)) | -2.03 (0.80) |
| uds.ef.rest (mean (SD)) | -2.09 (0.94) |
| flu_animal (mean (SD)) | 11.59 (5.06) |
| flu_veg (mean (SD)) | 7.70 (3.49) |
| flu_fwords (mean (SD)) | 7.17 (4.24) |
| flu_lwords (mean (SD)) | 6.71 (3.71) |
| traila_ratio (mean (SD)) | 3.32 (2.41) |
| udsvertn (mean (SD)) | 13.91 (7.60) |
| trailb_ratio (mean (SD)) | 13.60 (14.74) |
| dig_back_sum (mean (SD)) | 4.36 (1.90) |
| 0 | 0.5 | 1 | 2 | 3 | p | test | |
|---|---|---|---|---|---|---|---|
| n | 1 | 21 | 28 | 13 | 2 | ||
| days_between_visit (mean (SD)) | NaN (NA) | 310.45 (99.82) | 270.92 (69.39) | 261.46 (56.47) | 407.50 (26.16) | 0.038 | |
| age_at_visit (mean (SD)) | 80.00 (NA) | 68.38 (6.89) | 68.04 (6.54) | 70.15 (6.56) | 50.00 (7.07) | NA | |
| education (mean (SD)) | 18.00 (NA) | 15.81 (2.46) | 16.07 (2.43) | 14.46 (2.90) | 16.00 (2.83) | NA | |
| sex_at_birth = M (%) | 1 (100.0) | 11 (52.4) | 18 (64.3) | 6 (46.2) | 1 (50.0) | 0.698 | |
| genetic_status (%) | 0.002 | ||||||
| MAPT | 0 ( 0.0) | 0 ( 0.0) | 1 ( 3.6) | 0 ( 0.0) | 1 (50.0) | ||
| NONE-Research genetic testing completed and no mutation identified | 1 (100.0) | 18 (85.7) | 18 (64.3) | 11 (84.6) | 0 ( 0.0) | ||
| OTHER-Variant of unknown significance | 0 ( 0.0) | 0 ( 0.0) | 2 ( 7.1) | 0 ( 0.0) | 1 (50.0) | ||
| Pending results | 0 ( 0.0) | 3 (14.3) | 7 (25.0) | 2 (15.4) | 0 ( 0.0) | ||
| moca_total (mean (SD)) | 23.00 (NA) | 23.24 (3.46) | 21.70 (3.89) | 18.20 (5.49) | 8.00 (NA) | NA | |
| psprs_totalcln (mean (SD)) | 22.00 (NA) | 23.62 (10.01) | 30.21 (10.23) | 39.50 (8.98) | 50.50 (21.92) | NA | |
| ftldcdr_sob (mean (SD)) | 0.00 (NA) | 2.14 (0.95) | 4.86 (1.52) | 9.50 (2.28) | 18.50 (0.71) | NA | |
| uds3_ef (mean (SD)) | -1.07 (NA) | -1.86 (0.98) | -2.03 (0.72) | -2.32 (0.61) | -2.87 (NA) | NA | |
| uds.ef.rest (mean (SD)) | -1.04 (NA) | -1.78 (0.99) | -2.09 (0.92) | -2.62 (0.69) | -3.11 (NA) | NA | |
| flu_animal (mean (SD)) | 13.00 (NA) | 14.33 (5.55) | 11.22 (4.17) | 8.00 (3.50) | 3.00 (NA) | NA | |
| flu_veg (mean (SD)) | 10.00 (NA) | 9.42 (3.55) | 7.22 (3.03) | 6.11 (2.93) | 0.00 (NA) | NA | |
| flu_fwords (mean (SD)) | 11.00 (NA) | 8.63 (3.74) | 7.33 (4.33) | 4.45 (3.59) | 1.00 (NA) | NA | |
| flu_lwords (mean (SD)) | 9.00 (NA) | 7.61 (4.19) | 6.67 (3.73) | 5.27 (2.80) | 5.00 (NA) | NA | |
| traila_ratio (mean (SD)) | 0.96 (NA) | 2.85 (1.42) | 3.30 (2.61) | 4.63 (3.19) | NaN (NA) | NA | |
| udsvertn (mean (SD)) | 20.00 (NA) | 16.44 (7.55) | 14.00 (7.73) | 9.73 (6.00) | 6.00 (NA) | NA | |
| trailb_ratio (mean (SD)) | 3.29 (NA) | 12.59 (12.88) | 12.94 (13.09) | 18.29 (22.03) | NaN (NA) | NA | |
| dig_back_sum (mean (SD)) | 5.00 (NA) | 4.42 (2.24) | 4.28 (1.67) | 4.67 (1.94) | 2.00 (NA) | NA |
Each analysis below is based on the change over time in the data set described above. A difference score was calculated (Visit 2 score - Visit 1 score). This difference was then annualized: [difference score / days between visits ] * 365. I also created a version of this where the raw scores were converted to Z scores based on baseline distributions. Then that z score was annualized. Therefore we have 3 variables of interest (and SD) based on units:
Raw score units: Difference (Diff SD)
Annualized units: Annualized decline (Ann. SD)
Annualized Z score: Annualized Z-Score Decline (Ann. Z. SD)
I calculated necessary sample size for each measure to detect a hypothetical drug effect that reduced decline by 30%. Power was set at .8 with an alpha of .05. Let me know if you want any other values here.
I completed analyses first in the full sample, then in sub samples that were closer to what would be in the actual trial. The tables below present the estimated sample sizes for:
Raw score units: SampleSize_RawUnits
Annualized units: SampleSize_ann
Annualized Z score: SampleSize_AnnZ
| Variable | Sample Size | Difference | Diff. SD | Annualized Decline | Ann. SD | Annualized Z-score Decline | Ann. Z. SD | SampleSize_rawunits | SampleSize_ann | SampleSize_annZ |
|---|---|---|---|---|---|---|---|---|---|---|
| psprs_totalcln | 43 | 9.349 | 12.089 | 13.083 | 18.684 | 1.041 | 1.487 | 79 | 97 | 97 |
| perscare | 61 | 0.525 | 0.744 | 0.729 | 1.070 | 0.925 | 1.359 | 95 | 102 | 102 |
| ftldcdr_sob | 61 | 1.885 | 3.069 | 2.513 | 4.418 | 0.642 | 1.129 | 125 | 146 | 146 |
| homehobb | 61 | 0.402 | 0.670 | 0.534 | 0.934 | 0.736 | 1.287 | 132 | 145 | 145 |
| memory | 61 | 0.213 | 0.442 | 0.284 | 0.640 | 0.574 | 1.296 | 204 | 241 | 241 |
| moca_total | 49 | -1.878 | 3.998 | -2.337 | 5.352 | -0.512 | 1.172 | 215 | 248 | 248 |
| traila_ratio | 42 | 1.476 | 3.679 | 1.967 | 4.875 | 1.090 | 2.701 | 294 | 291 | 291 |
| commun | 61 | 0.230 | 0.596 | 0.289 | 0.808 | 0.419 | 1.170 | 319 | 368 | 368 |
| cdrlang | 61 | 0.254 | 0.681 | 0.328 | 0.973 | 0.596 | 1.767 | 340 | 415 | 415 |
| flu_animal | 47 | -1.319 | 4.192 | -1.494 | 5.656 | -0.313 | 1.183 | 478 | 677 | 677 |
| uds.ef.rest | 52 | -0.193 | 0.647 | -0.237 | 0.907 | -0.262 | 0.999 | 530 | 690 | 690 |
| judgment | 61 | 0.123 | 0.435 | 0.173 | 0.593 | 0.266 | 0.913 | 591 | 559 | 559 |
| trailb_ratio | 31 | 2.184 | 8.355 | 2.649 | 11.107 | 0.192 | 0.804 | 692 | 831 | 831 |
| flu_fwords | 50 | -0.880 | 3.420 | -1.121 | 4.730 | -0.264 | 1.112 | 715 | 841 | 841 |
| orient | 61 | 0.123 | 0.489 | 0.170 | 0.693 | 0.377 | 1.539 | 747 | 787 | 787 |
| flu_veg | 49 | -0.653 | 2.728 | -0.804 | 3.985 | -0.233 | 1.158 | 825 | 1163 | 1163 |
| uds3_ef | 51 | -0.122 | 0.552 | -0.144 | 0.755 | -0.182 | 0.956 | 962 | 1306 | 1306 |
| flu_lwords | 49 | -0.653 | 3.004 | -0.626 | 4.732 | -0.164 | 1.243 | 1001 | 2702 | 2702 |
| dig_back_sum | 47 | -0.340 | 1.857 | -0.482 | 2.515 | -0.242 | 1.266 | 1406 | 1289 | 1289 |
| comport | 61 | 0.016 | 0.619 | 0.006 | 0.993 | 0.008 | 1.422 | 67399 | 1339334 | 1339334 |
| Variable | Sample Size | Difference | Diff. SD | Annualized Decline | Ann. SD | Annualized Z-score Decline | Ann. Z. SD | SampleSize_rawunits | SampleSize_ann | SampleSize_annZ |
|---|---|---|---|---|---|---|---|---|---|---|
| psprs_totalcln | 36 | 9.944 | 12.510 | 14.026 | 19.191 | 1.285 | 1.758 | 75 | 89 | 89 |
| ftldcdr_sob | 46 | 2.141 | 3.078 | 2.850 | 4.387 | 1.510 | 2.325 | 98 | 112 | 112 |
| homehobb | 46 | 0.457 | 0.665 | 0.594 | 0.942 | 1.606 | 2.549 | 101 | 119 | 119 |
| perscare | 46 | 0.543 | 0.808 | 0.742 | 1.153 | 1.766 | 2.746 | 105 | 114 | 114 |
| memory | 46 | 0.217 | 0.360 | 0.291 | 0.550 | 0.849 | 1.601 | 130 | 168 | 168 |
| commun | 46 | 0.304 | 0.601 | 0.400 | 0.809 | 1.085 | 2.194 | 184 | 194 | 194 |
| moca_total | 39 | -2.000 | 4.236 | -2.464 | 5.671 | -0.752 | 1.732 | 212 | 251 | 251 |
| trailb_ratio | 27 | 3.265 | 7.060 | 4.301 | 8.777 | 0.563 | 1.148 | 221 | 197 | 197 |
| cdrlang | 46 | 0.293 | 0.663 | 0.372 | 0.879 | 0.876 | 2.071 | 242 | 264 | 264 |
| judgment | 46 | 0.174 | 0.411 | 0.242 | 0.563 | 0.546 | 1.271 | 264 | 257 | 257 |
| traila_ratio | 37 | 1.412 | 3.578 | 1.717 | 4.122 | 0.941 | 2.259 | 304 | 273 | 273 |
| uds.ef.rest | 42 | -0.228 | 0.683 | -0.264 | 0.956 | -0.290 | 1.051 | 425 | 621 | 621 |
| flu_fwords | 41 | -1.098 | 3.639 | -1.425 | 5.029 | -0.348 | 1.228 | 520 | 589 | 589 |
| flu_animal | 39 | -1.333 | 4.433 | -1.365 | 5.888 | -0.293 | 1.263 | 523 | 880 | 880 |
| flu_veg | 41 | -0.634 | 2.809 | -0.742 | 3.956 | -0.218 | 1.160 | 928 | 1345 | 1345 |
| flu_lwords | 40 | -0.725 | 3.250 | -0.575 | 5.099 | -0.147 | 1.302 | 950 | 3720 | 3720 |
| orient | 46 | 0.098 | 0.442 | 0.151 | 0.670 | 0.603 | 2.672 | 967 | 929 | 929 |
| uds3_ef | 41 | -0.117 | 0.583 | -0.131 | 0.807 | -0.160 | 0.982 | 1166 | 1783 | 1783 |
| comport | 46 | 0.054 | 0.529 | 0.058 | 0.852 | 0.125 | 1.830 | 4488 | 10070 | 10070 |
| dig_back_sum | 39 | -0.154 | 1.885 | -0.207 | 2.490 | -0.104 | 1.248 | 7102 | 6837 | 6837 |
| Variable | Sample Size | Difference | Diff. SD | Annualized Decline | Ann. SD | Annualized Z-score Decline | Ann. Z. SD | SampleSize_rawunits | SampleSize_ann | SampleSize_annZ |
|---|---|---|---|---|---|---|---|---|---|---|
| psprs_totalcln | 14 | 11.357 | 10.846 | 15.271 | 16.048 | 3.531 | 3.710 | 8 | 10 | 10 |
| ftldcdr_sob | 18 | 1.472 | 1.898 | 1.696 | 2.058 | 1.044 | 1.266 | 15 | 13 | 13 |
| memory | 18 | 0.167 | 0.243 | 0.207 | 0.318 | 0.697 | 1.071 | 19 | 21 | 21 |
| homehobb | 18 | 0.306 | 0.518 | 0.341 | 0.740 | 0.867 | 1.883 | 25 | 41 | 41 |
| perscare | 18 | 0.333 | 0.594 | 0.413 | 0.740 | 1.279 | 2.290 | 28 | 28 | 28 |
| judgment | 18 | 0.194 | 0.389 | 0.230 | 0.455 | 0.601 | 1.186 | 35 | 34 | 34 |
| flu_animal | 15 | -2.067 | 4.728 | -1.685 | 6.066 | -0.330 | 1.187 | 46 | 113 | 113 |
| commun | 18 | 0.222 | 0.521 | 0.276 | 0.623 | 0.754 | 1.702 | 48 | 44 | 44 |
| cdrlang | 18 | 0.167 | 0.454 | 0.127 | 0.486 | 0.334 | 1.281 | 64 | 128 | 128 |
| traila_ratio | 15 | 0.525 | 1.497 | 0.526 | 1.614 | 0.380 | 1.167 | 71 | 82 | 82 |
| trailb_ratio | 11 | 1.683 | 7.251 | 2.078 | 7.712 | 0.654 | 2.427 | 161 | 120 | 120 |
| flu_lwords | 16 | 0.688 | 3.497 | 1.574 | 5.479 | 0.344 | 1.198 | 225 | 105 | 105 |
| uds.ef.rest | 16 | -0.152 | 0.878 | -0.061 | 1.127 | -0.057 | 1.048 | 290 | 2951 | 2951 |
| comport | 18 | 0.056 | 0.379 | 0.098 | 0.527 | 0.251 | 1.355 | 405 | 253 | 253 |
| orient | 18 | 0.028 | 0.208 | 0.004 | 0.273 | 0.018 | 1.183 | 488 | 37345 | 37345 |
| flu_veg | 16 | -0.312 | 2.575 | -0.237 | 3.477 | -0.072 | 1.059 | 590 | 1863 | 1863 |
| dig_back_sum | 16 | 0.188 | 1.870 | 0.359 | 2.197 | 0.155 | 0.952 | 864 | 326 | 326 |
| moca_total | 14 | -0.214 | 3.926 | -0.553 | 5.275 | -0.136 | 1.295 | 2915 | 792 | 792 |
| flu_fwords | 16 | -0.188 | 4.262 | -0.086 | 5.459 | -0.019 | 1.217 | 4487 | 35299 | 35299 |
| uds3_ef | 16 | -0.023 | 0.752 | 0.064 | 0.957 | 0.062 | 0.935 | 9233 | 1973 | 1973 |